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• William Gosset was an English statistician who worked for the brewery of Guinness.

• He developed different methods for the selection of the best yielding varieties of barleyan

• important ingredient when making beer.

• Gosset found big samples tedious, so he was trying to develop a way to extract small samples

• but still come up with meaningful predictions.

• He was a curious and productive researcher and published a number of papers that are

• still relevant today.

• However, due to the Guinness company policy, he was not allowed to sign the papers with

• his own name.

• Therefore, all of his work was under the pen name: Student.

• Later on, a friend of his and a famous statistician, Ronald Fisher, stepping on the findings of

• Gosset, introduced the t-statistic, and the name that stuck with the corresponding distribution

• even today is Student’s t.

• The Student’s t distribution is one of the biggest breakthroughs in statistics, as it

• allowed inference through small samples with an unknown population variance.

• This setting can be applied to a big part of the statistical problems we face today

• and is an important part of this course.

• Alright, visually, the Student’s t-distribution looks much like a normal distribution but

• generally has fatter tails.

• Fatter tails as you may remember allows for a higher dispersion of variables, as there

• is more uncertainty.

• In the same way that the z-statistic is related to the standard normal distribution, the t-statistic

• is related to the Student’s t distribution.

• The formula that allows us to calculate it is: t with n-1 degrees of freedom and a significance

• level of alpha equals the sample mean minus the population mean, divided by the standard

• error of the sample.

• As you can see, it is very similar to the z-statistic; after all, this is an approximation

• of the normal distribution.

• The last characteristic of the Student’s t-statistic is that there are degrees of freedom.

• Usually, for a sample of n, we have n-1 degrees of freedom.

• So, for a sample of 20 observations, the degrees of freedom are 19.

• Much like the standard normal distribution table, we also have a Student’s t table.

• Here it is.

• The rows indicate different degrees of freedom, abbreviated as d.f., while the columnscommon

• alphas.

• Please note that after the 30th row, the numbers don’t vary that much.

• Actually, after 30 degrees of freedom, the t-statistic table becomes almost the same

• as the z-statistic.

• As the degrees of freedom depend on the sample, in essence, the bigger the sample, the closer

• we get to the actual numbers.

• A common rule of thumb is that for a sample containing more than 50 observations, we use

• the z-table instead of the t-table.

• Alright.

• Great!

• In our next lecture, we will apply our new knowledge in practice!

William Gosset was an English statistician who worked for the brewery of Guinness.

B1 中級

# 学生のT配布 (Student's T Distribution)

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林宜悉 に公開 2021 年 01 月 14 日