ANOVA and Post Hoc

ANOVA

technique used to examine differences between two or more groups

outcome for ANOVA

a numerical value for the F-Statistic

what does calculated F- ratio indicates 

the extent to which group means differ 

what does the calculated F-ratio take into account 

the variability within the groups

For ANOVA when is the null hypothesis rejected 

when the analysis yields a smaller p value than the α set for the study

what is obtaining an F-ratio as large as the obtained value in a given sample determined 

calculating the p value 

If the p value is greater than the level of significance set for the study or alpha 0.05…

than the results are nonsignificant and the F-ratio will be less than the critical values for F in the statistical table

If the results are nonsignificant

the researcher will accept the null hypothesis of no significant differences between the groups

what is One-Way ANOVA (simplest) used to analyze

data in studies with one independent variable and one dependent variable

what is Repeated-Measures ANOVA used to analyze

data from studies where the same variable(s) isrepeatedly measured over time on a group or group of subject

what is repeated-measures ANOVA used to determine

the change that occurs over time in the dependent variable(s) with exposure to the independent or intervention variables

ANOVA assumptions

1. The populations from which the samples were drawn (or the random samples) are normally distributed

2. The groups should be mutually exclusive

3. The groups should have equal variance (homogeneity)

4. The observations are independent

5. The dependent variable is measured at the interval or ratio level

ANOVA group DOF

k-1 (# of groups -1)

error DOF 

# of participants – k

• k= number of groups

F

statisitc for ANOVA

p

indicates the significance of the F-ratio in the study

what is the post hoc analysis developed to determine

where the differences lie, because some of the groups might be different and others might be similar

frequently used post hoc analysis

Newman-Keuls, Tukey, Scheffe, Dunnett

The alpha level is reduced in proportion to the number 

of additional tests required to locate the statistically significant differences

as the alpha level is decreased 

reaching the level of significance becomes increasingly more difficult

Newman-Keuls

compares all possible pairs of means

what type of test is newman-keuls 

the most liberal test (α is not as severely decreased)

Tukey HSD

computes one value with which all means within the data set are compared

how is Tukey HSD different than newman-keuls

more stringent

what does Tukey HSD require

approximately equal sample sizes in each group

what type od test is Scheffe

most conservative test

scheffe

with a decrease in the type I error there is an increase in the type II error (saying something is not significant when it is)

what does dunnet require

a control group

dunnett experimental groups

are compared with the control group without a decrease in α

ANOVA independent variable

active or attributional

ANOVA F staistic formula 

F = Mean Square Between Groups/ Mean Square Within Groups

• mean square can be interchangeable with variance

what does mean square/ variance between groups represents

differences between the groups/conditions being compared

what does mean square/ variance within groups represents

differences among/ within each groups data

how to calculate ANOVA

Step 1: compute the correction term: C

Step 2: Compute the total sum of squares and subtract C

Step 3: Compute between groups sum of squares

Step 4: Compute within groups sum of squares (subtract the between groups sum of squares (step 3) from total sum of squares (step 2)

Step 5: Create ANOVA Summary Table

Step 6: Locate the critical F value on the F distribution table (see Appendix C) and compare it to our obtained F

C

Square the grand sum (G) and divide by total N

Compute between groups sum of squares

Square the sum of each column, then divide by N; add each of the sums then subtract C

Mean square between groups dof

# groups – 1

Mean square within groups dof

N = # of groups