Empirical Direction in Design and Analysis

By Norman H. Anderson | Go to book overview
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Chapter 4
ELEMENTS OF ANALYSIS OF VARIANCE II

Three further topics in analysis of variance are considered in this chapter. The first two concern focused analyses beyond the overall Anova of the previous chapter. With more than two groups, a statsig Anova indicates that the means are not all equal, but this does little to localize the differences. All might be different, or all equal but one. Ways to localize differences are discussed in the first two main sections.

The other topic is power. If your experiment lacks power to detect a real difference between treatments, it seems better to find out before you do it. How can you find out? The power formula in the last main section can help. Weak experiments can be made stronger or avoided.


4.1 CONFIDENCE INTERVALS

Confidence intervals go beyond the overall Anova to assess differences between two treatment conditions. The width of the interval gives visual information on the reliability of the difference, as well as on its size.


4.1.1 CONFIDENCE INTERVAL AS SIGNIFICANCE TEST

The confidence interval of Section 2.2 provides a significance test of a difference between the means of two independent samples. In Expression 2 of Chapter 2 (page 34), the standard deviation, s, equals the square root of MSwithin from the overall Anova. The expression for confidence interval may then be rewritten in the following two equivalent forms, using either t* or F*.

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