Which of the following assumptions is NOT one of the underlying assumptions of Analysis of Covariance (ANCOVA)?

Correct option is B

Analysis of Covariance (ANCOVA) is a statistical method that combines ANOVA and regression by adjusting for the effects of covariates. It helps improve the accuracy of group comparisons by removing the variance attributed to covariates.

Correct Answer: (2) The treatment groups should be selected at random from the different population is NOT a core assumption of ANCOVA.
-ANCOVA assumes random assignment within a single population, not random selection from different populations.
-The goal is to ensure that any differences between groups are due to the independent variable, not pre-existing differences between separate populations.
-If groups come from different populations, it introduces biases that ANCOVA cannot fully control.

Information Booster

Key Assumptions of ANCOVA:

Homogeneity of variances (Within-group variance must be appropriately equal)
-The variance of the dependent variable should be similar across all groups (homoscedasticity).
-This ensures that comparisons between groups remain valid.

Additivity of variance (The contribution of variance in the total sample must be additive)
-The total variance should be decomposable into independent components, which is a requirement for ANCOVA to function correctly.

Linear Relationship Between Covariate and Dependent Variable (There should be a linear relationship between X and Y)
-ANCOVA assumes that the covariate (X) is linearly related to the dependent variable (Y) to effectively remove its influence.
-However, ANCOVA does not assume that X and Y must always be linearly related in a general sense, but only in the context of controlling covariates.