The Preamble to the Constitution

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- [Sal] Hello, everyone, this is Sal here,

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and I'm here with Jeffrey Rosen who's head

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of the National Constitution Center.

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What are we going to
talk about today, Jeff?

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- [Jeff] We're going to talk about

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the Preamble to the US Constitution.

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- [Sal] That sounds very important.

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- [Jeff] It is very important.

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The entire theory of popular sovereignty

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is contained within these beautiful words,

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so we've got a lot to talk about.

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- [Sal] And before we even get into it,

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what do you mean by the theory

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of popular sovereignty?

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- [Jeff] So the preamble
begins with the famous words,

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'We the people of the United States,'

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and those signal that
in the United States,

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power belongs to 'we the people.'

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It doesn't belong to our
representatives in Congress.

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It doesn't even belong
to the state governments.

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And that was a huge shift because

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an original draft of the Preamble read,

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'We the people of the
States of New Hampshire,

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Massachusetts, Rhode Island,
Connecticut,' and so forth.

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But, James Wilson, who
was the main drafter

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of the Preamble changed those words,

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and at some point, the
Preamble was changed

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to the famous words we know now,

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'We the people of the United States.'

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That meant that when some Southern states

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tried to secede from the Union,

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before the Civil War, arguing that they

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were sovereign as state governments,

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President Lincoln resisted their

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Constitutional ability to secede,

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saying that since 'we the people

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of the United States' had created

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the Constitution, a majority of

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'we the people of the United States'

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would have to agree before any state

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could leave it.

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So, that's why it was a huge shift

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in a conception of power that James Wilson

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embodied in these words.

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Before the Preamble, people believed

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that legislatures were sovereign.

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In Britain, the king in Parliament

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was sovereign.

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But, in America, thanks to Wilson

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and his brilliant colleagues,

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'we the people of the United States'

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as a whole became sovereign and

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that came to chart the entire course

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of Constitutional history.

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But then we have all of these purposes

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for which the Constitution was formed:

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to form a more perfect
union, establish justice,

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domestic tranquility, common defense,

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general welfare, and secure the blessings

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of liberty to ourselves and our posterity.

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And then we're saying that's the reason

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we established the Constitution.

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There's lots to unpack there, but maybe

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we should focus on those final words:

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'secure the blessings of liberty

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to ourselves and our posterity.'

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The framers believed that our rights

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come not from government,
but from God or nature,

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that we're born with
them, and when we move

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from the state of nature
into civil society

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to form a government, we surrender

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temporary control over
certain of those rights

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in order to secure the safety and security

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of the rights we've retained.

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So that means that certain
rights are unalienable,

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to use Jefferson's language

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in the Declaration.

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We can't alienate them to government

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when we form government, and the purpose

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of alienating temporary control

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over certain rights, like
allowing the government

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to punish murder, rather than, you know,

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having private violence, is to secure

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the blessings of liberty of the retained

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natural rights, the first of which

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the framers believed was complete

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freedom of conscience, the right

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to believe or not to believe according to

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the dictates of our conscience.

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So, we really see that that idea

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of securing the blessings of liberty

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is implicit in the idea that our rights

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come from God and not government,

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that government only has temporary control

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of them, and reinforces, once again,

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that we should never confuse the actions

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of the government, laws that Congress

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or the state governments pass,

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with the will of the people.

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'We the people' are sovereign.

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The government is our servants.

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We are the principles,
and when there's a clash

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between the will of the principles

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represented by the Constitution

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and the will of the servants

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represented by the legislatures,

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we prefer the principle to the agent.

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That was what Hamilton
said in Federalist 78

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in justifying the Supreme Court's power

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to strike down unconstitutional laws,

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because the Constitution
ratified in the name

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of 'we the people' represents our views

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more profoundly than
those of ordinary laws.

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That's why judges have to prefer

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the Constitution to ordinary laws.

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So, once again, we're seeing packed

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into this Preamble so
much natural law theory

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and theory of popular sovereignty.

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There's one other really important notion

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contained in those words
securing the blessings

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of liberty in the name of 'we the people,'

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and that's that the Constitution itself

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didn't get to speak for 'we the people'

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when it was proposed.

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It wasn't until it was ratified

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by special conventions
that had been elected

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for that purpose that it
earned the right to speak

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in the name of 'we the people' as a whole.

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James Wilson was very keen on the idea

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that it was the ratifying conventions

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not the Constitutional
Convention in Philadelphia

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that gave the document its status

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as supreme law and that
idea that only laws

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that go through a special procedure

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specified in the
Constitution in Article V,

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which is the amendment procedure,

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or by special Constitutional Conventions,

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get to speak in the
name of 'we the people,'

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is absolutely core to the whole theory

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of American Constitutionalism.

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- [Sal] Why were the
founding fathers so focused

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on this notion of popular sovereignty,

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of elected officials being servant

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to the people, and making it so strongly

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embedded even here in the Preamble?

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- [Jeff] They just fought a revolution

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based on the idea that
the tyrannical King George

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had infringed the natural
rights of the people,

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had refused to grant basic
powers of representation,

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and had broken the social contract,

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and therefore, had lost the right

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to govern people because he was governing

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without consent.

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One of the natural rights
that people believed

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were unalienable, retained by the people,

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was the right to alter
and abolish government

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whenever it threatens the
retained natural rights

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of the people.

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That's in the Declaration
of Independence and,

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in the Constitution, it
can be found in Article V.

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So, that right of revolution
was part and parcel

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of the idea that our basic natural rights

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are retained.

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And you have to remember
how revolutionary it was

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to be talking of popular
sovereignty in 1787.

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There were almost no democratic

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self-governments on earth then.

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There had been small-scale
democracies in Greek,

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Greece and Rome.

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In Athens, Solon, or in Sparta, Lycurgus,

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had been lawgivers, but no people

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had ever, as the scholar Akhil Amar says,

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voted on a written Constitution before,

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deliberated it, and had
it ratified in their name.

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So, that's what was so radical about it,

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that even the handful
of minor of the sort of

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partial democracies at the time, like the

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limited suffrage in the British Parliament

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or the Swiss Cantons hadn't had

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a written Constitution that was ratified

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by popular deliberation.

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So, that's what made it radical

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and that was Wilson's
distinct contribution

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to America's entire theory of democratic

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self-governments, and that's why

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if you had to talk about the essence

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of Constitutionalism
today, it's not populism.

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It's not a quick direct vote.

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It's not Brexit.

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It's not a referendum.

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It's long periods of deliberation,

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so the text earns the right to speak

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in the name of 'we the people,'

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and it was the very reason for which

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the revolutionaries fought
the American Revolution.

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- [Sal] Fascinating. Let's continue.

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So, we say that we have 'We the People

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of the United States,' it establishes

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the popular sovereignty, and then it says,

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'in order to,' and it lists a bunch

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of reasons why we are,
what we are trying to do.

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We already did 'secure
the blessings of liberty

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to ourselves and our posterity.'

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What are the other things
we want to talk about?

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- [Jeff] Let's go back in
order and the first purpose

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is 'in order to form
a more perfect union.'

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Well, that was the central goal of the

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Constitutional Convention.

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The previous union,
represented by the Articles

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of Confederation, had been imperfect.

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That was sovereign states that were unable

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to achieve common purposes.

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They couldn't raise money
to support forces in war.

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They couldn't put down
rebellions by debtors

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in Massachusetts, known
as Shay's Rebellion.

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They needed a unanimous
vote to achieve anything.

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And essentially, the
government didn't work.

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So, the framers came to Philadelphia

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in order to form a more perfect union

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by establishing a
Constitution strong enough

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to achieve common purposes,
but restrained enough

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to protect, retain natural rights.

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That's what a perfect union is.

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It's not a consolidated government,

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because states retained powers

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under the 10th Amendment.

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All powers not vested in
the United States as a whole

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are retained by the states or the people.

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And, ultimately, it's 'we the people'

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who retain the ultimate power,

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because we're the ones who are sovereign.

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But we can parcel that power out

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either to state governments or

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to the federal government in order

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to ensure the protections of liberty.

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So, that's what a more perfect union is

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and that's why it was so appropriate

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that Lincoln, in defending the Union

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during the Civil War,
resisted the authority

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of the state governments
to secede on the grounds

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that 'we the people of
the United States' needed

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to consent before the Union could become

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less perfect.

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- [Sal] I just want to
double-click on that a little bit

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because the words, 'more' and 'perfect'

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don't normally go together.

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You're either perfect or you're not.

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And so, part of the narrative that

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I think I'm hearing is that we had

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the Articles of Confederation,
which were imperfect,

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and we want to get
closer to being perfect.

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That's one of the reasons here.

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Many reasons when I look at, 'to form

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a more perfect union,'
it also, at least to me,

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kind of invokes this
notion of continuously

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trying to get better, even
from the starting point.

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- [Jeff] You're right to parse it closely.

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We're trying continuously to get better,

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but perfection doesn't mean amalgamation.

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In other words, the most perfect union

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wouldn't be a total union in which

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all power is united in
the federal government,

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for example, and not parceled out

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between the federal
government and the states,

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and also not separated out

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so the various branches
can check each other.

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We want a union perfect enough to achieve

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common purposes, but not so strong

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as to threaten liberty, and it was that

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delicate balance that was crucial

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to Madison's vision and that
led to most of the tensions

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in the Constitution Convention.

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- [Sal] And then, 'establish justice?'

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- [Jeff] Well, my goodness. There's a lot

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packed into that, and you might think

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that that mandate to establish justice

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gives judges the power to do justice,

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regardless of, let the heaven's fall,

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to use the expression.

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But that's not what the
Supreme Court has held.

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In a really interesting
case, the Supreme Court,

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it was called Jacobson vs Massachusetts.

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It came down in 1905.

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The Supreme Court rejected the claim

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that the Preamble to the Constitution

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conferred independent powers that could be

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enforced by judges.

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In other words, it
wasn't a general mandate

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that allowed judges to
do justice regardless.

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Instead, Justice Harlan
said in the Jacobson case,

00:10:41.489 --> 00:10:44.114
although the Preamble
indicates the general purposes

00:10:44.114 --> 00:10:46.009
for which the people
ordained and established

00:10:46.009 --> 00:10:47.915
the Constitution, it
has never been regarded

00:10:47.915 --> 00:10:50.273
as the source of any substantive power

00:10:50.273 --> 00:10:52.425
conferred on the government
of the United States

00:10:52.425 --> 00:10:53.712
or any of its departments.

00:10:53.712 --> 00:10:55.713
Such power is embraced
only those expressly

00:10:55.713 --> 00:10:58.240
granted in the body of the Constitution,

00:10:58.240 --> 00:11:00.678
or, and this is the final bit,

00:11:00.678 --> 00:11:04.255
and such as may be implied
from those so granted.

00:11:04.255 --> 00:11:05.624
So, 'establish justice' is a broad

00:11:05.624 --> 00:11:08.152
declaration of purposes.

00:11:08.152 --> 00:11:10.184
Many parts of the Constitution help

00:11:10.184 --> 00:11:11.786
the government to establish justice,

00:11:11.786 --> 00:11:13.753
including the Bill of
Rights, which requires

00:11:13.753 --> 00:11:15.519
that people can't be deprived of liberty

00:11:15.519 --> 00:11:17.167
without due process of law.

00:11:17.167 --> 00:11:18.375
If they are gonna have a criminal trial,

00:11:18.375 --> 00:11:19.993
they have all sorts of rights:

00:11:19.993 --> 00:11:22.143
to confront witnesses,
to be tried by jury,

00:11:22.143 --> 00:11:23.335
and so forth.

