PSYC 1010 - Final Exam Review - Unit 6 - Part 2

Understanding ANOVA and F-tests

• When F = 1.00 in an ANOVA test, there is no evidence that group means differ more than chance, indicated by MSbetween ≈ MSwithin.
• Violating the homogeneity of variance assumption in ANOVA, where group variances are extremely different, can distort F
• In a one-way ANOVA, "one-way" refers to one factor (independent variable), regardless of its levels.
• Larger MSbetween leads to a greater F-ratio

Interpreting F-Ratios and Hypothesis Testing

• If Fobtained (7.99) > Fcritical (2.69), you reject H₀ at α = 0.05.

ANOVA vs T-tests

• Conducting multiple t-tests instead of ANOVA increases the familywise Type I error rate; ANOVA avoids this by testing all groups simultaneously.
• Running post-hoc tests without adjusting α increases Type I error, leading to more false positives.

Sum of Squares Between (SSbetween)

• SSbetween, measures the variability due to group membership
• A high F-ratio in ANOVA is likely when between-group variance is large relative to within-group variance (Large MSbetween, small MSwithin).

Mean Squares Within (MSwithin)

• Increasing the number of participants per group (n) while keeping the number of groups (k) constant makes MSwithin more stable and may decrease it; more participants reduce error variability.
• MSwithin reflects random variability within each group and estimates error variance.

F value

• The F value is always positive because it's a ratio of two variances, so it cannot be negative, because variances are always ≥ 0.
• if group means are nearly identical, the F value gets closer to 1 because little between-group difference results in MSbetween ≈ MSwithin.

Post Hoc Tests

• Post-hoc tests are conducted only after a significant F-test to locate where group differences exist.

Factors

• In a study comparing taste across juice types, juice type is the factor (independent variable).

ANOVA Assumptions

• Violating homogeneity of variance in ANOVA risks an inaccurate or inflated F value, since unequal variances across groups violate core assumptions.

Degrees of Freedom

• If ANOVA output reports F(2, 27), dfbetween = 2 and dfwithin = 27; this indicates 3 groups (2 dfbetween) and a total of 30 participants (30 total - 3 = 27 dfwithin).
• dfbetween = k - 1, where k is the number of groups.
• dfwithin is used to calculate MSwithin, where MSwithin = SSwithin ÷ dfwithin.

Grand Mean

• The grand mean in ANOVA represents the average of all scores across all groups.

Detecting True Effects

• More participants per group increases the likelihood of detecting a true effect in ANOVA because a bigger n leads to lower standard error and more power.

Fcritical Value

• The Fcritical value sets the boundary for statistical significance; if F > Fcritical, reject H₀.

Interpreting ANOVA Results

• With F(2, 27) = 5.5, p = .01, at least one therapy differs in effect, but ANOVA does not tell you where or between which groups.

ANOVA Test Requirements

• ANOVA requires a minimum of 3 groups; with 2 means, use a t-test.

Post-Hoc Comparisons

• After a significant ANOVA result, use Bonferroni-corrected t-tests for post-hoc pairwise comparisons.

Statistical Significance

• If a study finds F = 2.89, p = .07, the conclusion at α = .05 is to fail to reject H₀ because p > .05, which means results are not statistically significant.

Factors Affecting dfbetween

• The number of groups (k) affects dfbetween.
• High variability among group means causes MSbetween to be large, where bigger spread between group means increases SSbetween.
• ANOVA tests all group differences in one test, keeping α fixed, providing a main advantage over repeated t-tests.