t-test: statistical tests that use the t-distribution and can be called a t–test
1. Two-Sample T-Test (Independent Samples T-Test)
Compare the sample means in two groups
ex: H0: µ1= µ2 vs. Ha:µ1≠ µ2
Do males and females spend the same amount of time on shopping in December?
Assumptions: 1. normal distribution - the observations within each group are normally distributed
2. homoscedasticity - equal variances in the two groups
2. One-Sample T-Test
Compares the sample mean to a theoretical mean
ex. H0: µ=c vs. Ha: µ≠c, where c is a constant
H0: µ≥c vs. Ha: µ<c, where c is a constant
Do people spend c hours on shopping in December?
Assumption: normal distribution - the observations within each group are normally distributed
3. Paired T-Test
A special case of the one-sample t-test. Tests whether there is a difference between the sample means in two groups
ex: µ1= µ2 vs. µ1≠ µ2
Does the recovery time of the treatment group differ from that of the control group?
Assumption: the differences between pairs are normally distributed (not normal distribution in each group)
4. Two-Sample T-Test vs. Paired T-Test
Two-sample t-test is used for independent samples, whereas paired t-test is used for matched pairs.
ex: symptoms of two randomly selected groups - two-sample t-test
symptoms before and after a treatment - paired t-test
