comparing means: introduction to t tests

Answer 1

t statistic compared against t distribution

Question 2

what is the t distribution

Answer 2

represents the mean of all possible samples with a given sample size

if the population mean is 5, SD is 1, and you are sampling 100 people at a time ,most of the averages will be close to 5, but some will be far off by chance

Question 3

what is significance

Answer 3

amount of area right of the score in the right tail

tells us how likely it is chance could produce the results

Question 4

two sample t test: null and alternative hypotheses

Answer 4

H0: two population means are not different

H1 two population means are different from each other

Question 5

how do we calculate the t statistic

Answer 5

we calculate the t statistic based on means and standard deviations of each sample, and then find the p-value from how much that t statistic cuts off in the tails of the t distribution

Question 6

what are the assumptions of the t test

Answer 6

independence - each PP only included once

normality - data is normally distributed

homogeneity of variance - both groups should share the same standard deviation

Question 7

why was the t test introduced

Answer 7

t test introduced as a statistical test to deal with small samples