Multiple Comparison Tests and ANOVA Analysis

ANOVA

Analysis of variance for comparing means.

Null hypothesis

Assumes no difference between group means.

Alternate hypothesis

Indicates at least one mean differs.

Significant F

Indicates at least one mean differs.

Multiple comparison tests

Post hoc tests for pairwise mean comparisons.

Post hoc tests

Conducted after ANOVA to explore differences.

Tukey's HSD test

Honestly significant difference for multiple comparisons.

John Tukey

Statistician who developed Tukey's HSD test.

Type I error

Incorrectly rejecting a true null hypothesis.

Type II error

Failing to reject a false null hypothesis.

Placebo

Control treatment with no active ingredient.

Mean driving ability

Average driving scores across treatment groups.

Degrees of freedom (df)

Number of independent values in a calculation.

HSD value

Critical value for Tukey's HSD test.

Effect size (ω²)

Measure of variance explained by treatment.

Significant difference

Difference exceeding critical HSD value.

Common superscripts

Indicate no significant difference between groups.

Absolute difference

Numerical difference between two means.

Mean (M)

Average of a set of values.

Standard deviation (SD)

Measure of data dispersion around the mean.

Computation of Tukey's HSD

Calculating HSD using q and MSW.

Experimentwise error

Cumulative probability of Type I error across tests.

Replication

Repetition of study for validation.

Control Group

Group with no guidance on exam preparation.

Study Group

Group receiving study guidance for exams.

Exam Group

Group receiving exam writing guidance.

Mean Score

Average performance score across groups.

Ho (Null Hypothesis)

Assumes no difference in group means.

Ha (Alternative Hypothesis)

At least one group mean is different.

MSB (Mean Square Between)

Variance among group means calculated.

MSW (Mean Square Within)

Variance within groups calculated.

Degrees of Freedom Total

Total cases minus one; df=29.

Degrees of Freedom Between

Number of groups minus one; df=2.

Degrees of Freedom Within

Total df minus between df; df=27.

F-Statistic

Ratio of MSB to MSW; F=3.63.

F-critical Value

Threshold to compare against F-calc; F=3.35.

Reject Ho

Decision made when F-calc exceeds F-critical.

ANOVA Table

Summarizes variance sources and statistics.

Effect Size (ω²)

Measures strength of group differences; ω²=0.15.

Tukey's HSD Test

Post-hoc test for multiple comparisons.

q Value

Critical value from Tukey's table; q=3.53.

HSD (Honestly Significant Difference)

Minimum difference to declare significance.

Absolute Difference

Difference in means between groups.

Significant Effect

Advice type significantly influenced exam performance.

Presentation of Results

Visual representation of mean test scores.

F-test

Statistical test for comparing variances.

Significant F

Indicates at least one group mean differs.

Multiple comparison tests

Post hoc tests after significant ANOVA results.

Tukey's HSD test

Used for comparing means across groups.

ANOVA

Analysis of variance for comparing multiple groups.

Within-subjects design

Same subjects tested under all conditions.

Between-subjects design

Different subjects tested under different conditions.

Null hypothesis

Assumes no effect or difference exists.

Alternate hypothesis

Assumes an effect or difference exists.

Degrees of freedom (d.f.)

Number of independent values in a calculation.

MSB

Mean square between groups in ANOVA.

MSW

Mean square within groups in ANOVA.

Q statistic

Used in Tukey's HSD for mean comparisons.

Critical t table

Table for determining t-test significance.

Critical F table

Table for determining ANOVA significance.

Pooled variance

Combined variance estimate from multiple samples.

Effect size

Quantifies the magnitude of a treatment effect.

Anxiety rating scale

Scale from 1 (no anxiety) to 10 (high anxiety).

Practice problem set

Exercises to prepare for midterm calculations.

Jamovi

Statistical software for data analysis.

Reporting decimal answers

Final answers should be to two decimal places.

Compelling reason

Justification for choosing an alternative test.

Random selection

Participants chosen randomly for study conditions.

Meditation intervention

Treatment involving meditation to assess anxiety effects.

Anxiety differences

Variations in anxiety ratings between meditation conditions.