text: Ttest - Below is an excerpt from Harris D.C Exploring Chemical Analysis,Freeman New York 1997 60 concerning significance testing and how it is done
  Ttest - Below is an excerpt from Harris D.C Exploring...
  Unformatted text preview: Below is an excerpt from Harris, D.C-, Exploring Chemical Analysis,Freeman, New York, 1997, 60 concerning significance testing and how it is done. Grams of nitrogen-rich gas isolated by Lord Rayleigh From chemical From air decomposition 2.310 1'? 2.301 43 2.309 86 2.298 90 2.310 10 2.298 16 2.310 01 2.301 82 2.310 24 2.298 69 2.310 10 2.299 40 2.310 28 2.298 49 — 2.298 89 Average 2.310 109 2.299 472 Standard deviation 0.000 143 0.001 379 60 Comparison of Means with Student's t Student's t is also used to compare two sets of measurements to decide whether they are "the same" or "different." We adopt the following standard: If there is less than 1 chance in 20 that the-difference between the two measurements arises from random variation in the data, then the difference is significant. This criterion gives us 95% confidence in concluding that two measurements are the same or different. There is a 5% probability that our conclusion is wrong. An example comes from the work of Lord Rayleigh (John W. Strutt), who received the Nobel Prize in 1904 for discovering the inert gas argon—a discovery that came about when he noticed a discrepancy between two sets of measurements of the density of nitrogen. In Rayleigh's time, it was known that dry air is composed of about one—fifth oxygen and four—fifths nitrogen. Rayleigh removed 02 from air by reaction with red—hot copper (Cu(s) + %Og(g) -—> CuO(s)) and measured the den- sity of the remaining gas by collecting it in a fixed volume at a constant tempera— ture and pressure. He then prepared the same volume of nitrogen by decomposition of nitrous oxide (N20), nitric oxide (NO), or ammonium nitrite [NI-Iii~ N 05 ). Table 4-3 and Figure 4—4 show the mass of gas collected in each experiment. The average mass from air was 0.46% greater than the average mass of the same volume of gas from chemical sources. If Rayleigh's measurements had not been performed with care, a 0.46% differ- ence might have been attributed to experimental error. Instead, Rayleigh understood that the discrepancy was outside his margin of error, and he postulated that nitrogen from the air was mixed with a heavier gas, which turned out to be argon. ...