00:11:23.335 --> 00:11:26.574
But, it's the specific
articulation of the rights

00:11:26.574 --> 00:11:29.018
that allow us to establish justice

00:11:29.018 --> 00:11:31.591
that are the ones the judges can enforce.

00:11:31.591 --> 00:11:33.793
The broad goal is the one set out

00:11:33.793 --> 00:11:34.998
in the Preamble.

00:11:34.998 --> 00:11:37.320
- [Sal] And then we have
'insure domestic tranquility,

00:11:37.320 --> 00:11:39.272
provide for the common defense,

00:11:39.272 --> 00:11:41.279
promote the general welfare?'

00:11:41.279 --> 00:11:42.944
- Yes, so domestic
tranquility is what some

00:11:42.944 --> 00:11:45.080
says of central concern to the framers.

00:11:45.080 --> 00:11:46.754
They're concerned about armed mobs

00:11:46.754 --> 00:11:48.903
like those I mentioned in Massachusetts

00:11:48.903 --> 00:11:51.798
in Shay's rebellion
where debtors and farmers

00:11:51.798 --> 00:11:53.280
in western Massachusetts are rebelling

00:11:53.280 --> 00:11:55.568
against their creditors.

00:11:55.568 --> 00:11:57.858
So, they want to allow the government

00:11:57.858 --> 00:12:00.672
enough power to put down
these insurrections,

00:12:00.672 --> 00:12:01.977
but they don't want a government

00:12:01.977 --> 00:12:04.191
so strong that it will
create standing armies

00:12:04.191 --> 00:12:05.687
that can be permanent threats to liberty,

00:12:05.687 --> 00:12:08.147
the kind that King George's army was.

00:12:08.147 --> 00:12:10.677
So, that's why the 2nd Amendment

00:12:10.677 --> 00:12:14.085
to the Constitution wants to provide

00:12:14.085 --> 00:12:16.818
for well-regulated militias that can help

00:12:16.818 --> 00:12:19.682
ensure domestic tranquility,
but doesn't want

00:12:19.682 --> 00:12:22.698
to empower a permanent standing army,

00:12:22.698 --> 00:12:23.873
because it believes that, ultimately,

00:12:23.873 --> 00:12:25.522
the people do have to retain the ability

00:12:25.522 --> 00:12:27.817
to take up arms to
defend their own liberty

00:12:27.817 --> 00:12:29.387
if the government is
threatening it as part

00:12:29.387 --> 00:12:32.682
of their unalienable right to
alter and abolish government.

00:12:32.682 --> 00:12:34.393
So that's the domestic tranquility part.

00:12:34.393 --> 00:12:35.617
And then, the common defense, of course,

00:12:35.617 --> 00:12:37.753
is hugely important and
Congress has the power

00:12:37.753 --> 00:12:39.642
to declare war.

00:12:39.642 --> 00:12:42.010
The President is Commander-in-Chief.

00:12:42.010 --> 00:12:44.192
The President has the power
to repel sudden attacks,

00:12:44.192 --> 00:12:46.130
but otherwise it's supposed to be Congress

00:12:46.130 --> 00:12:48.132
in theory at least, that authorizes

00:12:48.132 --> 00:12:50.799
the deployment of troops abroad,

00:12:51.790 --> 00:12:53.581
and the parts of Article I for Congress

00:12:53.581 --> 00:12:55.838
and Article II for the President

00:12:55.838 --> 00:12:59.261
that give those two
branches war-making powers,

00:12:59.261 --> 00:13:01.406
help to ensure that the Constitution

00:13:01.406 --> 00:13:04.430
provides for the common defense.

00:13:04.430 --> 00:13:06.857
The final clause, I
hestitated to introduce

00:13:06.857 --> 00:13:09.278
because it's so incredibly broad,

00:13:09.278 --> 00:13:11.022
'promote the general welfare,' wow.

00:13:11.022 --> 00:13:12.662
Well, I mean, that could be read

00:13:12.662 --> 00:13:15.238
as a kind of blank
check for the government

00:13:15.238 --> 00:13:17.190
to do whatever it thinks is necessary

00:13:17.190 --> 00:13:19.486
to promote the general welfare.

00:13:19.486 --> 00:13:22.303
But, both the Supreme
Court and also the framers,

00:13:22.303 --> 00:13:23.521
in ratifying the Constitution,

00:13:23.521 --> 00:13:25.727
made clear that the general welfare clause

00:13:25.727 --> 00:13:27.853
was not a blank check.

00:13:27.853 --> 00:13:30.767
It was that Congress and
the President could only

00:13:30.767 --> 00:13:33.055
exercise the powers that were either

00:13:33.055 --> 00:13:35.381
explicitly granted by the Constitution

00:13:35.381 --> 00:13:37.919
or could be fairly implied by them.

00:13:37.919 --> 00:13:38.975
And yet, at the same time,

00:13:38.975 --> 00:13:40.830
Chief Justice John Marshall and others

00:13:40.830 --> 00:13:43.158
suggested that those powers have to be

00:13:43.158 --> 00:13:45.998
broadly construed enough
to achieve the purposes

00:13:45.998 --> 00:13:47.846
of the Constitution,
which include promoting

00:13:47.846 --> 00:13:49.167
the general welfare.

00:13:49.167 --> 00:13:52.160
So, you might say that
promoting the general welfare

00:13:52.160 --> 00:13:53.975
is a different expression of the goal

00:13:53.975 --> 00:13:57.334
of promoting a more perfect union,

00:13:57.334 --> 00:13:59.630
except you could say
that there's a separate

00:13:59.630 --> 00:14:03.005
goal of passing laws that
are in the general welfare,

00:14:03.005 --> 00:14:04.871
again, without threatening liberty,

00:14:04.871 --> 00:14:06.878
and that clause, once again, embodies this

00:14:06.878 --> 00:14:10.698
tectonic balance between
empowering government,

00:14:10.698 --> 00:14:13.306
but also protecting retained rights.

00:14:13.306 --> 00:14:14.563
- [Sal] So, just to make sure that we got

00:14:14.563 --> 00:14:17.465
all of the big points, we've learned that,

00:14:17.465 --> 00:14:20.306
although the Preamble itself isn't a basis

00:14:20.306 --> 00:14:22.977
for justice, like the
body of the Constitution,

00:14:22.977 --> 00:14:26.498
it establishes that 'we
the people' are the source

00:14:26.498 --> 00:14:28.874
of political power in the United States.

00:14:28.874 --> 00:14:31.217
It explains that the
Constitution would form

00:14:31.217 --> 00:14:33.988
a more perfect union between the states

00:14:33.988 --> 00:14:35.954
and the federal government than the weak

00:14:35.954 --> 00:14:39.242
Articles of Confederation,
while ensuring that

00:14:39.242 --> 00:14:42.673
the people still retained
their natural rights.

00:14:42.673 --> 00:14:44.186
To learn more about the Preamble,

00:14:44.186 --> 00:14:46.225
which I encourage you to do, visit the

00:14:46.225 --> 00:14:49.739
National Constitution Center's
Interactive Constitution

00:14:49.739 --> 00:14:51.355
and Khan Academy's resources on

00:14:51.355 --> 00:14:54.173
U.S. Government and Politics.


Expenditure approach to calculating GDP examples

WEBVTT
Kind: captions
Language: en

00:00:02.052 --> 00:00:02.990
- [Instructor] What I
hope to do in this video

00:00:02.990 --> 00:00:06.470
is even more examples to make
sure we really understand

00:00:06.470 --> 00:00:08.810
how various things would be accounted for

00:00:08.810 --> 00:00:11.720
in the expenditure approach to GDP.

00:00:11.720 --> 00:00:13.660
Now we have talked about
this in other videos.

00:00:13.660 --> 00:00:16.650
There's many different
ways of calculating GDP,

00:00:16.650 --> 00:00:18.330
but in the expenditure approach,

00:00:18.330 --> 00:00:20.600
you can break it down as being made up of

00:00:20.600 --> 00:00:25.220
consumption by households
plus investment by firms

00:00:25.220 --> 00:00:28.370
plus government spending
on goods and services,

00:00:28.370 --> 00:00:31.250
by the government, and net exports.

00:00:31.250 --> 00:00:33.100
And so with that out of the way,

00:00:33.100 --> 00:00:36.000
pause this video and look
at each of these statements

00:00:36.000 --> 00:00:39.820
and think about what
effect would it have on GDP

00:00:39.820 --> 00:00:42.170
if we have the expenditure approach

00:00:42.170 --> 00:00:44.010
and how would it be accounted for

00:00:44.010 --> 00:00:46.240
in these various categories.

00:00:46.240 --> 00:00:47.990
Okay now let's work through this together.

00:00:47.990 --> 00:00:52.100
So this first scenario it
says Ford pays $1 million

00:00:52.100 --> 00:00:56.710
for a U.S.-made robot for
its factory in California.

00:00:56.710 --> 00:00:59.450
So we have a firm right over here.

00:00:59.450 --> 00:01:00.760
It is Ford.

00:01:00.760 --> 00:01:03.480
And it's investing in physical capital.

00:01:03.480 --> 00:01:04.890
And in most cases,

00:01:04.890 --> 00:01:06.210
well especially if you're
looking at some type

00:01:06.210 --> 00:01:08.440
of a standardized test on an AP exam,

00:01:08.440 --> 00:01:10.980
investment is firms investing
in physical capital,

00:01:10.980 --> 00:01:13.130
although it can also be
on intellectual capital,

00:01:13.130 --> 00:01:14.720
things like software.

00:01:14.720 --> 00:01:15.620
But this is very clear,

00:01:15.620 --> 00:01:19.450
it's Ford buying a U.S.-made
robot, physical capital.

00:01:19.450 --> 00:01:22.120
This robot is going to help
Ford make more cars or trucks

00:01:22.120 --> 00:01:23.490
or whatever it's trying to make.

00:01:23.490 --> 00:01:27.260
So this is a very clear
that it would increase GDP,

00:01:27.260 --> 00:01:29.830
so GDP would go up,

00:01:29.830 --> 00:01:33.540
by $1 million because of this, $1 million.

00:01:33.540 --> 00:01:35.240
And the place that it
would be accounted for

00:01:35.240 --> 00:01:36.590
is in investment.

00:01:36.590 --> 00:01:40.130
So I could say investment
would go up $1 million.

00:01:40.130 --> 00:01:42.870
Or the reason why GDP goes up $1 million

00:01:42.870 --> 00:01:44.980
or you would add $1 million to GDP

00:01:44.980 --> 00:01:47.980
is because you would add
$1 million to investment.

00:01:47.980 --> 00:01:51.540
This is a clear investment by a U.S. firm.

00:01:51.540 --> 00:01:53.480
All right now let's look
at the next scenario.

00:01:53.480 --> 00:01:57.020
A U.S. car rental
company spends $1 million

00:01:57.020 --> 00:02:01.110
to buy 30 new Fords that
were made in the U.S.

00:02:01.110 --> 00:02:03.307
So pause this video again
see if you can think of that.

00:02:03.307 --> 00:02:05.910
Well this is a very similar scenario.

00:02:05.910 --> 00:02:07.950
A U.S. car rental company,

00:02:07.950 --> 00:02:11.600
and it is investing in physical
capital right over here.

00:02:11.600 --> 00:02:14.197
By buying those 30 new
Fords, it can rent those out

00:02:14.197 --> 00:02:16.860
to create future benefit.

