Analysis of variance John W Worley Audio Group

Analysis of variance John W. Worley Audio. Group, WCL Department of Electrical and Computer Engineering University of Patras, Greece http: //www. wcl. ee. upatras. gr/Audio. Group/

Hypothesis Null Hyp. (H 0) Exp. Hyp. (H 1) Experiment I. V. Data Nominal Type I Ordinal Interval Analysis Ratio Type II Modify Hyp. Slide 2 of 25

Data Analysis · Descriptive • Mean. • Standard error the mean (SEM). · Inferential statistics • t-test. – Related-means t-test. – Independent-means t-test. Univariate Analysis of Variance (ANOVA). · Multivariate ANOVA (MANOVA). · Slide 3 of 25

Small Variance µ 1 µ 2 Variance Slide 4 of 25

Large Variance µ 1 µ 2 Variance Slide 5 of 25

Small Variance µ 1 µ 2 P < 0. 05 Slide 6 of 25

Large Variance µ 1 µ 2 P > 0. 05 Slide 7 of 25

Errors in statistical decisions · Type I error: • Rejecting Null Hyp. when it’s true. · Type II error: • Retaining Null Hyp. when its false. Slide 8 of 25

Factorial design: Definitions · Factor is a categorical predictor variable • e. g. A treatment. · Level is amount of the factor. • e. g. the amount of treatment. · One-way ANOVA • One factor, multiple levels. · Two-way ANOVA • Two factors, different levels within the factors. Slide 9 of 25

ANOVA: Assumptions · Normal distributed data. • Histogram • Kolmogorov-Smirnov test • Shapiro-Wilk test Interval or ratio data. · Independence. · Homogeneity of variance. · • Levens test Slide 10 of 25

One-way, Between-Subjects Design: - One between groups factor (with 2 levels). Mnemonic aid YES Levels of Factor Mnemonic NO n 1 n 2 Subjects nn Slide 11 of 25

One-way, Within-subjects Design: - One within groups factor (with 3 levels) Memory recall with practise Day-1 Day-2 Levels of Factor Time Day-3 n 1 n 2 Subjects nn Slide 12 of 25

Mixed Design: - One between groups factor (with 2 levels). - One within groups factor (with 3 levels) Mnemonic aid YES Day-1 Day-2 Day-3 NO Levels of Factors Mnemonic Levels of Factors Time Day-1 Day-2 Day-3 n 1 n 2 Subjects nn Slide 13 of 25

Variable Interaction Story recall is improved by mnemonic aid and practice, with no interaction. · An interaction, practice has a greater effect upon recall with a mnemonic aid. · Slide 14 of 25

Post-hoc tests · Least-significant difference (LSD) pairwise comparison. • No Type I error control. · Studentized Newman-Keuls (SNK). • Liberal, no Type I error control. · Bonferroni Method. • Controls Type I error • Good when comparisons small. · Tukey Test • Controls Type I error • Good when comparisons large. Slide 15 of 25

MANOVA Memory recall with practise Levels of Factor Time Day-1 Day-2 Day-3 Confidence Comprehension n 1 Recall n 2 Subjects nn Slide 16 of 25

Multivariate analysis of variance (MANOVA) 2 -stage test · For more than one DV. · Avoids Type I error, with multiple ANOVA’s. · Detects differences among a combination of variables · Slide 17 of 25

MANOVA: Pre-requisites. · What DV’s: • Correlations*. • Discriminate function variates. · Assumptions: - Independence. Random sampling. Interval data Multivariate normality Equality of covariance F Leven’s test F Box’s test *Cole et al (1994) Psych. Bulletin, 115(3), 465 -474. Slide 18 of 25

MANOVA: Output Pillai-Bartlett Trace (V). · Wilk’s Lamda (Λ). · Hotelling’s T 2. · Roy’s Largest Root. · Slide 19 of 25

Distributions leptokurtic platykurtic Slide 20 of 25

MANOVA: Output Pillai-Bartlett Trace (V). · Wilk’s Lamda (Λ). · Hotelling’s T 2. · Roy’s Largest Root. · Slide 21 of 25

MANOVA: Follow-up analysis · If MANOVA sig. FANOVA • Type I error – Bonferroni correction FDiscriminant analysis Slide 22 of 25

Practical Considerations · Controls - Standardisation. F Instructions Practise/fatigue effects F Counterbalance conditions. F Randomise trial order. Within- or Between-subjects design? · For MANOVA: · - Choose DV’s theoretically Do Follow-up analysis. Experimentwise errors Slide 23 of 25

Conclusions · · · Identify your DV type. Within- or Between-subjects design. Control for everything. Report descriptive and inferential statistics. ANOVA is highly useful. MANOVA is logical progression. Follow-up analysis. F Bonferroni correction. F Slide 24 of 25

Audio. Group, WCL Department of Electrical and Computer Engineering University of Patras, Greece http: //www. wcl. ee. upatras. gr/Audio. Group/