Question

To look for outliers, and to check the equal variance assumption, a ____________ should be created.

Answer 1

To look for outliers and verify the assumption of equal variances in one-way ANOVA, a residual plot should be made. If variances are not equal, it violates ANOVA assumptions, and statistical tests such as Levene's test, Bartlett's test, or an F test for comparing variances may be used.

Step-by-step explanation:

To look for outliers, and to check the equal variance assumption, a residual plot should be created. When conducting a one-way ANOVA test, key assumptions include that each sample comes from a normally distributed population, and that all populations have equal variances. A residual plot can help verify these assumptions by showing if the residuals are randomly dispersed around the horizontal axis, indicating equal variances and no outliers. If the standard deviations across samples differ significantly, it violates the ANOVA assumption of homogeneity of variances. To formally test for equal variances, statistical tests such as the Levene's test, Bartlett's test, or an F test for comparing the variances can be used. These tests are based on the chi-square or F distribution and test the null hypothesis that variances are equal. The F distribution is particularly used in ANOVA and the test of two variances. However, the F test is very sensitive to non-normal distributions, thus initial assessment of normality is crucial before proceeding.

Answer 2

To look for outliers and check the equal variance assumption, a residual plot should be created.

A residual plot is a scatterplot of the residuals against the independent variable or some other meaningful variable. Residuals are the differences between the observed values of the dependent variable and the predicted values based on the fitted regression model.

So, Outliers are data points that lie far away from the main body of the data. They can have a significant impact on the regression analysis, so it is important to identify and address them before drawing any conclusions from the model. Residual plots can help visualize outliers by showing data points that deviate significantly from the horizontal line at zero.