Everything T-Tests
One-Sample T-Tests
➔very similar to steps to z-tests
➔use when you’re given population mean but not population SD
◆ working with population mean, sample mean, and sample SD
➔formula:
◆ (sample mean - population mean) / sample standard deviation
➔the critical values change as the sample size changes
◆ not static like z-test
◆ the critical value is based on the degree of freedom (n-1)
◆ as sample size increases, the t-distribution starts approaching a normal distribution (as it
starts out more platykurtic)
● larger sample size = less variability within sampling distribution
➔you would read a t-table based on the kind of test you do (one-tail vs two-tail) and the alpha
criterion used (i.e. .05)
➔assumptions(diagnosing the data)
◆ dependent variable isnormally distributed
◆ theobservations within the sample are independentfrom each other
◆ no outliers+/- 4 SD
➔effect size
◆ d = (sample mean - population mean) / sample SD
Independent-Samples T-Test
➔when comparing two groups but population parameters (pop. mean and pop. SD) are not
available
➔formula
◆ t = difference of means / √s2/n + s2/n
● even n
◆ t = difference of means / pooled variance
● uneven n
➔use N-2 for degrees of freedom
◆ because you’re accounting for 2 samples
◆ N is also the total number, so both the samples combined
➔effect size:
One-Sample T-Tests
➔very similar to steps to z-tests
➔use when you’re given population mean but not population SD
◆ working with population mean, sample mean, and sample SD
➔formula:
◆ (sample mean - population mean) / sample standard deviation
➔the critical values change as the sample size changes
◆ not static like z-test
◆ the critical value is based on the degree of freedom (n-1)
◆ as sample size increases, the t-distribution starts approaching a normal distribution (as it
starts out more platykurtic)
● larger sample size = less variability within sampling distribution
➔you would read a t-table based on the kind of test you do (one-tail vs two-tail) and the alpha
criterion used (i.e. .05)
➔assumptions(diagnosing the data)
◆ dependent variable isnormally distributed
◆ theobservations within the sample are independentfrom each other
◆ no outliers+/- 4 SD
➔effect size
◆ d = (sample mean - population mean) / sample SD
Independent-Samples T-Test
➔when comparing two groups but population parameters (pop. mean and pop. SD) are not
available
➔formula
◆ t = difference of means / √s2/n + s2/n
● even n
◆ t = difference of means / pooled variance
● uneven n
➔use N-2 for degrees of freedom
◆ because you’re accounting for 2 samples
◆ N is also the total number, so both the samples combined
➔effect size:
