From this we calculate the standard error s W= SQRT( MS W) = 24.2.
In Figure 1, we calculate MS Was we did in Example 3 of Basic Concepts for ANOVA. Any deviations from these norms can be viewed as indicating the presence of potential outliers.Įxample 1: Determine whether there are any outliers for the data in Example 2 of Basic Concepts for ANOVA if we change the first sample for Method 4 to 185 (instead of 85).įigure 1 – Identifying outliers for data in Example 1 Thus approximately 4.56% of the observations should be more than 2 standard deviations away from its group mean, 1.24% should be more than 2.5 standard deviations away, 0.26% should be more than 3 standard deviations away, etc. To determine how large a residual must be to be classified as an outlier we use the fact that if the population is normally distributed, then the residuals are also normally distributed with distribution If an observation has a large residual, we consider it a potential outlier. The residual is a measure of how far away an observation is from its group mean value (our best guess of the value). Residuals are defined as for Levene’s test, namely:
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