00:02:16.860 --> 00:02:19.290
And so once again it
would be the same thing.

00:02:19.290 --> 00:02:22.380
In that first case, GDP
would go up by a million

00:02:22.380 --> 00:02:23.880
because investment goes up by a million,

00:02:23.880 --> 00:02:25.510
and in this case as well,

00:02:25.510 --> 00:02:28.520
GDP would go up by $1
million because investment

00:02:28.520 --> 00:02:29.950
went up by $1 million.

00:02:31.040 --> 00:02:32.660
Now let's look at this third scenario.

00:02:32.660 --> 00:02:35.460
A U.S. car rental
company spends $1 million

00:02:35.460 --> 00:02:38.500
to buy 30 new Toyotas
that were made in Japan.

00:02:38.500 --> 00:02:40.900
So how is this different?

00:02:40.900 --> 00:02:42.180
Well in this scenario,

00:02:42.180 --> 00:02:45.870
you still would have a U.S. firm investing

00:02:45.870 --> 00:02:48.660
in physical capital,
it's spending $1 million.

00:02:48.660 --> 00:02:50.180
So you actually would,

00:02:50.180 --> 00:02:54.890
you would actually have
investment go up by $1 million.

00:02:54.890 --> 00:02:57.420
But it's not investing
in things that are made

00:02:57.420 --> 00:02:58.253
in the United States.

00:02:58.253 --> 00:03:00.900
It's investing in things
that are made in Japan.

00:03:00.900 --> 00:03:03.060
So in this particular scenario,

00:03:03.060 --> 00:03:06.290
it will be counteracted by net exports.

00:03:06.290 --> 00:03:09.400
Here we are importing $1
million worth of things,

00:03:09.400 --> 00:03:12.140
and so that would take net exports,

00:03:12.140 --> 00:03:16.890
so net exports would
go down by $1 million.

00:03:16.890 --> 00:03:19.130
A $1 million import is the same thing

00:03:19.130 --> 00:03:22.763
as a negative $1 million net export.

00:03:22.763 --> 00:03:24.720
And so because of these two,

00:03:24.720 --> 00:03:27.140
this will have no impact on GDP.

00:03:27.140 --> 00:03:28.900
No impact

00:03:29.940 --> 00:03:31.800
on GDP.

00:03:31.800 --> 00:03:33.890
And the reason why this
makes intuitive sense

00:03:33.890 --> 00:03:36.890
is remember GDP is supposed to measure

00:03:36.890 --> 00:03:40.350
how much a, how much was produced,

00:03:40.350 --> 00:03:43.270
and in this scenario a car
rental company is investing

00:03:43.270 --> 00:03:45.280
but it was produced someplace else.

00:03:45.280 --> 00:03:48.230
It wasn't produced in the United States.

00:03:48.230 --> 00:03:49.480
Now this third scenario,

00:03:49.480 --> 00:03:52.530
a Japanese car rental
company spends $1 million

00:03:52.530 --> 00:03:55.430
to buy 30 new Fords that were
made in the United States.

00:03:55.430 --> 00:03:58.640
So this is almost a
symmetrically opposite scenario.

00:03:58.640 --> 00:04:00.530
So we would not add to investment here

00:04:00.530 --> 00:04:02.780
because this was a
Japanese car rental company

00:04:02.780 --> 00:04:04.810
and we're calculating
GDP for the United States

00:04:04.810 --> 00:04:06.360
or at least that's the assumption.

00:04:06.360 --> 00:04:10.820
But because the U.S. would
export these 30 new Fords

00:04:10.820 --> 00:04:13.500
for $1 million, that
would add to net exports.

00:04:13.500 --> 00:04:15.710
So in this case, net exports,

00:04:15.710 --> 00:04:17.310
let me do the net export color,

00:04:18.220 --> 00:04:23.220
net exports would go up by $1 million.

00:04:23.560 --> 00:04:26.520
And because net exports
went up by $1 million

00:04:26.520 --> 00:04:28.614
and nothing else here is impacted,

00:04:28.614 --> 00:04:33.614
GDP, GDP would go up by $1 million.

00:04:33.940 --> 00:04:35.690
And once again the reason
why this makes sense

00:04:35.690 --> 00:04:38.800
is United States produced
$1 million worth of stuff.

00:04:38.800 --> 00:04:40.220
It happened to export them out,

00:04:40.220 --> 00:04:41.680
and that's where it got accounted for,

00:04:41.680 --> 00:04:45.760
but definitely GDP is $1
million higher because of this.

00:04:45.760 --> 00:04:47.150
So this next one is interesting.

00:04:47.150 --> 00:04:50.820
You buy $100,000 of IBM stock.

00:04:50.820 --> 00:04:51.653
What do you think this is?

00:04:51.653 --> 00:04:52.790
Pause this video again.

00:04:53.870 --> 00:04:56.090
So you in traditional language,

00:04:56.090 --> 00:04:59.870
you might say I invested
$100,000 of IBM stock.

00:04:59.870 --> 00:05:02.700
But I'm a household,
so how does this work?

00:05:02.700 --> 00:05:05.350
Well it turns out that
this does not move any

00:05:05.350 --> 00:05:07.920
of these dials right over
here because at least

00:05:07.920 --> 00:05:09.720
the assumption here is that you are buying

00:05:09.720 --> 00:05:13.260
that $100,000 of IBM
stock from someone else.

00:05:13.260 --> 00:05:16.500
It is not, it is not because
something is being made

00:05:16.500 --> 00:05:17.880
in the United States,

00:05:17.880 --> 00:05:20.220
there's some new productivity
that's happening.

00:05:20.220 --> 00:05:21.940
And so even though in everyday language

00:05:21.940 --> 00:05:24.200
we sometimes think of
this as in investment,

00:05:24.200 --> 00:05:27.370
this has no impact on
any of these categories.

00:05:27.370 --> 00:05:29.180
So no,

00:05:29.180 --> 00:05:30.520
no impact.

00:05:30.520 --> 00:05:32.630
And I really wanna emphasize that.

00:05:32.630 --> 00:05:34.660
Investment is sometimes
associated with things

00:05:34.660 --> 00:05:36.120
like buying stocks,

00:05:36.120 --> 00:05:39.530
but investment in the
GDP sense is when a firm

00:05:39.530 --> 00:05:42.350
is buying some type of capital

00:05:42.350 --> 00:05:43.730
that'll give it some future benefit,

00:05:43.730 --> 00:05:45.390
help it make things better.

00:05:45.390 --> 00:05:46.910
Oftentimes it's physical capital.

00:05:46.910 --> 00:05:49.370
More and more it's often
things like software

00:05:49.370 --> 00:05:52.500
or some type of intellectual capital.

00:05:52.500 --> 00:05:56.030
Microsoft buys $100 million of IBM stock.

00:05:56.030 --> 00:05:57.840
This one might be even
more tempting to put

00:05:57.840 --> 00:06:00.650
in the investment category
because Microsoft for sure

00:06:00.650 --> 00:06:03.520
is a firm, and it looks
like it's investing

00:06:03.520 --> 00:06:05.070
in another firm.

00:06:05.070 --> 00:06:06.070
But once again,

00:06:06.070 --> 00:06:09.130
Microsoft isn't buying some
type of physical machinery

00:06:09.130 --> 00:06:10.970
or it isn't buying an accounting system

00:06:10.970 --> 00:06:12.980
or some type of intellectual capital.

00:06:12.980 --> 00:06:15.820
It's just buying shares from someone else.

00:06:15.820 --> 00:06:18.350
So once again nothing
new is being produced

00:06:18.350 --> 00:06:21.540
in the country, so this has no impact.

00:06:21.540 --> 00:06:23.840
I really wanna emphasize these last two

00:06:23.840 --> 00:06:25.900
because this shows up on some exams

00:06:25.900 --> 00:06:27.960
where it says oh this kinda
feels like an investment,

00:06:27.960 --> 00:06:29.160
at least in everyday language,

00:06:29.160 --> 00:06:30.720
so people would account for it there.

00:06:30.720 --> 00:06:32.330
But remember, no new capital.

00:06:32.330 --> 00:06:35.070
Microsoft isn't buying
something that's going

00:06:35.070 --> 00:06:37.760
to help Microsoft produce more of whatever

00:06:37.760 --> 00:06:40.060
Microsoft is trying to produce.

00:06:40.060 --> 00:06:41.150
All right this next one,

00:06:41.150 --> 00:06:43.300
the Social Security Administration makes

00:06:43.300 --> 00:06:45.780
a $2,000 payment to a retiree.

00:06:45.780 --> 00:06:47.690
What do you think's going on there?

00:06:47.690 --> 00:06:50.290
So you might be tempted to
say hey that's a government

00:06:50.290 --> 00:06:53.190
expenditure, the Social
Security Administration,

00:06:53.190 --> 00:06:55.560
they're spending $2,000.

00:06:55.560 --> 00:06:57.460
But we have to remind ourselves,

00:06:57.460 --> 00:06:59.750
this G category is government expenditure

00:06:59.750 --> 00:07:01.660
on goods and services,

00:07:01.660 --> 00:07:03.820
not a transfer payment like this.

00:07:03.820 --> 00:07:08.080
And so this would have no, no impact.

00:07:08.080 --> 00:07:09.650
Another intuitive way to think about it,

00:07:09.650 --> 00:07:11.870
and we've been talking
about this for awhile,

00:07:11.870 --> 00:07:14.850
nothing new is being
produced in the United States

00:07:14.850 --> 00:07:16.890
because of this payment.

00:07:16.890 --> 00:07:19.340
Now we can contrast that
with the next scenario

00:07:19.340 --> 00:07:20.660
right over here.

00:07:20.660 --> 00:07:23.080
The Social Security Administration buys

00:07:23.080 --> 00:07:25.290
a new accounting system.

00:07:25.290 --> 00:07:26.640
Well in this scenario,

00:07:26.640 --> 00:07:30.260
the government is buying
a good or service.

00:07:30.260 --> 00:07:31.840
It might be a combination of both.

00:07:31.840 --> 00:07:33.890
They might have to buy some computers,

00:07:33.890 --> 00:07:36.770
some software, maybe hire some consultants

00:07:36.770 --> 00:07:38.160
to implement it for them.

00:07:38.160 --> 00:07:41.150
So it is the government
paying for goods and services.

00:07:41.150 --> 00:07:42.540
So in this situation,

00:07:42.540 --> 00:07:44.950
our government category would go up

00:07:44.950 --> 00:07:46.510
by however much they're spending.

00:07:46.510 --> 00:07:47.790
Let's say they spend,

00:07:47.790 --> 00:07:49.200
let's say this was

00:07:49.200 --> 00:07:50.940
I don't know $1 million again.

00:07:50.940 --> 00:07:52.930
So then the government would,

00:07:52.930 --> 00:07:55.450
the government category
would go up by $1 million

00:07:55.450 --> 00:07:57.040
because it's a good or
service it's spending,

00:07:57.040 --> 00:07:59.960
and because of that GDP would go up

00:07:59.960 --> 00:08:02.060
by $1 million.

00:08:03.050 --> 00:08:04.580
Hopefully you enjoyed that.


Impact of mutations on translation into amino acids

WEBVTT
Kind: captions
Language: en

00:00:01.010 --> 00:00:02.200
- [Instructor] So, let's start looking

00:00:02.200 --> 00:00:04.860
at a short sequence of DNA,

00:00:04.860 --> 00:00:06.600
and the letters I'm going to use,

00:00:06.600 --> 00:00:09.570
these are the shorthands for
the various nucleotide bases

00:00:09.570 --> 00:00:11.870
that make up a sequence of DNA.

