Mean
\begin{align}
\bar x = \frac{\sum_{i=1}^n x_i}{n}
\end{align}

Variance
\begin{align}
\sigma^2 = \frac{\sum_{i=1}^n (\bar x - x_i)^2}{n}
\end{align}

Standard Deviation (Population)
\begin{align}
\sigma = \sqrt{\frac{\sum_{i=1}^n (\bar x - x_i)^2}{n}}
\end{align}

Standard Deviation (Sample)
\begin{align}
s = \sqrt{\frac{\sum_{i=1}^n (\bar x - x_i)^2}{n-1}}
\end{align}

Standard Error
\begin{align}
SE = \frac{\sigma}{\sqrt n}
\end{align}

z-score
\begin{align}
z = \frac{x - \mu}{\sigma}
\end{align}

Margin of error
\begin{align}
ME = Z^* \frac{\sigma}{\sqrt{n}}
\end{align}

Confidence Interval
\begin{align}
CI = \bar x \pm Z^* \frac{\sigma}{\sqrt{n}}
\end{align}

t-stat
\begin{align}
t = \frac{\bar x - \mu}{\frac{\sigma}{\sqrt{n}}}
\end{align}

df
\begin{align}
df = n - 1
\end{align}

Cohen’s d
\begin{align}
d = \frac{\bar x_1 - \bar x_2}{s}
\end{align}

where
\begin{align}
s = \sqrt{\frac{(n_1-1)s_1^2+(n_2-1)s_2^2}{n_1+n_2-2}}
\end{align}

Standard Error
\begin{align}
SE = \sqrt{\frac{S_1^2}{n_1}+\frac{S_2^2}{n_2}}
\end{align}

Pooled Variance
\begin{align}
S_p^2 = \frac{SS_1+SS_2}{df_1+df_2}
\end{align}

New Standard Error
\begin{align}
SE = \sqrt{\frac{S_p^2}{n_1}+\frac{S_p^2}{n_2}}
\end{align}

Percentual de variabilidade
\begin{align}
r^2 = \frac{t^2}{t^2 + df}
\end{align} 

R2 mede a proporção de uma diferença nas médias que pode ser explicada pela variável independente.

O d de Cohen é a medida do tamanho do efeito.



```python

```

16622e84a8a6dbcdc13d17862118a26f0d11c117
ipynb
Jupyter Notebook
Summary.ipynb
tassotirap/data-science-summary
384bd84e25df8e9abb05f20cf9a6e80ab9385751
Apache-2.0
Summary.ipynb
tassotirap/data-science-summary
384bd84e25df8e9abb05f20cf9a6e80ab9385751
Apache-2.0
Summary.ipynb
tassotirap/data-science-summary
384bd84e25df8e9abb05f20cf9a6e80ab9385751
Apache-2.0
Qwen/Qwen-72B
1. YES
2. YES