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What are the assumptions underlying the analysis of variance?

Jul 1st, 2015

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Assumptions can pertain to:

• Measurement scale

• Method of sampling and/or assigning subjects to treatments

• Selection of factor levels

• Etc.

 Assumptions in analysis of variance:

1. The normality assumption

 2. The homogeneity of variance assumption

3. The independence assumption

What can be done?

• In general: –

 Analysis of variance is robust.

 • Nominal α level ≈ actual α level – No normality – Heterogeneous variances (cell frequencies large and equal) – But: small violations of the independence assumption can have dramatic effects.

 • This is a requirement of the design

Normality of variances and homogeneity:

• Normality of variances – The distribution is skewed – The dependent variable is not an interval variable – Kolmogorov-Smirnov and Shapiro-Wilk normality tests

• Homogeneity of variances – Levine’s test => Welch’s test

Example:

 • Dyslexia

• Communicative Developmental Inventory

 • Closed-class words

• 17m, 23m & 29m

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jul 1st, 2015

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