00:00:11.870 --> 00:00:14.260
So, let's say that I have some thymine,

00:00:14.260 --> 00:00:19.100
thymine, cytosine,
guanine, cytosine, thymine,

00:00:19.100 --> 00:00:22.160
adenine, thymine, thymine,

00:00:22.160 --> 00:00:24.270
and let's throw another thymine in there.

00:00:24.270 --> 00:00:26.150
So, that would be our sequence of DNA,

00:00:26.150 --> 00:00:28.220
and what would be the
corresponding sequence

00:00:28.220 --> 00:00:31.190
of RNA that it would be transcribed into?

00:00:31.190 --> 00:00:33.410
If you remember this from previous videos,

00:00:33.410 --> 00:00:35.830
pause this video and
try to figure that out.

00:00:35.830 --> 00:00:37.680
Well, the key thing to appreciate is,

00:00:37.680 --> 00:00:40.050
if we're talking base pairs in DNA,

00:00:40.050 --> 00:00:41.960
adenine pairs with thymine,

00:00:41.960 --> 00:00:44.190
cytosine pairs with guanine,

00:00:44.190 --> 00:00:47.730
but if we're talking
about pairing into RNA,

00:00:47.730 --> 00:00:50.610
well then, instead of thymine in the RNA,

00:00:50.610 --> 00:00:51.710
you would have uracil.

00:00:52.770 --> 00:00:54.590
So, the RNA here is,

00:00:54.590 --> 00:00:56.780
well, the thymine in
the DNA would correspond

00:00:56.780 --> 00:00:59.580
to an adenine in the RNA,

00:00:59.580 --> 00:01:01.570
adenine, guanine,

00:01:01.570 --> 00:01:04.500
cytosine, guanine, adenine,

00:01:04.500 --> 00:01:06.150
and now, since this is an RNA strand,

00:01:06.150 --> 00:01:08.270
instead of having a
thymine right over here,

00:01:08.270 --> 00:01:12.910
this would be a uracil,
adenine, adenine, adenine.

00:01:12.910 --> 00:01:15.380
So, this process that we just did,

00:01:15.380 --> 00:01:18.126
this is transcription.

00:01:18.126 --> 00:01:21.250
Transcription,

00:01:21.250 --> 00:01:22.600
transcription

00:01:23.790 --> 00:01:25.460
from DNA,

00:01:25.460 --> 00:01:27.670
DNA to

00:01:27.670 --> 00:01:28.930
RNA.

00:01:28.930 --> 00:01:30.390
Now, the next step, if we're talking about

00:01:30.390 --> 00:01:32.740
the whole process of, how
does this information actually

00:01:32.740 --> 00:01:35.560
have an effect on the
body, is we're gonna go

00:01:35.560 --> 00:01:39.360
from the RNA and translate that into

00:01:39.360 --> 00:01:41.210
a protein.

00:01:41.210 --> 00:01:43.780
And the way we do that, we've
seen this in previous videos,

00:01:43.780 --> 00:01:47.520
is every three of these
bases, that's a codon,

00:01:47.520 --> 00:01:50.850
and it codes for a particular amino acid.

00:01:50.850 --> 00:01:53.660
Now, to figure out what
amino acid it codes for,

00:01:53.660 --> 00:01:55.850
we look at an amino
acid translation table,

00:01:55.850 --> 00:01:58.100
and there's different
types that you might see.

00:01:58.100 --> 00:01:59.890
This is the most typical type,

00:01:59.890 --> 00:02:02.840
so the first base is A, second base is A,

00:02:02.840 --> 00:02:04.270
third base is G.

00:02:04.270 --> 00:02:07.300
First base, A, second base, A,

00:02:07.300 --> 00:02:09.470
we're in this cell, third base is G,

00:02:09.470 --> 00:02:12.440
and so that will code for
the amino acid, lysine,

00:02:12.440 --> 00:02:16.450
so we could write l-y-s,
short for lysine here.

00:02:16.450 --> 00:02:17.680
And we could've also gotten that

00:02:17.680 --> 00:02:19.520
from a different type
of translation table.

00:02:19.520 --> 00:02:21.390
For example,

00:02:21.390 --> 00:02:25.220
you might see a circular
one that looks like that,

00:02:25.220 --> 00:02:26.430
but we would've gotten the same result.

00:02:26.430 --> 00:02:28.840
AAG, start at the center, AAG

00:02:29.830 --> 00:02:31.630
codes for lysine.

00:02:32.500 --> 00:02:34.670
Then, the next codon,
and if you're getting

00:02:34.670 --> 00:02:36.100
as excited about this as I am,

00:02:36.100 --> 00:02:37.230
I encourage you to pause this video

00:02:37.230 --> 00:02:39.350
and try to keep translating this.

00:02:39.350 --> 00:02:40.660
The next codon is CGA.

00:02:42.548 --> 00:02:43.381
CGA,

00:02:44.480 --> 00:02:45.313
arginine.

00:02:46.290 --> 00:02:48.960
Arginine, and then the next one is UAA.

00:02:51.113 --> 00:02:52.650
UAA.

00:02:52.650 --> 00:02:54.920
Well here, they have this
little black, circular dot,

00:02:54.920 --> 00:02:56.230
what does that mean?

00:02:56.230 --> 00:02:58.350
Well, that means stop codon,

00:02:58.350 --> 00:03:01.000
and sometimes they'll just
write the word stop there.

00:03:01.000 --> 00:03:02.460
So, this is stop.

00:03:02.460 --> 00:03:04.970
There is not an amino acid called stop,

00:03:04.970 --> 00:03:07.650
this actually signals
to, and this is happening

00:03:07.650 --> 00:03:10.540
at a ribosome, this is signaling for

00:03:10.540 --> 00:03:12.240
the translation process to stop,

00:03:12.240 --> 00:03:15.480
this is the end of our amino acid chain,

00:03:15.480 --> 00:03:17.940
of our polypeptide chain.

00:03:17.940 --> 00:03:20.450
And so, we will stop right over there.

00:03:20.450 --> 00:03:22.670
But now, let's do some interesting things.

00:03:22.670 --> 00:03:24.230
Let's think about situations where

00:03:24.230 --> 00:03:27.280
there are mutations,
where some of these bases,

00:03:27.280 --> 00:03:28.740
maybe something gets inserted,

00:03:28.740 --> 00:03:30.310
maybe something gets deleted,

00:03:30.310 --> 00:03:33.110
maybe something gets swapped out.

00:03:33.110 --> 00:03:34.800
And so, let's start with what's known

00:03:34.800 --> 00:03:38.050
as a point mutation, so let's say this C

00:03:38.050 --> 00:03:40.370
gets swapped out for an A.

00:03:40.370 --> 00:03:43.900
Well, if that happened,
then on the RNA strand,

00:03:43.900 --> 00:03:46.770
all of a sudden this would be a uracil,

00:03:46.770 --> 00:03:50.480
and if that is a uracil, this
AAG would still be there,

00:03:50.480 --> 00:03:54.060
coding for lysine, but this
second codon is now different.

00:03:54.060 --> 00:03:55.780
What would it now code for?

00:03:55.780 --> 00:03:57.655
Well, CUA.

00:03:57.655 --> 00:04:02.655
CUA, it'll now code for
leucine instead of arginine.

00:04:03.210 --> 00:04:04.854
Leucine,

00:04:04.854 --> 00:04:06.170
l-e-u.

00:04:06.170 --> 00:04:09.920
This is fairly typical for
a substitution mutation.

00:04:09.920 --> 00:04:14.210
It might change a particular amino acid,

00:04:14.210 --> 00:04:17.030
but sometimes, it could
be more significant.

00:04:17.030 --> 00:04:18.260
For example,

00:04:18.260 --> 00:04:22.230
if this G was swapped out for an A,

00:04:22.230 --> 00:04:24.810
then this C on the RNA

00:04:24.810 --> 00:04:27.000
would then be a U,

00:04:27.000 --> 00:04:28.710
and then what would happen?

00:04:28.710 --> 00:04:31.340
Well, this first codon
would still code for lysine,

00:04:31.340 --> 00:04:32.940
but the second one would be UGA.

00:04:34.030 --> 00:04:34.863
UGA.

00:04:35.770 --> 00:04:40.170
Now, all of a sudden, it
codes for a stop codon,

00:04:40.170 --> 00:04:43.240
and so, the actual translation
process would stop,

00:04:43.240 --> 00:04:45.530
which could be a very, very big deal

00:04:45.530 --> 00:04:47.770
if this DNA sequence,

00:04:47.770 --> 00:04:50.600
if the normal, non-mutated polypeptide

00:04:50.600 --> 00:04:52.690
had to keep going on, and on, and on.

00:04:52.690 --> 00:04:55.310
Over here, it just happened
to have a stop codon next,

00:04:55.310 --> 00:04:56.950
but you could imagine, if
they had just, you know,

00:04:56.950 --> 00:04:58.950
another thousand codons before the end,

00:04:58.950 --> 00:05:01.140
but all of a sudden, you had a
point mutation to stop early,

00:05:01.140 --> 00:05:03.760
that would significantly
affect the protein

00:05:03.760 --> 00:05:05.300
that it's coding for.

00:05:05.300 --> 00:05:07.560
Now, another type of
mutation that typically

00:05:07.560 --> 00:05:09.050
has a fairly significant affect

00:05:09.050 --> 00:05:12.810
is a frameshift mutation,
and that's where something

00:05:12.810 --> 00:05:16.360
gets inserted or deleted
and shifts everything.

00:05:16.360 --> 00:05:19.100
So, for example, instead of the A

00:05:19.100 --> 00:05:21.000
being swapped in for the G,

00:05:21.000 --> 00:05:22.930
what if the A got inserted here?

00:05:22.930 --> 00:05:25.460
So then, our sequence
would look like this.

00:05:25.460 --> 00:05:28.200
T-T-C,

00:05:28.200 --> 00:05:32.740
and then we have A, and
then you have G-C-T,

00:05:32.740 --> 00:05:37.740
G-C-T-A-T-T-T.

00:05:38.070 --> 00:05:39.150
So, what just happened here,

00:05:39.150 --> 00:05:41.660
this was our original sequence,
but the A got inserted here,

00:05:41.660 --> 00:05:43.730
it didn't replace the G, and so everything

00:05:43.730 --> 00:05:45.500
got shifted to the right.

00:05:45.500 --> 00:05:47.490
Now, what are we coding for?

00:05:47.490 --> 00:05:51.530
Well, when we transcribe
to RNA, this will be

00:05:51.530 --> 00:05:56.530
A-A-G-U-C-G-A-U-A-A-A,

00:06:01.400 --> 00:06:04.860
and now this first codon
still codes for lysine,

00:06:04.860 --> 00:06:06.490
we've seen that multiple times.

00:06:06.490 --> 00:06:08.190
But, what about this second codon?

00:06:09.130 --> 00:06:12.424
This second codon over here, UCG.

00:06:12.424 --> 00:06:13.560
UCG,

00:06:13.560 --> 00:06:15.560
that's serine,

00:06:15.560 --> 00:06:18.100
we got a different amino acid.

00:06:18.100 --> 00:06:20.070
And what's interesting is, it's not just

00:06:20.070 --> 00:06:22.080
that one amino acid is changing,

00:06:22.080 --> 00:06:24.200
we're gonna see that keeps happening.

00:06:24.200 --> 00:06:25.850
So now, we have AUA.

00:06:27.756 --> 00:06:28.589
AUA.

