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    The answer is simple: Levene's test is a form of an ANOVA itself, which means that we couldn't introduce it until we had finished introducing the ANOVA model.
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    Residuals versus fitted values for cancer survival times What does Levene's test tell us?
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    Download hearthstone fontsSupplementary Exercises A: Transforming to equalize standard deviations.
    Download hearthstone fontsBut, in its favor, it has a small chance of missing actual differences that exist.
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    Additional Topics in Analysis of Variance In Chapters 5 and 6, we introduced you to what we consider to be the basics of analysis of variance.
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    Compute the means and standard deviations for the four groups.
    This exercise was invented to show the method described above at work using simple numbers.
    Download hearthstone fontsCompute the average and standard deviation for each group.
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    So our decision to proceed with the ANOVA model in Chapter 5 for these data is justified.
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    Download hearthstone fontsMoreover, the residual plot also carries a lot of subjectivity with it: No two groups will have exactly the same spread.
    Test for Homogeneity of Variances Levene's Test for Homogeneity of Variances tests the null hypothesis of equality of variances by computing the absolute deviations between the observations and their group medians, and then applying an ANOVA model to those absolute deviations.
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    That is, our data are consistent with the idea that the (population) variances are the same among all five groups.
    In that case, when we looked at the original data, we had some concerns about the equality of the variances.
    It does so by using a smaller individual error rate for each of the intervals.
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    Download hearthstone fontsWhat differs between the methods is the critical value.
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    Do the points suggest a line?
    Download hearthstone fontsThe procedure, as described above, sounds somewhat complicated if we need to compute every step, but most software will perform this test for you from the original data, without you having to make the intermediate calculations.
    Download hearthstone fontsWe also discuss the relative merits of all three methods.
    If the null hypothesis is not rejected, then the condition of equality of variances required for the original ANOVA analysis can be considered met.
    This method is the most liberal of the three we will discuss, producing intervals that are often much narrower than those produced by the other two methods and thus is more likely to identify differences (either real or false).
    Download hearthstone fontsIn particular, we discussed the fact that all error terms need to come from a distribution with the same variance.
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    If you ignore the two outliers, the remaining six points lie very close to a line (see the figure below).
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    Download hearthstone fontsWe observed in Chapter 5 that the spreads seem to be rather similar in this graph.
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    Download hearthstone fontsOne question to ask would be: Which groups are different from which other groups?
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    Download hearthstone fontsWe find our data to be consistent with the condition that the population variances are equal.
    Thus, Levene's test operates on four groups (cells) of data, corresponding to the four combinations of factor levels.
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    Or, put another way, our data are consistent with the null hypothesis.
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    Download hearthstone fontsBonferroni Adjustment: A Conservative Approach On the other end of the spectrum is the Bonferroni method.
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    Download hearthstone fontsUse a calculator to transform the data and compute new group means and standard deviations.
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