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 barley – an 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 columns – common 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!

thx for the explanation. it helped!

I liked the way how it was presented!

Great!

I missed one lecture, and I was like why are you keep talking about our T distribution, Professor?

I used this in my statistics paper, all credited, thank you very much for helping me understand it.

Hey everyone, check out our super-informative webinar “Data Science for Beginners”! It’s free and places are limited, so don’t miss out! Save your spot today here: http://bit.ly/2YqhPeD

Hope to see you there!