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# Homogeneous Error Variance

## Heterogeneity Of Variance

demonstrate how to perform the three different levene's tests:http://www.youtube.com/watch?v=81Yi0c... Category Education License Standard YouTube License Show more Show less Loading... Advertisement Autoplay When autoplay is enabled, a suggested video will automatically play next. Up next Homogeneity of Variance (part 2) - Duration: 5:04. how2stats 26,104 views 5:04 Homogeneity of Variance (part 3) - Duration: 5:54. how2stats 13,266 views 5:54 Conducting and Interpreting a Levene's Test in SPSS - Duration: 7:35. Todd Grande 20,560 views 7:35 Levene's Test of Equal Variances (Part 1) - Equal Variance Test - Duration: 6:10. Quantitative Specialists 25,525 views 6:10 ANOVA - Unequal Variances Unequal Sample Sizes - Brown-Forsythe & Welch F tests - Duration: 5:04. how2stats 7,657 views 5:04 Normality test using SPSS: How to check whether data are normally distributed - Duration: 9:15. Kent Löfgren 222,241 views 9:15 Chi-Square Test of Homogeneity example - Duration: 8:07. American Public University 12,534 views 8:07 F test example - Duration: 8:29. mathguyzero 83,720 views 8:29 ANOVA (Part A) - Sources of Variance in an Experiment - Duration: 7:43. ProfKelley 43,523 views 7:43 Dancing statistics: explaining the statistical concept of variance through dance - Duration: 4:44. bpsmediacentre 42,724 views 4:44 Levene's test - SPSS (part 2) - Duration: 5:03. how2stats 39,855 vi

## Homogeneity Of Variance Anova

equal variances. Equal variances across samples is called homogeneity of variance. Some statistical tests, for example http://www.itl.nist.gov/div898/handbook/eda/section3/eda35a.htm the analysis of variance, assume that variances are equal across groups https://statistics.laerd.com/statistical-guides/independent-t-test-statistical-guide.php or samples. The Levene test can be used to verify that assumption. Levene's test is an alternative to the Bartlett test. The Levene test is less sensitive than the Bartlett test to departures from normality. If you have strong evidence that of variance your data do in fact come from a normal, or nearly normal, distribution, then Bartlett's test has better performance. Definition The Levene test is defined as: H0: $$\sigma_{1}^{2} = \sigma_{2}^{2} = \ldots = \sigma_{k}^{2}$$ Ha: $$\sigma_{i}^{2} \ne \sigma_{j}^{2}$$ for at least one pair (i,j). Test Statistic: Given a variable homogeneity of variance Y with sample of size N divided into k subgroups, where Ni is the sample size of the ith subgroup, the Levene test statistic is defined as: $W = \frac{(N-k)} {(k-1)} \frac{\sum_{i=1}^{k}N_{i}(\bar{Z}_{i.}-\bar{Z}_{..})^{2} } {\sum_{i=1}^{k}\sum_{j=1}^{N_i}(Z_{ij}-\bar{Z}_{i.})^{2} }$ where Zij can have one of the following three definitions: $$Z_{ij} = |Y_{ij} - \bar{Y}_{i.}|$$ where $$\bar{Y}_{i.}$$ is the mean of the i-th subgroup. $$Z_{ij} = |Y_{ij} - \tilde{Y}_{i.}|$$ where $$\tilde{Y}_{i.}$$ is the median of the i-th subgroup. $$Z_{ij} = |Y_{ij} - \bar{Y}_{i.}'|$$ where $$\bar{Y}_{i.}'$$ is the 10% trimmed mean of the i-th subgroup. $$\bar{Z}_{i.}$$ are the group means of the Zij and $$\bar{Z}_{..}$$ is the overall mean of the Zij. The three choices for defining Zij determine the robustness and power of Levene's test. By robustness, we mean the ability of the test to not falsely detect unequal variances when the underlying data are not normally distributed and the variables are in fact equal. By po