ANOVA (
F-tests)
T-Test Limitations
➔t-tests may be fun (😀) but they have a fewlimitations,3 to be exact
◆ can only comparetwo group meansat a time
◆ can only analyzeone independent variableat a time
◆ conducting too many testsincreases the Type 1errorrate
➔to combat these limitations, we conductANOVAs
◆ theanalysis of variance
◆ essentially a t-test that’s been expanded to hold more than 2 groups of variables at a time
What Can ANOVA Do?
➔comparetwo or more groupsat a time
➔analyzeone or more independent variablessimultaneously
➔test forinteractionsbetween independent variables
➔controls for type 1 error rate
➔the ANOVA uses thef statistic
◆ F = t2
Assumptions
➔same as the ones used for independent samples t-tests as they’re equivalent tests
➔the data/observations areindependent
➔assume theDV is normally distributedforall groups
➔assume that thevariances are homogenousacrossallgroups
➔no outliersbeyond +/- 4sd in all groups
Logic of Using ANOVA
➔thepurposeof collecting samples is toestimate thepopulations parameters from sample
statistics
➔two ways of estimating population variance
◆ error estimate(σ2e) -within group variance
● the variance found within samples
◆ treatment estimate(σ2t) -between group variance
F-tests)
T-Test Limitations
➔t-tests may be fun (😀) but they have a fewlimitations,3 to be exact
◆ can only comparetwo group meansat a time
◆ can only analyzeone independent variableat a time
◆ conducting too many testsincreases the Type 1errorrate
➔to combat these limitations, we conductANOVAs
◆ theanalysis of variance
◆ essentially a t-test that’s been expanded to hold more than 2 groups of variables at a time
What Can ANOVA Do?
➔comparetwo or more groupsat a time
➔analyzeone or more independent variablessimultaneously
➔test forinteractionsbetween independent variables
➔controls for type 1 error rate
➔the ANOVA uses thef statistic
◆ F = t2
Assumptions
➔same as the ones used for independent samples t-tests as they’re equivalent tests
➔the data/observations areindependent
➔assume theDV is normally distributedforall groups
➔assume that thevariances are homogenousacrossallgroups
➔no outliersbeyond +/- 4sd in all groups
Logic of Using ANOVA
➔thepurposeof collecting samples is toestimate thepopulations parameters from sample
statistics
➔two ways of estimating population variance
◆ error estimate(σ2e) -within group variance
● the variance found within samples
◆ treatment estimate(σ2t) -between group variance
