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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

an inferential statistical test that determines whether there is a statistically significant difference between the means in two unrelated groups. Null and alternative hypotheses for the independent t-test The null hypothesis for the independent t-test is that the population means from the two unrelated groups are equal: H0: u1 = u2 In most cases, we are looking to see if we can show that we can reject the null hypothesis and accept the alternative hypothesis, which is that the population means are not equal: HA: u1 ≠ u2 To do this, we need to set a significance level (also called alpha) that allows us to either reject or accept the alternative hypothesis. Most commonly, this value is set at 0.05. What do you need to run an independent t-test? In order to run an independent t-test, you need the following: One independent, categorical variable that has two levels/groups. One continuous dependent variable. Unrelated groups Unrelated groups, also called unpaired groups or independent groups, are groups in which the cases (e.g., participants) in each group are different. Often we are investigating differences in individuals, which means that when comparing two groups, an individual in one group cannot also be a member of the other group and vice versa. An example would be gender - an individual would have to be classified as either male or female – not both. Join the 10,000s of students, academics and professionals who rely on Laerd Statistics. TAKE THE TOUR PLANS & PRICING Assumption of normality of the dependent variable The independent t-test requires that the dependent variable is approximately normally distributed within each group. Note: Technically, it is the residuals that need to be normally distributed, but for an independent t-test, both will give you the same result. You can test for this using a number of different tests, but the Shapiro-Wilks test of normality or a graphical method, such as a Q-Q Plot, ar

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