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Between-Groups ANOVA. Chapter 12. When to use an F distribution Working with more than two samples ANOVA Used with two or more nominal independent variables and an interval dependent variable. Why not use multiple t -tests?. The problem of too many t tests Fishing for a finding

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Presentation Transcript
When to use an F distribution
    • Working with more than two samples
    • Used with two or more nominal independent variables and an interval dependent variable
why not use multiple t tests
Why not use multiple t-tests?
  • The problem of too many t tests
    • Fishing for a finding
    • Problem of Type I error
the f distribution
The F Distribution
  • Analyzing variability to compare means
    • F = variance between groups

variance within groups

  • That is, the difference among the sample means divided by the average of the sample variances
types of variance
Types of Variance
  • Between groups: estimate of the population variance based on differences among group means
  • Within groups: estimate of population variance based on differences within (3 or more) sample distributions
check your learning
Check Your Learning
  • If between-groups variance is 8 and within-groups variance is 2, what would F be?
types of anova
Types of ANOVA

One-Way: hypothesis test including one nominal variable with more than two levels and a scale DV

Within-Groups: more than two samples, with the same participants; also called repeated-measures

Between-Groups: more than two samples, with different participants in each sample

assumptions of anovas
Assumptions of ANOVAs

Random selection of samples

Normally distributed sample

Homoscedasticity: samples come from populations with the same variance

one way between groups anova
One-Way Between-Groups ANOVA
  • Everything about ANOVA but the calculations
      • 1. Identify the populations, distribution, and assumptions.
      • 2. State the null and research hypotheses.
      • 3. Determine the characteristics of the comparison distribution.
      • 4. Determine the critical value, or cutoff.
      • 5. Calculate the test statistic.
      • 6. Make a decision.

Step 3. Characteristics

  • What are the degrees of freedom?
    • If there are three levels of the independent variable?
    • If there are a total of 20 participants in each of the three levels?
logic behind the f statistic
Logic behind the F Statistic
  • Quantifies overlap
  • Two ways to estimate population variance
    • Between-groups variability
    • Within-groups variability
the source table
The Source Table
  • Presents important calculations and final results in a consistent, easy-to-read format
bringing it all together
Bringing it All Together
  • What is the ANOVA telling us to do about the null hypothesis?
  • Do we reject or accept the null hypothesis?

An F Distribution

Here the F statistic is 8.27 while the cutoff is 3.86. Do we reject the null hypothesis?

making a decision
Making a Decision

Step 1. Compare the variance (MS) by diving the sum squares by the degrees of freedom.

Step 2. Divide the between-groups MS by the within-groups MS value.

Step 3. Compare the calculated F to the critical F (in Appendix B).

If calculated is bigger than critical, we have a significant difference between means

calculating effect size
Calculating Effect Size

R2 is a common measure of effect size for ANOVAs.

post hoc tests to determine which groups are different
Post-Hoc Tests to Determine Which Groups Are Different
  • When you have three groups, and F is significant, how do you know where the difference(s) are?
    • Tukey HSD
    • Bonferonni
  • A priori (planned) comparisons
tukey hsd test
Tukey HSD Test
  • Widely used post hoc test that uses means and standard error
the bonferroni test
The Bonferroni Test
  • A post-hoc test that provides a more strict critical value for every comparison of means.
  • We use a smaller critical region to make it more difficult to reject the null hypothesis.
    • Determine the number of comparisons we plan to make.
  • Divide the p level by the number of comparisons.