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Inferential statistics

How do we know whether group differences are big enough? Used to test hypothesis about data and to draw conclusions about reliability and generalizability of findings (t-tests, ANOVAs, chi-square)

Scores differ for two reasons

-Variation between groups (good)

-Variation within groups (bad)

-We want big variation between groups relative to variation within groups

-Variation within groups (bad)

-We want big variation between groups relative to variation within groups

How inferential statistics work

-estimate variation within groups and between groups

-estimate how much the groups differ by chance alone (use critical values)

-determine whether your group differences are larger than the difference expected by chance alone

-estimate how much the groups differ by chance alone (use critical values)

-determine whether your group differences are larger than the difference expected by chance alone

P-values

-an estimate of the probability that your effect (group differences) is due to chance alone

-arbitrary cut-off 0.5 (5% probability is due to chance, that is a fluke)

-arbitrary cut-off 0.5 (5% probability is due to chance, that is a fluke)

T-tests for 2-group designs: statistical difference: sample size

-typically for experiments & quasi-experiments

-compares the mean difference between 2 groups to variation within each group

-compares the mean difference between 2 groups to variation within each group

Effect size measures

-(cohen's d, eta-squared)

-important in eliminating the influence of sample size

-important in eliminating the influence of sample size

Designs with 3 or more groups (1 IV)

-Type 1 error

-alpha level (5% probability of type 1 error)

-the chance the test will show an effect when none exists

-Type 2 error

-beta level (20% probability of type 2 error)

-the chance the test will not show an effect when one does exist

-alpha level (5% probability of type 1 error)

-the chance the test will show an effect when none exists

-Type 2 error

-beta level (20% probability of type 2 error)

-the chance the test will not show an effect when one does exist

Alpha inflation

as we conduct more and more statistical tests, the chance of a Type 1 error increases across the entire collection of tests

One-way ANOVA

-omnibus tests - checks to see if there is any difference between groups

-F statistic - life the t-test

-if one-way ANOVA is significant

-F statistic - life the t-test

-if one-way ANOVA is significant