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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.


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B1 中級

學生的T分佈 (Student's T Distribution)

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    林宜悉 發佈於 2021 年 01 月 14 日