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What are the assumptions of ANOVA? In a one-way between-groups ANOVA, what degrees of freedom do...

  1. What are the assumptions of ANOVA?
  1. In a one-way between-groups ANOVA, what degrees of freedom do I need to know?
  1. In a one-way within groups ANOVA, what degrees of freedom do I need to know?
  1. Name one pro and one con of using a within-groups ANOVA.
  1. What is a post hoc test? When and why are they used? What is the name of one post hoc test?

Solutions

Expert Solution

The assumptions of ANOVA are

  • Independence of cases – this is an assumption of the model that simplifies the statistical analysis.
  • Normality – the distributions of the residuals are normal.
  • Equality (or "homogeneity") of variances, called homoscedasticity

In one-way anova the degrees of freedom(df) of treatment effects(between group) is k-1 and that of error(within group) is n-k. Hence the total df is n-1. Here there are n independent random sample observations classified into k classes.

The pro is

• More costly

The con is

It often leads to misleading results.

Post hoc tests are an integral part of ANOVA. When you use ANOVA to test the equality of at least three group means, statistically significant results indicate that not all of the group means are equal. However, ANOVA results do not identify which particular differences between pairs of means are significant. Use post hoc tests to explore differences between multiple group means while controlling the experiment-wise error rate.

Tukey's method is a post hoc test.

orchestra answered 1 year ago
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