ANOVA, Post Hoc, Chi Square

ANOVA

Examines differences in 3+ groups with repeated measures

Calculated F-Ratio (ANOVA)

Indicates the extent to which group means differ taking into account the variability within the groups

Does the result of an ANOVA test tell us WHERE the difference is or IF there is a difference?

Tells us IF there is a difference

P Value > 0.05 

Insignificant 

If the results are insignificant, what does the researcher do to the null hypothesis: ACCEPT/DENY?

Accepts Null Hypothesis

One-Way ANOVA (Simplest)

1 Independent Variable, 1 Dependent Variable

Repeated ANOVA

Same variable(s) are repeatedly measured over time (determines the change that occurs in the dependent variable with exposure to independent variable) 

ANOVA Assumptions

1. Randomly Sampled + Normally Distributed

2. Mutually Exclusive

3. Equal Variance (Homogeneity)

4. Indepdent Observations

5. DV = Interval/Ratio

Statistic for ANOVA

F

Group Degrees of Freedom (ANOVA)

(# of Groups - 1)

Error Degrees of Freedom (ANOVA)

(# of Participants - # of Groups)

What does P indicate in an ANOVA?

Significance of F-Ratio

Post Hoc Analyses

Developed to determine WHERE the differences lie (example: using a experimental, placebo, and comparison group)

What happens to the alpha level in a post hoc analyses when trying to locate the statistically significant difference?

Reduces/decreases in proportion to the number of additional tests required

As the alpha value level is decreased, reaching the level of significance becomes

Increasingly more difficult

Newman-Keuls

Compares ALL possible pairs of means and is the most liberal (alpha value is not as severely decreased)

Tukey HSD

Computes 1 value with which all means within the data set are compared: requires approximately equal sample sizes in each group (more stringent than Newman)

Dunnett

Requires a control group: the experimental groups are compared with the control group without a decrease in alpha

ANOVA Research Designs

1. Randomized Experimental

2. Quasi-Experimental

3. Comparative Design

Independent Variable in ANOVA

Active or Attributional

ANOVA (F) Formula

F = (Variance Between Groups) ÷ (Variance Within Groups)

What does the between groups variance represent?

Difference between the groups/conditions being compared

What does the within groups variance represent?

Differences among/within each group’s data

Pearson Chi-Square

Inferential statistical test to examine differences among groups with variables measure at the nominal level 

Pearson Chi-Square Statistic 

X²

Pearson-Chi Square Assumptions

Nominal level, adequate sample size, independent observations

What does Pearson-Chi Square compare?

Compares the frequencies that are observed with the frequencies that are expected (Calculated X² values are compared with the critical X² values)

If the result is greater than or equal to the value in the table… (Pearson-Chi Square)

Significant differences exist and thus the null hypothesis is rejected

Pearson Chi-Square Degrees of Freedom

(Rows - 1) (Columns - 1)
Example: In a 2×2 table → (2 - 1) (2 - 1) = 1

Pearson Chi-Square Research Design

Randomized experimental, quasi-experimental, comparative design

Pearson Chi-Square Variables

Active and/or Attributional

One Way X²

Statistic that only compares different levels of 1 variable only 

Two Way X²

Statistic that tests whether proportions in levels of 1 nominal variable are significantly different from proportions of the second nominal variable

What analysis determines the location of the difference?

Post Hoc Analysis

What is the weaker statistical test used? (The results are only reported if statistically significant results were found)

Pearson Chi Square (X²)

Pearson Chi-Square Requirements

1 data entry made for each subject, nominal level, mutually exclusive and exhaustive, sensitive to small sample sizes and other tests