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    Download hearthstone fontsThat is, our data are consistent with the idea that the (population) variances are the same among all five groups.
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    Download hearthstone fontsUse a calculator to transform the data and compute new group means and standard deviations.
    Download hearthstone fontsOne question to ask would be: Which groups are different from which other groups?
    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).
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    It does so by using a smaller individual error rate for each of the intervals.
    Download hearthstone fontsResiduals versus fitted values for cancer survival times What does Levene's test tell us?
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    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.
    Thus, Levene's test operates on four groups (cells) of data, corresponding to the four combinations of factor levels.
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    Download hearthstone fontsThe 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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    Download hearthstone fontsUse a calculator or spreadsheet to compute the comparison values.
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    Then the median value of each group is computed.
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    We find our data to be consistent with the condition that the population variances are equal.
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    Download hearthstone fontsIf you ignore the two outliers, the remaining six points lie very close to a line (see the figure below).
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    Bonferroni Adjustment: A Conservative Approach On the other end of the spectrum is the Bonferroni method.
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    And the more intervals we compute, the more likely it is that we will have at least one interval that doesn't capture its intended parameter.
    But, in its favor, it has a small chance of missing actual differences that exist.
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    Compute the means and standard deviations for the four groups.
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    Download hearthstone fontsCompute the average and standard deviation for each group.
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    Download hearthstone fontsWe observed in Chapter 5 that the spreads seem to be rather similar in this graph.
    Why Worry about Multiple Tests?
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    We prefer to think of the sections of this chapter as topics rather than subdivisions of a single theme.
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    So our decision to proceed with the ANOVA model in Chapter 5 for these data is justified.
    Finally, the absolute deviation between each point and the median of its group is calculated.
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    Plot the residuals versus the comparison values.
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    In that case, when we looked at the original data, we had some concerns about the equality of the variances.
    Moreover, the residual plot also carries a lot of subjectivity with it: No two groups will have exactly the same spread.
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    If the null hypothesis is not rejected, then the condition of equality of variances required for the original ANOVA analysis can be considered met.
    What differs between the methods is the critical value.
    Download hearthstone fontsAdditional 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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    What transformation, if any, is suggested?
    They also kept track of which month the data came from since there was likely to be a relationship between admissions and the season of the year.
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    Download hearthstone fontsWe also discuss the relative merits of all three methods.
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    Supplementary Exercises A: Transforming to equalize standard deviations.
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    ANOVA and introduces you to ideas that, while not strictly necessary for a beginning analysis, will substantially strengthen an analysis of data.
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