Math help in statistics please?

Question

A two sample t test is being conducted with 10 observations in the first and 9 observation in the second sample. What is the number of degrees of freedom for the test statistic?

a. 18

b. 17

c. 37

d. 38

Answer 1

Degrees of freedom is a measure of the sample size with regards to the computation of the standard deviation.  To compute the standard deviation you collect the sum of the variance between each data point and the average value of that data set.  Thus, in the computation of the standard deviation of one data set you use up one degree - and the degrees of freedom for that test is n-1.  Each test will have a degree of freedom of n-1 independently of one another (because you have two sets of data being sampled independently, you will have two different averages and two of your "degrees" will have been used up in your calculation of the standard deviation).  Degrees are simply the amount of data points in your data set (n).

Also, another fun fact, the man who created the Student t distribution was William Gosset, and he worked for Guinness Brewers in Ireland.  Guinness employees weren't allowed to publish research under their own names, so he published it under A. Student.  Hope that gets you extra credit or something.