00:06:29.720 --> 00:06:32.330
Here, we have isoleucine.

00:06:32.330 --> 00:06:33.310
So, isoleucine,

00:06:35.250 --> 00:06:37.700
right over here, which is different

00:06:37.700 --> 00:06:40.540
than what we had before, we
don't have a stop codon anymore,

00:06:40.540 --> 00:06:43.310
and we would keep going on and on.

00:06:43.310 --> 00:06:46.240
And so, you could imagine
a frameshift mutation

00:06:46.240 --> 00:06:48.010
where you either insert something

00:06:48.010 --> 00:06:51.470
or you take it out so that
the whole frame gets shifted,

00:06:51.470 --> 00:06:53.850
can have a dramatic impact on what

00:06:53.850 --> 00:06:57.590
it will transcribe and then translate for.

00:06:57.590 --> 00:07:00.040
Now, lucky for us, even though mutations

00:07:00.040 --> 00:07:03.550
are always going on, there are
many proofreading mechanisms

00:07:03.550 --> 00:07:06.660
in biological systems to
make them less frequent

00:07:06.660 --> 00:07:08.110
than they otherwise would be,

00:07:08.110 --> 00:07:09.560
and people are still understanding

00:07:09.560 --> 00:07:13.410
how these proofreading
mechanisms fully happen.

00:07:13.410 --> 00:07:15.140
Another thing to appreciate is,

00:07:15.140 --> 00:07:17.860
we often associate a mutation

00:07:17.860 --> 00:07:18.820
as

00:07:18.820 --> 00:07:21.280
being equal to a bad thing,

00:07:21.280 --> 00:07:24.020
and often times, it is a bad thing.

00:07:24.020 --> 00:07:25.890
What used to be a functional protein

00:07:25.890 --> 00:07:28.010
may no longer be a functional protein

00:07:28.010 --> 00:07:31.740
because the amino acids,
the coding got stopped short

00:07:31.740 --> 00:07:33.180
or there was a frameshift mutation

00:07:33.180 --> 00:07:35.910
that's just coding for
completely different things.

00:07:35.910 --> 00:07:38.030
So, sometimes it could be very bad,

00:07:38.030 --> 00:07:40.140
and some diseases actually are caused

00:07:40.140 --> 00:07:43.340
by strange mutations
like that, that show up.

00:07:43.340 --> 00:07:46.660
Often times, the mutation
might not be a big deal.

00:07:46.660 --> 00:07:48.450
Maybe something gets swapped out,

00:07:48.450 --> 00:07:50.280
maybe only one amino acid changes

00:07:50.280 --> 00:07:51.760
and it doesn't really change

00:07:51.760 --> 00:07:54.880
the ability of the protein to do its job,

00:07:54.880 --> 00:07:56.430
in which case it doesn't matter,

00:07:56.430 --> 00:07:58.130
but every now and then,
a mutation can actually

00:07:58.130 --> 00:07:58.963
be a good thing.

00:07:58.963 --> 00:08:01.010
In fact, we need the mutation in order

00:08:01.010 --> 00:08:03.210
to have variation in a population,

00:08:03.210 --> 00:08:05.560
and variation is what natural selection

00:08:05.560 --> 00:08:06.810
and evolution run off of.

00:08:06.810 --> 00:08:08.070
If you don't have variation,

00:08:08.070 --> 00:08:09.880
then you're not going
to have different things

00:08:09.880 --> 00:08:11.450
that get selected in
different environments

00:08:11.450 --> 00:08:14.780
and you're not going to have
that gradual change over time.

00:08:14.780 --> 00:08:17.350
So, a big picture, hopefully
you got a better appreciation

00:08:17.350 --> 00:08:21.490
for how transcription,
and then translation,

00:08:21.490 --> 00:08:22.910
let me write that down.

00:08:22.910 --> 00:08:25.800
And then, so that's
transcription from DNA to RNA,

00:08:25.800 --> 00:08:27.820
and then this is translation.

00:08:27.820 --> 00:08:28.730
Translation

00:08:31.160 --> 00:08:32.630
from RNA

00:08:34.820 --> 00:08:36.340
to protein,

00:08:36.340 --> 00:08:37.410
to protein.

00:08:37.410 --> 00:08:39.570
We have appreciation of how that happens,

00:08:39.570 --> 00:08:42.320
we got appreciation of how to
use these translation tables,

00:08:42.320 --> 00:08:45.300
but also how either a point mutation

00:08:45.300 --> 00:08:49.030
or a frameshift mutation
can eventually affect

00:08:49.030 --> 00:08:51.210
the protein that gets coded for.


Meet Sean, a creator of AP Physics on Khan Academy

WEBVTT
Kind: captions
Language: en

00:00:06.490 --> 00:00:11.490
- I have taught AP Physics
classes for the last seven years.

00:00:11.580 --> 00:00:14.070
AP Physics One, AP Physics B,

00:00:14.070 --> 00:00:16.740
back in the day, and AP Physics C now.

00:00:16.740 --> 00:00:20.060
I try to make my lessons personable,

00:00:20.060 --> 00:00:22.630
relate to the student,
offer them real life

00:00:22.630 --> 00:00:24.870
examples where things happen,

00:00:24.870 --> 00:00:27.560
but also focus on, instead of,

00:00:27.560 --> 00:00:30.640
a bunch of little memorization facts,

00:00:30.640 --> 00:00:32.550
like, what's the big idea that helps

00:00:32.550 --> 00:00:35.770
you figure out all these
different situations for,

00:00:35.770 --> 00:00:38.420
allows you to be a more
robust problem solver.

00:00:38.420 --> 00:00:41.350
So, we're focusing on the big core ideas

00:00:41.350 --> 00:00:44.880
of our subject, being physics,

00:00:44.880 --> 00:00:46.650
and I think you'll find that across

00:00:46.650 --> 00:00:49.920
all the different AP content subjects.

00:00:49.920 --> 00:00:52.460
We are finely tuned

00:00:52.460 --> 00:00:55.130
to what the AP exam

00:00:55.130 --> 00:00:57.600
is gonna be like, directly.

00:00:57.600 --> 00:01:01.970
And we are building in
videos for instructions,

00:01:01.970 --> 00:01:04.680
specific to that, and also we have

00:01:04.680 --> 00:01:07.840
practice exercises that
I'm really excited about,

00:01:07.840 --> 00:01:09.820
that, you can assign it to students,

00:01:09.820 --> 00:01:13.260
and there's hints, and there's feedback,

00:01:13.260 --> 00:01:15.400
why a certain problem is wrong,

00:01:15.400 --> 00:01:16.850
and why a certain problem is right.

00:01:16.850 --> 00:01:19.470
And then it shows you the solution path

00:01:19.470 --> 00:01:21.320
of how you would get to the solution.

00:01:21.320 --> 00:01:24.770
So, when you assign a student a problem,

00:01:24.770 --> 00:01:26.320
they don't have to wait a whole

00:01:26.320 --> 00:01:28.470
24 hours, until they get back to class.

00:01:28.470 --> 00:01:31.735
They can get it wrong, fail early,

00:01:31.735 --> 00:01:34.200
try another one, fail often,

00:01:34.200 --> 00:01:36.240
and do a couple times on that.

00:01:36.240 --> 00:01:37.550
And I actually think my students

00:01:37.550 --> 00:01:39.730
might actually do more,

00:01:39.730 --> 00:01:41.380
homework, 'cause they're getting

00:01:41.380 --> 00:01:43.390
instant feedback on the process,

00:01:43.390 --> 00:01:45.050
rather than just trying a couple,

00:01:45.050 --> 00:01:46.250
and getting stuck, and like,

00:01:46.250 --> 00:01:48.530
"Ah, I'm frustrated, I'm outta here."

00:01:48.530 --> 00:01:49.950
They can really

00:01:50.800 --> 00:01:51.810
get in the seat,

00:01:51.810 --> 00:01:52.890
and stay in it, because they're getting

00:01:52.890 --> 00:01:54.830
instant feedback and help as they're

00:01:54.830 --> 00:01:55.810
working through problems.

00:01:55.810 --> 00:01:57.740
I think that's gonna be really powerful.


Meet Kim, one of the creators of Khan Academy's AP US History lessons

WEBVTT
Kind: captions
Language: en

00:00:04.260 --> 00:00:07.210
- I have been working on
the US history content here

00:00:07.210 --> 00:00:09.790
for more than two years now.

00:00:09.790 --> 00:00:12.900
And we have a team of experts who've been

00:00:12.900 --> 00:00:14.890
in the classroom for many years,

00:00:14.890 --> 00:00:17.570
who have advanced degrees in US history,

00:00:17.570 --> 00:00:21.030
who really rigorously write, tape,

00:00:21.030 --> 00:00:23.010
and edit each other's work.

00:00:23.010 --> 00:00:24.960
And I think it would be kind of,

00:00:24.960 --> 00:00:27.770
I would judge it as like
a day's worth of class.

00:00:27.770 --> 00:00:30.560
Everything that we've done
on the Khan Academy website

00:00:30.560 --> 00:00:32.550
meets the AP requirements.

00:00:32.550 --> 00:00:34.420
So teachers can feel confident

00:00:34.420 --> 00:00:36.460
that when they send their students

00:00:36.460 --> 00:00:39.680
to watch a video or read an article

00:00:39.680 --> 00:00:43.170
or practice with an
exercise on Khan Academy,

00:00:43.170 --> 00:00:47.180
that students are taking away
the key learning objectives

00:00:47.180 --> 00:00:49.440
that they should get for the AP exam.

00:00:49.440 --> 00:00:51.800
- [Instructor] It's a frequent
misconception that people

00:00:51.800 --> 00:00:54.530
in this time period thought
that the world was flat.

00:00:54.530 --> 00:00:57.090
- We really wanted to make this material

00:00:57.090 --> 00:00:58.940
approachable and fun.

00:00:58.940 --> 00:01:01.430
And so throughout, I
think, students will see

00:01:01.430 --> 00:01:05.270
a real enthusiasm for the
material and a sense of humor,

00:01:05.270 --> 00:01:09.240
so that it's not just
reading a history textbook.

00:01:09.240 --> 00:01:10.073
- [Instructor] So I've brought you here

00:01:10.073 --> 00:01:11.320
to talk about the Gilded Age,

00:01:11.320 --> 00:01:14.930
which is one of my favorite
eras of American history.

00:01:14.930 --> 00:01:16.870
- [Man] Because everything
was great and covered in gold?

00:01:16.870 --> 00:01:18.680
- It's really interacting with some

00:01:18.680 --> 00:01:20.970
of the big questions of history,

00:01:20.970 --> 00:01:25.520
and having an opportunity to
explore those with enthusiasm.

00:01:25.520 --> 00:01:27.670
- [Instructor] No,
because it is the only era

00:01:27.670 --> 00:01:29.230
of American history I can think of

00:01:29.230 --> 00:01:31.477
that has a sarcastic name.

00:01:31.477 --> 00:01:32.310
(man laughs)

00:01:32.310 --> 00:01:33.340
- Because it is fun.

00:01:33.340 --> 00:01:37.130
We hope to give students that sense

00:01:37.130 --> 00:01:39.350
that history is not a boring subject.

00:01:39.350 --> 00:01:40.440
It's really fun.


Examples thinking about power in significance tests

WEBVTT
Kind: captions
Language: en

00:00:00.460 --> 00:00:02.600
- [Instructor] A significance
test is going to be performed

00:00:02.600 --> 00:00:06.350
using a significance level of 5/100.

