1980 census of population: Ancestry of the population by by United States. Bureau of the Census. Population Division

By United States. Bureau of the Census. Population Division

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3╇NORMALITY The assumption of normality, that the conditional distributions of the scores on the dependent variable, or the prediction errors, are normal in shape, is an assumption that is applicable to many multivariate procedures. In the multivariate world, normality is an assumption that is usually considered both in the context of univariate as well as in the context of multivariate. We will first touch on univariate normality. Violation of the normality assumption may be the result of outliers.

2. They Univariate and Bivariate Statistics Review ↜渀屮 ↜渀屮 are referred to as mean squares because they represent a summed quantity that is weighted by the number of observations used in the sum itself, like the mean. The mean squares terms are also variance estimates because they represent the sum of the squared deviations from a mean divided by their degrees of freedom, like the sample variance s2. The last column in the ANOVA summary table, the F value, is the summary test statistic of the summary table.

This is why: The alpha level is too conservative in cases where the cells that have the larger sample sizes also have the larger variance (thus, results that are not statistically significant may have been had there been equal variance-covariance matrices—so if you do find statistical significance in this situation, there is little reason for concern for violation of the assumption). The alpha level is too liberal in cases where the cells that have the smaller sample sizes have the larger variances (thus, results that are statistically significant may not have been had there been equal variance-covariance matrices—this situation is extremely problematic; so if you do not find statistical significance in this situation, there is little reason for concern for violation of the assumption).

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