tailieunhanh - Exploratory Data Analysis_8

Tham khảo tài liệu 'exploratory data analysis_8', kỹ thuật - công nghệ, điện - điện tử phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | . Levene Test for Equality of Variances ENGINEERING STATISTICS HANDBOOK hW tools raids lỉEÂtCH BACK Nixf 1. Exploratory Data Analysis . EDA Techniques . Quantitative Techniques . Levene Test for Equality of Variances Purpose Levene s test Levene 1960 is used to test if k samples have equal Test for variances. Equal variances across samples is called homogeneity of Homogeneity variance. Some statistical tests for example the analysis of variance of Variances assume that variances are equal across groups 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 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 a2 . ffjt Ha rĩ- Ĩ4 for at least one pair ij . a Test Given a variable Y with sample of size N divided into k Statistic subgroups where Ni is the sample size of the ith subgroup the Levene test statistic is defined as w N-k ELflfe-V where Zj can have one of the following three definitions 1. 2 where Yị is the mean of the ith subgroup. n I where Ỹ- is the median of the ith subgroup. http div898 handbook eda section3 1 of 4 5 1 2006 9 57 20 AM . Levene Test for Equality of Variances u. where V-f is the 10 trimmed mean of the z th subgroup. are the group means of the Zjj and is the overall mean of the Zịj. The three choices for defining Zjj 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 power we mean the ability of the test to detect unequal variances when the variances are in fact unequal. Levene s original paper only proposed .