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Pairwise Comparisons Dependent variable: weight (kg) Mean 95% conﬁdence interval (I) gender (J) gender difference (I − J) Std buy 250 mg aleve fast delivery treatment for nerve pain from shingles. Univariate Tests Dependent variable: weight (kg) Sum of squares df Mean square F Sig generic 250mg aleve visa pain treatment doctors. This test is based on the linearly independent pairwise comparisons among the estimated marginal means buy flagyl 500 mg on-line. By rerunning the model with different options, statistics can be obtained to test that the residuals are normally distributed, that there are no inﬂuential multivariate outliers, that the variance is homogeneous and that there are no interac- tions between the covariate and the factors. Here, the assumptions are being tested only when the ﬁnal model is obtained but in practice the assumptions would be tested at each stage in the model building process. If the variances are not equal, an option would be to halve the critical P values for any between-group differences say to P = 0. A less rigorous option would be to select a post-hoc test that adjusts for unequal variances. Analysis of variance 151 Univariate Analysis of Variance Levene’s test of equality of error variancesa Dependent variable: weight (kg) F 1 df S ig. However, the main effects must always be included in the model even though they are no longer of interest. However, any signiﬁcant interaction that includes the covariate would violate the assumption of the model. Lack of Fit Tests Dependent variable: weight (kg) Source Sum of squares df Mean square F Sig. If the variance is not related to the cell means then unequal variances will not be a problem. However, if there is a relation such as the variance increasing with the mean of the cell, then unequal variances will bias the F value. However, the range in standard deviations is relatively small, that is, from approximately 0. If the variances are widely unequal, it is sometimes possible to reduce the differences by transforming the measurement. If there is a linear relation between the variance and the means of the cells and all the data values are positive, taking the square root or logarithm of the measurements may be helpful. In practice, the use of a different statistical test such as multiple regression analysis may be preferable because the assumptions are not as restrictive. This means that the differences between the observed and predicted values for each participant are not systematically different from one another. This plot shows that the observed and predicted values have a linear relationship with no systematic differences Analysis of variance 153 Spread vs. Residual Model: Intercept + gender + parity1 + length + length + gender * parity1 + length Figure 5. In addition, the negative and positive residuals balance one another with a random scatter around a horizontal centre line.   