Final answer:
Assumptions in ONE-WAY ANCOVA are essential to confirm the test's validity, and violations can lead to incorrect conclusions. These assumptions include normal distribution of populations, random and independent samples, equal variances, the factor being a categorical variable, and a numerical response.
Step-by-step explanation:
Assumptions are necessary for ONE-WAY ANCOVA because they ensure the validity of the test's results. These assumptions are very similar to those required for a one-way ANOVA. They include:
- Each population from which a sample is drawn should be normally distributed.
- Samples must be randomly selected and independent from each other.
- Populations should have equal standard deviations or variances.
- The factor being tested is a categorical variable.
- The response should be a numerical variable.
Violations of these assumptions can affect the interpretation of the results by increasing the likelihood of Type I or Type II errors, leading to incorrect conclusions about the effect of the categorical independent variable on the dependent variable. For instance, if populations have unequal variances, the test might become too strict for some groups and too lenient for others, which could mask or exaggerate differences in group means.
We test these assumptions to ensure the robustness and reliability of the ANCOVA results. Only when the assumptions are met, the resulting F ratios and p-values from the ANCOVA can be trusted to accurately reflect whether the means of the groups differ significantly or not.