Stats Ch. 13 - One-Way Within-Subjects (Repeated-Measures) Design

within-subjects design

observe the same participants at each level of one factor with two or more levels

one-way within-subjects (or repeated measures) ANOVA

a statistical procedure used to test hypotheses for one factor with two or more levels concerning the variance among group means

when the same participants are observed as each level of a factor and the variance in any one population is unknown

when to use one-way within-subjects ANOVA?

within-subjects design

n subjects are observed k times

selected from a single population and are observed as each level of one factor

how are participants selected in a within-subjects design?

1. between-groups variation
2. between-persons variation
3. within-groups variation

3 sources of variation in one-way within-subjects ANOVA

between-groups variation

variability attributed to difference b/w group means

between-persons variation

variability attributed to differences b/w person means averaged across groups

within-groups variation

variability associated with differences in participant scores in each group (denominator)

1. between-persons variation
2. within-groups variation

two sources of error using the one-way within-subjects ANOVA

-same participants observed in each group
-individual differences in participant characteristics are same in each group - bc same part. in each group
-can assume any differences in characteristics of part. across groups are same
-so b/w-persons variation can be removed from error term in denominator of stat
-leaves within-groups variation as error term in denominator of stat

error variation in one-way within-subjects ANOVA

split into 3 calculations: one for each variation
1. between-groups variation: dfBG = k-1
2. between-persons variation: dfBP = n-1
3. within-groups variation: dfE = (k-1)(n-1)

The df for the one-way within-subjects ANOVA are what?

1. normality - the population sampled is normally distributed, especially for small sample sizes

2. independence within groups - participants w/in groups are independently observed, not b/w groups

3. homogeneity of variance - variance in each pop. is equal to that of the others

4. homogeneity of covariance - participant scores in each group are related bc same part. observed in each groups

4 assumptions for one-way within-subjects ANOVA

Sphericity

the assumptions of homogeneity of variance and homogeneity of covariance

likelihood of committing a Type I error will increase

what happens if we violate sphericity?

use four steps of hypothesis testing to conduct one-way within-subjects ANOVA:

1. state H0 and H1

-H0: group means will not vary in the pop.

-H1: group means in the pop. do vary

2. set the criteria for a decision: level of sig .05; refer to F table to find critical values (need df for b/w-groups, b/w-persons, error)

3. compute test statistic:

4. make decision: compare obtained value to crit. value to make decision to retain or reject the H0

what do you do after the 4 one-way within-subjects ANOVA assumptions are met?

reject H0

the group means in at least one pair significantly differ

compute post hoc test

the group means in at least one pair significantly differ from one another but we do not know which pair or pairs of means differ. how do we determine which pair or pairs of means differ?

experimentwise alpha

post hoc tests control for what?

Bonferroni procedure

post hoc test for within-subjects design

Bonferroni post hoc test

adjusts the alpha level for each test called testwise alpha like the experimentwise alpha

compute partial proportion of variance

how do we determine the size of an effect in the population in a within-subjects design?

partial proportion of variance

variance in the dependent variable that can be accounted for by levels of the factor

1. partial eta-squared
2. partial omega-squared

two measures of partial proportion of variance

participant responding is consistent b/w groups

the one-way within-subjects ANOVA has greater power than a one-way b/w-subjects ANOVA only when what?

consistency

extent to which a dependent variable changes in a predictable pattern across groups

1. test statistic
2. df
3. p-value
4. effect size for significant analyses
5. means, standard error or SDs
6. identify which post hoc test used and p-value for sig results

What to include in reports for a paired samples t test?