Student's T Distribution

Key Takeaways

William Gossett 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 Gossett 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 Gossett introduced the t-statistic and the name that stuck with the corresponding distribution even today is students tea 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 statistical problems we face today and is an important part of this course all right 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 minus 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 students T statistic is that there are degrees of freedom usually for a sample of n we have n minus 1 degrees of freedom so for a sample of 20 observation the degrees of freedom are 19 much like the standard normal distribution table we also have a student's tea table here it is the rows indicate different degrees of freedom abbreviated as DF 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 for more videos like this one please subscribe [Music]