Question

Outline, define, and explain the assumptions for the three major analyses discussed in this unit: the independent-groups t-test, the correlated-groups t-test, and the one-way between-subjects ANOVA. Why are these assumptions important? How are these assumptions assessed/tested by statisticians? What do they have to do with the robustness of a statistical test? Explain and be specific, and treat this question as an essay (i.e., write in complete sentences and be thorough)!

Answer 1

Assumptions

One-Way ANOVA

• Normality – That each sample is taken from a normally distributed population
• Sample independence – that each sample has been drawn independently of the other samples
• Variance Equality – That the variance of data in the different groups should be the same
• Your dependent variable – here, “weight”, should be continuous – that is, measured on a scale which can be subdivided using increments (i.e. grams, milligrams)

Independent Samples T Test

· Assumption of Independence: you need two independent, categorical groups that represent your independent variable. In the above example of test scores “males” or “females” would be your independent variable.

· Assumption of normality: the dependent variable should be approximately normally distributed. The dependent variable should also be measured on a continuous scale. In the above example on average test scores, the “test score” would be the dependent variable.

· Assumption of Homogeneity of Variance: The variances of the dependent variable should be equal.

Correlated Groups t Test

1. The dependent variable is quantitative and measured on an interval level

2. The independent variable is within subjects in nature

3. The independent variable has only two levels