That is, the variance of the sampling distribution of the mean is the population variance divided by N, the sample size (the number of scores used to compute a mean). The standard error of the mean is the standard deviation of the sampling distribution of the mean.
Consequently, what is the Student t distribution used for?
Student's t Distribution. The t distribution (aka, Student's t-distribution) is a probability distribution that is used to estimate population parameters when the sample size is small and/or when the population variance is unknown.
What is the distribution of F?
The F distribution is a right-skewed distribution used most commonly in Analysis of Variance. When referencing the F distribution, the numerator degrees of freedom are always given first, as switching the order of degrees of freedom changes the distribution (e.g., F(10,12) does not equal F(12,10) ).
Why do they call it the Student's t distribution?
The t distributions were discovered by William S. Gosset in 1908. Gosset was a statistician employed by the Guinness brewing company which had stipulated that he not publish under his own name. He therefore wrote under the pen name ``Student.''