00:00:06.350 --> 00:00:09.950
Suppose that the null
hypothesis is actually false.

00:00:09.950 --> 00:00:14.160
If the significance level
was lowered to 1/100,

00:00:14.160 --> 00:00:15.850
which of the following would be true?

00:00:15.850 --> 00:00:16.930
So pause this video

00:00:16.930 --> 00:00:19.450
and see if you can answer it on your own.

00:00:19.450 --> 00:00:21.160
Okay, now let's do this together.

00:00:21.160 --> 00:00:23.390
Let's see, they're talking
how the probability

00:00:23.390 --> 00:00:28.050
of a type II error and/or
the power would change.

00:00:28.050 --> 00:00:29.490
So before I even look at the choices,

00:00:29.490 --> 00:00:30.800
let's think about this.

00:00:30.800 --> 00:00:32.920
We have talked about in previous videos

00:00:32.920 --> 00:00:35.550
that if we increase our
level of significance,

00:00:35.550 --> 00:00:38.170
that will increase our power.

00:00:38.170 --> 00:00:42.610
And power is the probability
of not making a type II error,

00:00:42.610 --> 00:00:44.960
so that would decrease the probability

00:00:44.960 --> 00:00:49.030
of making a type II error.

00:00:49.030 --> 00:00:51.160
But in this question
we're going the other way.

00:00:51.160 --> 00:00:53.640
We're decreasing the
level of significance,

00:00:53.640 --> 00:00:57.370
which would lower the probability
of making a type I error,

00:00:57.370 --> 00:00:59.920
but this would decrease the power.

00:00:59.920 --> 00:01:01.850
It actually would increase.

00:01:01.850 --> 00:01:03.590
It actually would increase the probability

00:01:03.590 --> 00:01:08.590
of making a type II error.

00:01:08.850 --> 00:01:11.330
Which of these choices
are consistent with that?

00:01:11.330 --> 00:01:14.360
Well, choice A says that
both the type II error

00:01:14.360 --> 00:01:15.730
and the power would decrease.

00:01:15.730 --> 00:01:17.900
Well, these two things
don't move together.

00:01:17.900 --> 00:01:20.020
If one increases, the other decreases.

00:01:20.020 --> 00:01:21.570
So we rule that one out.

00:01:21.570 --> 00:01:24.100
Choice B also has these
two things moving together,

00:01:24.100 --> 00:01:24.960
which can't be true.

00:01:24.960 --> 00:01:28.010
If one increases, the other decreases.

00:01:28.010 --> 00:01:31.310
Choice C, the probability of a
type II error would increase.

00:01:31.310 --> 00:01:33.400
That's consistent with what we have here.

00:01:33.400 --> 00:01:35.770
And the power of the test would decrease.

00:01:35.770 --> 00:01:37.730
Yep, that's consistent
with what we have here,

00:01:37.730 --> 00:01:38.890
so that looks good.

00:01:38.890 --> 00:01:41.410
And choice D is the opposite of that.

00:01:41.410 --> 00:01:44.840
The probability of a type
II error would decrease.

00:01:45.740 --> 00:01:47.500
They're talking about
this scenario over here,

00:01:47.500 --> 00:01:48.333
and that would have happened

00:01:48.333 --> 00:01:51.110
if they increased our significance
level, not decreased it,

00:01:51.110 --> 00:01:53.110
so we could rule that one out as well.

00:01:53.110 --> 00:01:54.380
Let's do another example.

00:01:56.090 --> 00:01:58.720
Asha owns a car wash
and is trying to decide

00:01:58.720 --> 00:02:00.660
whether or not to
purchase a vending machine

00:02:00.660 --> 00:02:03.570
so that customers can buy
coffee while they wait.

00:02:03.570 --> 00:02:07.320
She'll get the machine if she's
convinced that more than 30%

00:02:07.320 --> 00:02:09.570
of her customers would buy coffee.

00:02:09.570 --> 00:02:12.560
She plans on taking a
random sample of n customers

00:02:12.560 --> 00:02:15.020
and asking them whether or
not they would buy coffee

00:02:15.020 --> 00:02:18.470
from the machine, and she'll
then do a significance test

00:02:18.470 --> 00:02:22.660
using alpha equals 0.05 to
see if the sample proportion

00:02:22.660 --> 00:02:26.820
who say "yes" is significantly
greater than 30%.

00:02:26.820 --> 00:02:28.510
Which situation below would result

00:02:28.510 --> 00:02:30.490
in the highest power for her test?

00:02:30.490 --> 00:02:33.300
So, again, pause this
video and try to answer it.

00:02:33.300 --> 00:02:35.050
Well, before I even look at the choices,

00:02:35.050 --> 00:02:37.700
we could think about what
her hypotheses would be.

00:02:37.700 --> 00:02:39.880
Her null hypothesis is,

00:02:39.880 --> 00:02:41.400
you can kind of view it as the status quo.

00:02:41.400 --> 00:02:42.840
No news here.

00:02:42.840 --> 00:02:45.340
And that would be that the
true population proportion

00:02:45.340 --> 00:02:49.970
of people who want to buy coffee is 30%

00:02:49.970 --> 00:02:53.200
and that her alternative
hypothesis is that no,

00:02:53.200 --> 00:02:54.860
the true population proportion,

00:02:54.860 --> 00:02:58.950
the true population parameter
there is greater than

00:02:58.950 --> 00:03:01.810
is greater than 30%.

00:03:02.720 --> 00:03:04.420
If we're talking about what would result

00:03:04.420 --> 00:03:07.700
in the highest power for her test.

00:03:07.700 --> 00:03:10.660
So, a high power.

00:03:10.660 --> 00:03:14.640
A high power means the lowest probability

00:03:14.640 --> 00:03:18.150
of making a type II error.

00:03:18.150 --> 00:03:19.660
And in other videos we've talked about it.

00:03:19.660 --> 00:03:22.210
It looks like she's dealing
with the sample size.

00:03:22.210 --> 00:03:24.740
And what is the true proportion

00:03:24.740 --> 00:03:26.280
of customers that would buy coffee?

00:03:26.280 --> 00:03:28.430
And the sample size is under her control.

00:03:28.430 --> 00:03:29.930
The true proportion isn't.

00:03:29.930 --> 00:03:31.500
Don't wanna make it seem

00:03:31.500 --> 00:03:34.040
like somehow you can
change the true proportion

00:03:34.040 --> 00:03:35.680
in order to get a higher power.

00:03:35.680 --> 00:03:37.950
You can change the sample size.

00:03:37.950 --> 00:03:39.730
But the general principle is,

00:03:39.730 --> 00:03:42.190
the higher the sample
size, the higher the power.

00:03:42.190 --> 00:03:44.410
So you want the highest
possible sample size.

00:03:44.410 --> 00:03:46.690
And you're going to have a higher power

00:03:46.690 --> 00:03:49.130
if the true proportion is further

00:03:49.130 --> 00:03:53.120
from your null hypothesis proportion.

00:03:54.310 --> 00:03:56.480
We want the highest possible n,

00:03:56.480 --> 00:04:00.040
and that looks like an n of
200, which is there and there.

00:04:00.040 --> 00:04:03.370
And we want a true proportion of customers

00:04:03.370 --> 00:04:04.630
that would actually buy coffee

00:04:04.630 --> 00:04:09.040
as far away as possible
from our null hypothesis,

00:04:09.040 --> 00:04:12.540
which, once again, would
not be under Asha's control.

00:04:12.540 --> 00:04:16.230
But you can clearly see
that 50% is further from 30

00:04:16.230 --> 00:04:18.340
than 32 is, so this one,

00:04:18.340 --> 00:04:20.250
choice D is the one that looks good.


Introduction to power in significance tests

WEBVTT
Kind: captions
Language: en

00:00:00.180 --> 00:00:02.070
- [Instructor] What we are
going to do in this video

00:00:02.070 --> 00:00:05.280
is talk about the idea of power

00:00:05.280 --> 00:00:08.230
when we are dealing
with significance tests.

00:00:08.230 --> 00:00:10.960
And power is an idea
that you might encounter

00:00:10.960 --> 00:00:13.950
in a first year statistics course.

00:00:13.950 --> 00:00:16.610
It's turns out that it's
fairly difficult to calculate,

00:00:16.610 --> 00:00:19.240
but it's interesting to know what it means

00:00:19.240 --> 00:00:21.790
and what are the levers that
might increase the power

00:00:21.790 --> 00:00:24.920
or decrease the power
in a significance test.

00:00:24.920 --> 00:00:28.860
So just to cut to the chase,
power is a probability.

00:00:28.860 --> 00:00:30.961
You can view it as the probability

00:00:30.961 --> 00:00:33.570
that you are doing the right thing

00:00:33.570 --> 00:00:36.660
when the null hypothesis is not true,

00:00:36.660 --> 00:00:39.580
and the right thing is you
should reject the null hypothesis

00:00:39.580 --> 00:00:40.413
if it's not true.

00:00:40.413 --> 00:00:44.240
So it's a probability of rejecting,

00:00:44.240 --> 00:00:47.190
rejecting your null hypothesis

00:00:47.190 --> 00:00:50.860
given that the null hypothesis is false.

00:00:50.860 --> 00:00:53.950
So we can view it as a
conditional probability like that.

00:00:53.950 --> 00:00:55.780
But there's other ways
to conceptualize it.

00:00:55.780 --> 00:00:58.570
We can connect it to Type II errors.

00:00:58.570 --> 00:01:01.270
For example, you could
say this is equal to

00:01:01.270 --> 00:01:06.021
one minus the probability
of not rejecting,

00:01:06.021 --> 00:01:09.086
one minus the probability
of not rejecting,

00:01:09.086 --> 00:01:13.360
not rejecting the null hypothesis

00:01:13.360 --> 00:01:17.000
given that the null hypothesis is false.

00:01:17.000 --> 00:01:19.130
And this thing that I just described,

00:01:19.130 --> 00:01:21.490
not rejecting the null hypothesis

00:01:21.490 --> 00:01:23.970
given that the null hypothesis is false,

00:01:23.970 --> 00:01:27.480
this is, that's the
definition of a Type II error.

00:01:30.292 --> 00:01:32.937
So you could view it
as just the probability

00:01:32.937 --> 00:01:34.750
of not making a Type II error,

00:01:34.750 --> 00:01:37.320
or one minus the probability
of making a Type II error.

00:01:37.320 --> 00:01:38.630
Hopefully that's not confusing.

00:01:38.630 --> 00:01:40.270
So let me just write it the other way.

00:01:40.270 --> 00:01:41.896
So you could say it's the probability

00:01:41.896 --> 00:01:46.790
of not making a Type II error.

00:01:52.470 --> 00:01:57.150
So what are the things that
would actually drive power?

00:01:57.150 --> 00:01:59.370
And to help us conceptualize that,

00:01:59.370 --> 00:02:01.840
I'll draw two sampling distributions,

00:02:01.840 --> 00:02:05.430
one, if we assume that the
null hypothesis is true,

00:02:05.430 --> 00:02:08.900
and one where we assume that
the null hypothesis is false,

00:02:08.900 --> 00:02:11.140
and the true population
parameter is something different

00:02:11.140 --> 00:02:13.150
than the null hypothesis is saying.

00:02:13.150 --> 00:02:17.991
So for example, let's say
that we have a null hypothesis

00:02:17.991 --> 00:02:22.150
that our population mean is
equal to, let's just call it,

00:02:22.150 --> 00:02:27.150
mu one, and we have an
alternative hypothesis,

00:02:27.220 --> 00:02:31.570
so H sub a, that says, "Hey, no.

