Question

What are the assumptions of between-subjects analysis of variance?

Short answer

Key assumptions include independence, normality, homogeneity of variance, and random sampling.

Step-by-step solution

Define Between-Subjects ANOVA

Between-subjects ANOVA is a statistical test that compares means across different groups of subjects to determine if there is a significant difference between them. Each participant is in one group only, and comparisons are made between these separate groups.

Assumption of Independence

Independence implies that the scores of participants in one group are not influenced by the scores of participants in another group. Each group should be randomly selected, and participants should be randomly assigned to these groups to ensure independence.

Assumption of Normality

The normality assumption states that within each group of the study, the distribution of the dependent variable should be approximately normally distributed. This is generally tested using statistical tests such as the Shapiro-Wilk test or by visual inspection of histograms.

Assumption of Homogeneity of Variance

The homogeneity of variance assumption indicates that the variances among the different groups should be approximately equal. This is often assessed using Levene's test for equality of variances.

Assumption of Random Sampling

This assumption requires that the samples are drawn from the population in a manner where every potential sample has an equal probability of being selected. This ensures the external validity of the results.

Key concepts

Assumption of Independence

In the context of a between-subjects ANOVA, the assumption of independence is crucial for obtaining valid test results. Independence means that the scores in one group should not be influenced by the scores in another group.
To achieve this, several measures can be taken:

• Randomly select participants for each group to prevent biases that may arise if participants are systematically chosen.
• Ensure that participants do not communicate or interact with participants in other groups, as this could lead to influence or bias.
• Use different settings or times for each group to further eliminate potential interactions that could violate the independence assumption.

By maintaining strict independence, researchers can be more confident that any differences observed between groups are due to the manipulation of the independent variable, and not other extraneous factors.

Assumption of Normality

The assumption of normality is another key requirement for performing a between-subjects ANOVA. This assumption states that the data within each group should be normally distributed. Although ANOVA is relatively robust to deviations from normality, meeting this assumption helps to ensure the accuracy of p-values and confidence intervals.
There are several methods to assess normality in a dataset:

• Shapiro-Wilk Test: A statistical test that determines if the data significantly deviates from a normal distribution.
• Histogram: A graphical representation of the data that shows whether the data distribution roughly follows a bell-shaped curve.
• Normal Q-Q Plot: A plot that compares the quantiles of the sample data to the quantiles of a normal distribution.

If the data does not follow a normal distribution, consider transformations or non-parametric tests as alternatives.

Assumption of Homogeneity of Variance

The homogeneity of variance assumption requires that the variances within each group are equal. This is critical because ANOVA compares the variability within groups to the variability between groups.
A common method to test for homogeneity of variance is Levene's Test, which checks if the variances across groups are significantly different. If Levene's Test indicates a violation of this assumption, adjustments like using a Welch ANOVA—an alternative that does not assume equal variances—may be considered.
Maintaining homogeneity allows ANOVA to correctly attribute the variance to group differences rather than to unequal variances, ensuring that the ANOVA's conclusions about group differences are valid.