Question

You conduct an ANOVA to compare three groups,imagine the possibilities then EXPLAIN why.

Is it possible that all of the residuals in one group are positive? Explain how this could happen, or why it cannot happen.

Answer 1

Yes, it is possible for all of the residuals in one group to be positive in an ANOVA.

Step-by-step explanation:

Yes, it is possible for all of the residuals in one group to be positive in an ANOVA. Residuals represent the differences between the observed data points and the predicted values from the ANOVA model. If the observed values in one group are consistently higher than the predicted values, then all of the residuals for that group would be positive.

For example, let's say we are comparing three groups: A, B, and C. If all of the residuals in group A are positive, it means that the observed values in group A are consistently higher than what we would expect based on the overall model. This could happen if group A has a higher mean than the other groups, leading to positive residuals.

However, it is important to note that the sign of the residuals does not determine the statistical significance of the differences between the groups. Statistical significance is determined by the ANOVA test itself, which takes into account the magnitude and variability of the residuals.