00:02:31.570 --> 00:02:36.310
"The population mean is
not equal to mu one."

00:02:36.310 --> 00:02:40.740
So if you assumed a world where
the null hypothesis is true,

00:02:40.740 --> 00:02:41.960
so I'll do that in blue,

00:02:41.960 --> 00:02:45.690
so if we assume the
null hypothesis is true,

00:02:45.690 --> 00:02:47.920
what would be our sampling distribution?

00:02:47.920 --> 00:02:50.098
Remember, what we do in significance tests

00:02:50.098 --> 00:02:53.640
is we have some form of a population.

00:02:53.640 --> 00:02:54.850
Let me draw that.

00:02:54.850 --> 00:02:58.090
You have a population right over here.

00:02:58.090 --> 00:03:02.010
And our hypotheses are
making some statement about

00:03:02.010 --> 00:03:04.110
a parameter in that population.

00:03:04.110 --> 00:03:09.110
And to test it, we take a
sample of a certain size.

00:03:09.150 --> 00:03:11.990
We calculate a statistic, in this case,

00:03:11.990 --> 00:03:14.120
it would be the sample mean,

00:03:14.120 --> 00:03:18.300
and we say if we assume that
our null hypothesis is true,

00:03:18.300 --> 00:03:21.670
what is the probability of
getting that sample statistic?

00:03:21.670 --> 00:03:23.290
And if that's below a threshold,

00:03:23.290 --> 00:03:24.630
which we call a significance level,

00:03:24.630 --> 00:03:26.676
we reject the null hypothesis.

00:03:26.676 --> 00:03:29.910
And so that world that
we have been living in,

00:03:29.910 --> 00:03:30.880
one way to think about it.

00:03:30.880 --> 00:03:33.910
In a world where you assume
the null hypothesis is true,

00:03:33.910 --> 00:03:36.620
you might have a sampling distribution

00:03:36.620 --> 00:03:38.470
that looks something like this.

00:03:38.470 --> 00:03:40.780
If the null hypothesis is true,

00:03:40.780 --> 00:03:42.900
then the center of your
sampling distribution

00:03:42.900 --> 00:03:45.790
would be right over here at mu one,

00:03:45.790 --> 00:03:48.494
and given your sample size,

00:03:48.494 --> 00:03:51.670
you would get a certain
sampling distribution

00:03:51.670 --> 00:03:53.380
for the sample means.

00:03:53.380 --> 00:03:56.080
If your sample size increases,
this will be narrower.

00:03:56.080 --> 00:03:59.980
If it decreases, this
thing is going to be wider.

00:03:59.980 --> 00:04:03.790
And you set a significance
level, which is essentially

00:04:03.790 --> 00:04:07.448
your probability of
rejecting the null hypothesis

00:04:07.448 --> 00:04:09.175
even if it is true.

00:04:09.175 --> 00:04:11.720
You could even view it as,
and we've talked about it,

00:04:11.720 --> 00:04:13.330
you can view your significance level

00:04:13.330 --> 00:04:16.400
as the probability of
making a Type I error.

00:04:16.400 --> 00:04:19.052
So your significance level is some area.

00:04:19.052 --> 00:04:22.390
And so let's say it's
this area that I'm shading

00:04:22.390 --> 00:04:23.920
in orange right over here.

00:04:23.920 --> 00:04:25.930
That would be your significance level.

00:04:25.930 --> 00:04:28.750
So if you took a sample right over here

00:04:28.750 --> 00:04:30.720
and you calculated its sample mean

00:04:30.720 --> 00:04:34.090
and you happened to fall
in this area, this area,

00:04:34.090 --> 00:04:36.680
or this area right over
here, then you would

00:04:36.680 --> 00:04:39.072
reject your null hypothesis.

00:04:39.072 --> 00:04:42.800
Now if the null hypothesis
actually was true,

00:04:42.800 --> 00:04:44.970
you would be committing a Type I error

00:04:44.970 --> 00:04:46.700
without knowing about it.

00:04:46.700 --> 00:04:50.021
But for power, we are
concerned with a Type II error.

00:04:50.021 --> 00:04:52.670
So in this one, it's a
conditional probability

00:04:52.670 --> 00:04:54.910
that our null hypothesis is false.

00:04:54.910 --> 00:04:57.950
And so let's construct
another sampling distribution

00:04:57.950 --> 00:05:00.620
in the case where our
null hypothesis is false.

00:05:00.620 --> 00:05:03.870
So let me just continue
this line right over here,

00:05:03.870 --> 00:05:05.340
and I'll do that.

00:05:05.340 --> 00:05:09.236
So let's imagine a world where
our null hypothesis is false

00:05:09.236 --> 00:05:14.236
and it's actually the case
that our mean is mu two,

00:05:15.270 --> 00:05:18.520
and let's say that mu
two is right over here,

00:05:18.520 --> 00:05:21.916
and in this reality, our
sampling distribution

00:05:21.916 --> 00:05:25.197
might look something like this.

00:05:25.197 --> 00:05:28.250
Once again, it will be
for a given sample size.

00:05:28.250 --> 00:05:29.550
The larger the sample size,

00:05:29.550 --> 00:05:32.850
the narrower this bell curve would be.

00:05:32.850 --> 00:05:36.530
And so it might look something like this.

00:05:36.530 --> 00:05:39.200
So in which situation, so in this world,

00:05:39.200 --> 00:05:42.294
we should be rejecting
the null hypothesis.

00:05:42.294 --> 00:05:46.530
But what are the samples in
which case we are not rejecting

00:05:46.530 --> 00:05:48.615
the null hypothesis even though we should?

00:05:48.615 --> 00:05:51.743
Well, we're not going to
reject the null hypothesis

00:05:51.743 --> 00:05:56.743
if we get samples in,
if we get a sample here,

00:05:57.220 --> 00:06:00.300
or a sample here, or a sample here,

00:06:00.300 --> 00:06:02.990
a sample, where if you
assume the null hypothesis

00:06:02.990 --> 00:06:06.490
is true, the probability
isn't that unlikely.

00:06:06.490 --> 00:06:10.570
And so the probability
of making a Type II error

00:06:10.570 --> 00:06:13.780
when we should reject the
null hypothesis but we don't

00:06:13.780 --> 00:06:18.150
is actually this area right over here.

00:06:18.150 --> 00:06:20.630
And the power, the
probability of rejecting

00:06:20.630 --> 00:06:23.000
the null hypothesis given that it's false,

00:06:23.000 --> 00:06:25.690
so given that it's false would
be this red distribution,

00:06:25.690 --> 00:06:29.997
that would be the rest of
this area right over here.

00:06:29.997 --> 00:06:32.584
So how can we increase the power?

00:06:32.584 --> 00:06:35.700
Well, one way is to increase our alpha,

00:06:35.700 --> 00:06:37.490
increase our significance level.

00:06:37.490 --> 00:06:40.151
If we increase our significance
level, say from that,

00:06:40.151 --> 00:06:42.020
well, the significance level is an area.

00:06:42.020 --> 00:06:45.240
So if we want it to go up,
if we increase the area,

00:06:45.240 --> 00:06:46.990
and it looks something like that,

00:06:48.210 --> 00:06:51.240
now by expanding that significance area,

00:06:51.240 --> 00:06:54.890
we have increased the power
because now this yellow area

00:06:54.890 --> 00:06:56.100
is larger.

00:06:56.100 --> 00:06:59.140
We've pushed this boundary
to the left of it.

00:06:59.140 --> 00:07:00.690
Now you might say, "Oh, well, hey.

00:07:00.690 --> 00:07:01.950
"If we want to increase the power,

00:07:01.950 --> 00:07:03.710
"power sounds like a good thing,

00:07:03.710 --> 00:07:06.190
"why don't we just always increase alpha?"

00:07:06.190 --> 00:07:09.330
Well, the problem with that
is if you increase alpha,

00:07:09.330 --> 00:07:12.770
so let me write this down,
so if you take alpha,

00:07:12.770 --> 00:07:14.730
your significance level,
and you increase it,

00:07:14.730 --> 00:07:16.534
that will increase the power.

00:07:16.534 --> 00:07:18.675
That will increase the power,

00:07:18.675 --> 00:07:21.802
but it's also going to
increase your probability

00:07:21.802 --> 00:07:26.802
of a Type I error, because remember,

00:07:26.980 --> 00:07:30.750
that's one way to
conceptualize what alpha is,

00:07:30.750 --> 00:07:32.120
what your significance level is.

00:07:32.120 --> 00:07:35.080
It's a probability of a Type I error.

00:07:35.080 --> 00:07:37.920
Now what are other ways
to increase your power?

00:07:37.920 --> 00:07:40.290
Well, if you increase your sample size,

00:07:40.290 --> 00:07:42.640
then both of these distributions will,

00:07:42.640 --> 00:07:45.900
these sampling distributions
are going to get narrower.

00:07:45.900 --> 00:07:47.692
And so if these sampling distributions,

00:07:47.692 --> 00:07:52.182
if both of these sampling
distributions get narrower,

00:07:52.182 --> 00:07:57.154
then that situation where
you are not rejecting

00:07:57.154 --> 00:08:01.160
your null hypothesis
even though you should

00:08:01.160 --> 00:08:03.870
is going to have a lot less area.

00:08:03.870 --> 00:08:05.100
There's gonna be, one
way to think about it,

00:08:05.100 --> 00:08:07.040
there's going to be a lot less overlap

00:08:07.040 --> 00:08:09.710
between these two sampling distributions.

00:08:09.710 --> 00:08:11.320
And so let me write that down.

00:08:11.320 --> 00:08:16.240
So another way is to, if you
increase n, your sample size,

00:08:16.240 --> 00:08:19.290
that's going to increase your power.

00:08:19.290 --> 00:08:22.490
And this in general is always a good thing

00:08:22.490 --> 00:08:23.580
if you can do it.

00:08:23.580 --> 00:08:26.115
Now other things that may or
may not be under your control

00:08:26.115 --> 00:08:29.796
is well, the less variability
there is in the dataset,

00:08:29.796 --> 00:08:33.420
that would also make the
sampling distributions narrower,

00:08:33.420 --> 00:08:36.200
and that would also increase the power.

00:08:36.200 --> 00:08:39.480
So less variability and
you could measure that

00:08:39.480 --> 00:08:42.590
as by variance or standard deviation

00:08:42.590 --> 00:08:47.165
of your underlying dataset,
that would increase your power.

00:08:47.165 --> 00:08:50.590
Another thing that
would increase the power

00:08:50.590 --> 00:08:54.699
is if the true parameter is further away

00:08:54.699 --> 00:08:57.920
than what the null hypothesis is saying.

00:08:57.920 --> 00:09:00.700
So if you say true parameter,

00:09:02.490 --> 00:09:07.490
far from null hypothesis what it's saying,

00:09:07.710 --> 00:09:10.310
that also will increase the power.

00:09:10.310 --> 00:09:13.960
So these two are not
typically under your control

00:09:13.960 --> 00:09:17.640
but the sample size is and
the significance level is.

00:09:17.640 --> 00:09:19.720
Significance level,
there's a trade-off though.

00:09:19.720 --> 00:09:21.870
If you increase the power through that,

00:09:21.870 --> 00:09:24.309
you're also increasing the
probability of a Type I error.

00:09:24.309 --> 00:09:26.380
So for a lot of
researchers, they might say,

00:09:26.380 --> 00:09:29.230
"Hey, if a Type II error is worse,

00:09:29.230 --> 00:09:30.720
"I'm willing to make this trade-off.

