ANOVA tests

  • Assumptions to check:

    • Normal distribution (testable by e.g. Kolmogorov–Smirnov test, Shapiro–Wilk test, the Anderson-Darling test, Q-Q plot)

    • Equal variances (homoscedasticity) of group samples (testable by e.g. F-test, Levene’s test, Bartlett’s test, Brown-Forsythe test)

    • Group independence (for independent/unpaired test) or full dependence (for dependent/paired test)

  • Report design in Method section:

    • Specify the number of factors included in the ANOVA test (one way ANOVA, two-way ANOVA, more factors ANOVA)

    • For each factor, specify the name and level of the factor and state whether the factor was within-subjects (independent) factor or between subjects (dependent) factor. 

    • If the ANOVA has two or more factors, specify whether the interaction term was included.

    • Specify post hoc test (e.g. Tuckey, Newman-Keuls, Scheffee, Bonferroni, Dunnett) 

    • Name the statistical package or program used in the analysis. 

  • Report statistics in Result section: 

    • Report the F-statistics, degrees of freedom and exact p-value for each factor or interaction. 

    • Strongly recommended: report on descriptive statistics

  • Example:

    • One way ANOVA: 

      • Method section: To test whether there is a difference in BMI for people with different exercising routines, we used one-way ANOVA without repeated measures, with exercise as an independent factor (levels: ALWAYS, OCCASIONALLY, NEVER) and BMI as a dependent factor. The Tuckey’s  post hoc was used. The analysis was performed in GraphPad Prism (RRID:SCR_002798).

      • Results section:  We used one-way ANOVA which indicated a significant difference between the groups (F(2,97) = 68.255, p < 0.001, ω2 = 0.574).
        According to the Shapiro-Wilk and Levene tests, the data met the assumptions of normality (W = 0.989, p = 0.598) and homoscedasticity (F(2,97) = 0.635, p = 0.532).
        To identify between which groups a difference occurred, we used Tukey's post hoc test. There was no significant difference between mean BMI (t(97) = 0.073, p = 0.997, d = 0.018) of the groups that exercised ALWAYS (M = 26.3, SD = 1.5) and OCCASIONALLY (M = 26.2, SD = 1.4). However, the group that NEVER (M = 30.3, SD = 1.9) exercised had a significantly higher mean BMI than those that OCCASIONALLY (t(97) = -10.204, p < 0.001, d = -2.493) and ALWAYS (t(97) = -10.057, p < 0.001, d = -2.476) exercised.

    • Two way ANOVA: 

      • Methods section: To test whether the BMI is affected by the factors sex and exercise we used two-way Anova test with sex (levels: female, male) and exercise (levels: never, occasionally, always) as independent factors and BMI as the dependent factor with Tukey’s post hoc. We used R software (RRID:SCR_001905) to perform the analysis. 

      • Results section: According to the Shapiro-Wilk and Levene tests, the normality (W = 0.983, p = 0.237) and homoscedasticity (F(5,94) = 1.581, p = 0.173) assumptions were not violated.

        The two-way ANOVA overall model was statistically significant (F(5,94) = 42.176, p < 0.001), and the factors SEX (F(1,94) = 29.915, p < 0.001, ω2 = 0.184) and EXERCISE affected the BMI (F(2,94) = 15.746, p < 0.001, ω2 = 0.187). The interaction between these two factors (SEX*EXERCISE), however, was not statistically significant (F(2,94) = 0.480, p = 0.620, ω2 = -0.007).FEMALEs had a higher BMI (M = 29.3, SD = 2.1) than MALEs (M = 25.8, SD = 1.5). 

        Tukey's post hoc test indicated which groups of the EXERCISE factor were different. The BMIs of the groups that ALWAYS (M = 26.2, SD = 1.5) or EVENTUALLY (M = 26.2, SD = 1.6) exercised were equal (t(94) = -0.568, p = 0.838, d = -0.152). However, the group that NEVER (M = 30.3, SD = 1.9) exercised had a higher BMI than those that EVENTUALLY (t(94) = -4.915; p < 0.001; d = -1.768) and ALWAYS (t(94) = -5.415; p < 0.001; d = -1.920) exercised.