## Statistics & Methods Centre - (M)AN(C)OVA models

Analysis-of-variance (ANOVA) models belong to the family of general linear models with one or more response (dependent) variables and at least one (multi-)categorical predictor or factor. Factorial analysis-of-variance models are models with more than one categorial predictor. Multivariate ANOVA models have several response variables, ANCOVA models have at least one numerical and one categorical predictor. In Repeated measures ANOVA subjects are measured on more than once on the same response variable, a situation which typically arises in longitudinal studies.
Detailed information on the tests is contained in the books mentioned.

One-way analysis-of-variance models - ANOVA
Moore & McCabe, Chapter 12: One-way analysis of variance;
Field, Chapter 10: Comparing several means: ANOVA (GLM 1)
Effect sizes: Field, Chapter 10, section: 10.5
Field, Chapter 10, 12, 13; later sections of these chapters
Software
Means and st. deviations:
SPSS => Analyze => Univariate => Options => Descriptive
One-way ANOVA:
SPSS => Analyze => Compare Means => One-Way ANOVA
Effect sizes:
SPSS => Analyze => General Linear Model => Options => Estimate effect size
Reporting analysis of variance in publications
The results of an One-way ANOVA are reported with between brackets the appropriate degrees-of-freedom of first the between sum-of-squares and then the within sum-of-squares, the value of the F-statistic in two decimals (F(dfbetween,dfwithin), followed by the descriptive level of significance (p). Also report effect sizes (mostly partial eta-squared), and if appropriate post-hoc comparisons.
Example: A statistically significant main effect for treatments was observed, F(2,145) = 5.43, p < .01. (Mexp1 = 7.5, SD = 1.00, N = 30; Mexp2 = 8.5, SD = 1.00, N = 30; Mcontrol = 5.5, SD = 1.00, N = 30). The partial eta-squared (η2 = .06) was of medium size.
Suggested norms for partial eta-squared: small = 0.01; medium = 0.06; large = 0.14.
Reporting - Advice: Field (2005), Section 8.6; Pallant (2007), p. 248.
Power: Power calculator
Effect size: Calculated in SPSS via the Generalized Linear Models program; see also Field (2005), section 8.5.

Factorial analysis-of-variance models - ANOVA
Moore & McCabe, Chapter 13: Two-way analysis of variance;
Field, Chapter 10: Factorial ANOVA (GLM 3)
Effect sizes: Field, Chapter xx, section:
Software

The results for a Factorial ANOVA can best be reported in a table.
Example:
Table 8

Response variable: Aggresion of children during play with war toys (N=146)
SourceSSdfMSFpη2
Family composition7.1823.594.46.013.060
Attitude towards war toys33.93133.9342.12<.001.231
Interaction5.6022.803.470.340.47
Within (Residual)112.79140.81
Total165.56145
Power:
Effect size:

Multivariate analysis-of-variance models - MANOVA
ModelTextbook
Multivariate ANOVA:Field, Chapter xx: xxxxxxx
Effect sizes: Field, Chapter xx, section:
Software
Power:
Effect size:

Analysis of covariance - ANCOVA
Moore & McCabe, Chapter 13: Two-way analysis of variance;
Field, Chapter 10: Factorial ANOVA (GLM 3)
Effect sizes: Field, Chapter xx, section:
Software
Power:
Effect size:

Repeated-measures analysis of variance - Repeated Measures ANOVA