00:09:30.720 --> 00:09:32.640
"I'll increase the significance level.

00:09:32.640 --> 00:09:36.020
"But if a Type I error is
actually what I'm afraid of,

00:09:36.020 --> 00:09:38.010
"then I wouldn't want top use this lever."

00:09:38.010 --> 00:09:40.731
But in any case, increasing
your sample size,

00:09:40.731 --> 00:09:43.780
if you can do it, is
going to be a good thing.


Examples identifying Type I and Type II errors

WEBVTT
Kind: captions
Language: en

00:00:00.260 --> 00:00:01.290
- [Instructor] We are told,

00:00:01.290 --> 00:00:04.080
"A large nationwide poll recently showed

00:00:04.080 --> 00:00:07.730
"an unemployment rate of
9% in the United States.

00:00:07.730 --> 00:00:10.100
"The mayor of a local town wonders

00:00:10.100 --> 00:00:13.460
"if this national result
holds true for her town,

00:00:13.460 --> 00:00:15.370
"so she plans on taking a sample

00:00:15.370 --> 00:00:18.000
"of her residents to see
if the unemployment rate

00:00:18.000 --> 00:00:21.910
"is significantly different
than 9% in her town.

00:00:21.910 --> 00:00:26.000
"Let P represent the
unemployment rate in her town.

00:00:26.000 --> 00:00:28.480
"Here are the hypotheses she'll use."

00:00:28.480 --> 00:00:30.850
So, her null hypothesis is that,

00:00:30.850 --> 00:00:32.190
hey, the unemployment rate in her town

00:00:32.190 --> 00:00:34.500
is the same as for the country,

00:00:34.500 --> 00:00:36.100
and her alternative hypothesis

00:00:36.100 --> 00:00:37.980
is that it is not the same.

00:00:37.980 --> 00:00:40.020
"Under which of the following conditions

00:00:40.020 --> 00:00:44.320
"would the mayor commit a Type I error?"

00:00:44.320 --> 00:00:46.960
So, pause this video,
and see if you can figure

00:00:46.960 --> 00:00:47.910
it out on your own.

00:00:49.060 --> 00:00:50.570
Now, let's work through this together,

00:00:50.570 --> 00:00:55.320
so let's just remind
ourselves what a Type I

00:00:55.320 --> 00:00:57.470
error even is.

00:00:57.470 --> 00:00:59.900
This is a situation where we reject

00:00:59.900 --> 00:01:03.140
the null hypothesis,
even though it is true.

00:01:03.140 --> 00:01:05.600
Reject null hypothesis,

00:01:05.600 --> 00:01:06.910
even

00:01:06.910 --> 00:01:08.140
though,

00:01:08.140 --> 00:01:12.290
even though our null hypothesis is true.

00:01:12.290 --> 00:01:15.080
And in general, if you're
committing either a Type I

00:01:15.080 --> 00:01:17.810
or a Type II error, you're
doing the wrong thing,

00:01:17.810 --> 00:01:20.470
you're doing something that
somehow contradicts reality,

00:01:20.470 --> 00:01:23.000
even though you didn't intend to.

00:01:23.000 --> 00:01:25.020
And so, in this case,

00:01:25.020 --> 00:01:28.330
that would be rejecting the hypothesis

00:01:28.330 --> 00:01:32.690
that the unemployment
rate is 9% in this town,

00:01:32.690 --> 00:01:35.620
even though it actually
is 9% in this town,

00:01:35.620 --> 00:01:38.300
so let's see which of these
choices match up to that.

00:01:38.300 --> 00:01:40.720
"She concludes the
town's unemployment rate

00:01:40.720 --> 00:01:45.040
"is not 9% when it actually is."

00:01:45.040 --> 00:01:47.210
Yeah, in this situation,

00:01:47.210 --> 00:01:48.990
in order to conclude that
the unemployment rate

00:01:48.990 --> 00:01:52.220
is not 9%, she would have to reject

00:01:52.220 --> 00:01:55.430
the null hypothesis, even
though the null hypothesis

00:01:55.430 --> 00:01:57.520
is actually true, even
though the unemployment rate

00:01:57.520 --> 00:01:59.310
actually is 9%.

00:01:59.310 --> 00:02:01.240
So, I'm liking this choice,

00:02:01.240 --> 00:02:03.610
but let's read the other
ones, just to make sure.

00:02:03.610 --> 00:02:08.200
"She concludes the town's
unemployment rate is not 9%

00:02:08.200 --> 00:02:10.970
"when it actually is not."

00:02:10.970 --> 00:02:12.590
Well, this wouldn't be an error.

00:02:12.590 --> 00:02:15.790
If the null hypothesis isn't true,

00:02:15.790 --> 00:02:17.440
it's not a problem to reject it,

00:02:17.440 --> 00:02:19.320
so this one wouldn't be an error.

00:02:19.320 --> 00:02:23.420
"She concludes the town's
unemployment rate is 9%

00:02:23.420 --> 00:02:25.970
"when it actually is."

00:02:25.970 --> 00:02:28.450
Well, once again, this
would not be an error.

00:02:28.450 --> 00:02:30.360
This would be failing to reject

00:02:30.360 --> 00:02:32.750
the null hypothesis
when the null hypothesis

00:02:32.750 --> 00:02:34.850
is actually true, not an error.

00:02:34.850 --> 00:02:39.590
Choice D, "She concludes the
town's unemployment rate is 9%

00:02:39.590 --> 00:02:42.600
"when it actually is not."

00:02:42.600 --> 00:02:45.130
So, this is a situation where she fails

00:02:45.130 --> 00:02:47.250
to reject the null hypothesis,

00:02:49.480 --> 00:02:51.960
even though the null
hypothesis is not true,

00:02:51.960 --> 00:02:53.050
so this one right over here,

00:02:53.050 --> 00:02:55.270
this one would actually
be, this is an error.

00:02:55.270 --> 00:02:59.530
This is an error, but
this is a Type II error.

00:02:59.530 --> 00:03:00.430
So, one way to think about it,

00:03:00.430 --> 00:03:02.070
first you say, "Okay,
am I making an error?

00:03:02.070 --> 00:03:04.190
"Am I rejecting something that's true,

00:03:04.190 --> 00:03:06.930
"or am I failing to reject
something that's false?"

00:03:06.930 --> 00:03:09.320
And the rejecting something that is true,

00:03:09.320 --> 00:03:12.580
that's Type I, and failing
to reject something

00:03:12.580 --> 00:03:14.360
that is false, that is Type II.

00:03:15.262 --> 00:03:17.970
And so, with that in mind,
let's do another example.

00:03:17.970 --> 00:03:19.960
"A large university is curious

00:03:19.960 --> 00:03:22.460
"if they should build another cafeteria.

00:03:22.460 --> 00:03:24.950
"They plan to survey a
sample of their students

00:03:24.950 --> 00:03:27.180
"to see if there is strong evidence

00:03:27.180 --> 00:03:29.810
"that the proportion
interested in a meal plan

00:03:29.810 --> 00:03:32.890
"is higher than 40%, in which case they

00:03:32.890 --> 00:03:35.720
"will consider building a new cafeteria.

00:03:35.720 --> 00:03:37.480
"Let P represent the proportion

00:03:37.480 --> 00:03:39.860
"of students interested in a meal plan.

00:03:39.860 --> 00:03:43.300
"Here are the hypotheses they'll use."

00:03:43.300 --> 00:03:45.620
So, the null hypothesis is that 40%

00:03:45.620 --> 00:03:47.800
or fewer of the students are interested

00:03:47.800 --> 00:03:50.190
in a meal plan, while the
alternative hypothesis

00:03:50.190 --> 00:03:52.670
is that more than 40% are interested.

00:03:52.670 --> 00:03:54.200
"What would be the consequence

00:03:54.200 --> 00:03:57.690
"of a Type II error in this context?"

00:03:57.690 --> 00:03:59.140
So, once again, pause this video

00:03:59.140 --> 00:04:00.940
and try to answer this for yourself.

00:04:01.800 --> 00:04:02.740
Okay, now let's do it together.

00:04:02.740 --> 00:04:04.980
Let's just remind ourselves
what a Type II error is,

00:04:04.980 --> 00:04:06.140
we just talked about it.

00:04:06.140 --> 00:04:07.480
So, failing,

00:04:08.720 --> 00:04:10.350
failing to

00:04:10.350 --> 00:04:11.600
reject,

00:04:11.600 --> 00:04:14.560
in this case, our null hypothesis,

00:04:16.340 --> 00:04:17.970
even though

00:04:18.810 --> 00:04:20.270
it

00:04:20.270 --> 00:04:21.810
is false.

00:04:22.760 --> 00:04:25.520
So, this would be a scenario
where this is false,

00:04:26.950 --> 00:04:29.180
which would mean that more than 40%

00:04:29.180 --> 00:04:31.090
actually do want a meal plan,

00:04:31.090 --> 00:04:33.080
but you fail to reject this.

00:04:33.080 --> 00:04:34.080
So, what would happen is,

00:04:34.080 --> 00:04:35.870
is that you wouldn't
build another cafeteria

00:04:35.870 --> 00:04:37.790
'cause you'd say, "Hey, no,
there's not that many people

00:04:37.790 --> 00:04:39.950
"who are interested in the meal plan,"

00:04:39.950 --> 00:04:42.170
but you wouldn't, but,
actually there are a lot

00:04:42.170 --> 00:04:43.370
of people who are
interested in the meal plan,

00:04:43.370 --> 00:04:45.870
and so you probably wouldn't
have enough cafeteria space.

00:04:45.870 --> 00:04:47.790
And so, this says, "They
don't consider building

00:04:47.790 --> 00:04:49.740
"a new cafeteria when they should."

00:04:49.740 --> 00:04:51.250
Yeah, this is exactly right.

00:04:52.190 --> 00:04:55.060
"They don't consider
building a new cafeteria

00:04:55.060 --> 00:04:57.360
"when they shouldn't."

00:04:57.360 --> 00:04:59.720
Well, this would just
be a correct conclusion.

00:04:59.720 --> 00:05:02.190
"They consider building a new cafeteria

00:05:02.190 --> 00:05:04.940
"when they shouldn't,"

00:05:04.940 --> 00:05:08.490
and so, this is a scenario
where they do reject

00:05:08.490 --> 00:05:12.560
the null hypothesis, even
though the null hypothesis

00:05:12.560 --> 00:05:16.450
is true, so this right over
here would be a Type I error.

00:05:16.450 --> 00:05:17.580
Type

00:05:17.580 --> 00:05:18.600
I

00:05:18.600 --> 00:05:19.780
error.

00:05:19.780 --> 00:05:22.190
Because if they're considering
building a new cafeteria,

00:05:22.190 --> 00:05:24.420
that means they rejected
the null hypothesis,

00:05:24.420 --> 00:05:25.410
even when they shouldn't.

00:05:25.410 --> 00:05:28.340
That means that the null
hypothesis was true, so Type I.

00:05:28.340 --> 00:05:31.060
"They consider building a new
cafeteria when they should."

00:05:31.060 --> 00:05:32.520
Well, once again, this
wouldn't be an error at all,

00:05:32.520 --> 00:05:33.660
this would be a correct conclusion.

00:05:33.660 --> 00:05:35.960
This one and this one
are correct conclusions.

00:05:37.130 --> 00:05:39.340
A and C are the consequences

00:05:39.340 --> 00:05:42.570
of a Type II and a Type
I error, respectively.