One-Way ANOVA: Theory And Practice

January 05, 2021

One-way analysis of variance (ANOVA) tells you whether there are significant differences in the mean values on the dependent variable across groups of the independent variable.

It involves one independent variable (referred to as a factor), which has a number of different levels; and these levels correspond to the different groups or conditions.

The ‘one-way’ part of the title indicates there is only one independent variable, and ‘between-groups’ means that you have different subjects or cases in each of the groups.

Non-parametric alternative: Kruskal-Wallis Test.

  • Test of Homogeneity of Variances:
  • The homogeneity of variance option gives you Levene’s test for homogeneity of variances, which tests whether the variance in scores is the same for each of the three groups.
  • Check the significance value (Sig.) for Levene’s test. If this number is greater than 0.05 (e.g. 0.08, 0.12, 0.28), then you have not violated the assumption of homogeneity of variance.
  • You will need to consult the table in the output headed Robust Tests of Equality of Means if the assumption of homogeneity of variance is violated.
  • The two tests shown there (Welsh and Brown-Forsythe) are preferable when the assumption of the homogeneity of variance is violated.
  • Multiple Comparisons (Post-Hoc Tests):
  • You should look at this table only if you found a significant difference in your overall ANOVA. That is, if the Sig. value was equal to or less than 0.05.
  • The post-hoc tests in this table will tell you exactly where the differences among the groups occur. Look down the column labelled Mean Difference.
  • Two of the most commonly used post-hoc tests are Tukey’s Honestly Significant Different test (HSD) and the Scheffe test. Of the two, Tukey has more statistical power to detect a difference between your groups.
  • Effect Size (Partial Eta-Squared):
  • This is a set of statistics which indicates the relative magnitude of the differences between means.
  • It represents the proportion of variance of the dependent variable that is explained by the independent variable.
  • Cohen’s (1988) classifies 0.01 as a small effect, 0.06 as a medium effect and 0.14 as a large effect. From the ANOVA result, simply divide btw groups by total to generate the effect size.

Dr. Obumneke Ezie

Youtube: Obezip Universal Statisticals

Click to watch practical:


Jan 07, 2021 at 12:27 PM
Jan 07, 2021 at 12:27 PM
Is this mathematics or biostatistics?
Jan 07, 2021 at 12:28 PM
Can't understand any shit
Jan 07, 2021 at 04:00 PM
That's why you need to check the video on YouTube
Jan 07, 2021 at 04:41 PM
[Reply] Onuigbo Emmanuel said:
Jan 07, 2021 at 12:28 PM
Can't understand any shit

Watch the practical here:
Jan 21, 2021 at 03:08 PM
Jan 31, 2021 at 03:03 PM

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