What assumption is checked when looking at the predicted values vs residuals plot in a one-way ANOVA model?
The correct answer and explanation is:
The assumption checked when looking at the predicted values vs residuals plot in a one-way ANOVA model is the homogeneity of variance, also known as homoscedasticity. This assumption states that the variance of the residuals (errors) should be constant across all levels of the independent variable. If the variance of the residuals differs significantly across groups, it suggests that the assumption of homogeneity of variance has been violated, which could lead to inaccurate conclusions.
The plot of predicted values versus residuals is often used to visually assess this assumption. In this plot, the residuals should be randomly scattered around the horizontal axis (the zero line) without any discernible patterns. If the residuals form patterns, such as a funnel shape (increasing or decreasing spread), it indicates that the variance is not constant, which violates the assumption of homoscedasticity. Such patterns suggest that the variability in the data may depend on the level of the independent variable, undermining the validity of the ANOVA test.
Additionally, the plot can be used to check for other assumptions, such as normality of residuals and linearity, but the main assumption being checked in this specific plot is homoscedasticity. If homoscedasticity is violated, researchers may need to consider alternative methods, such as transforming the data or using a more robust statistical method like Welch’s ANOVA, which does not assume equal variances. It is important to check this assumption because violating it could lead to inflated Type I error rates, where the model incorrectly rejects the null hypothesis, or reduced power to detect true effects.