Question

give me an exampe to perform levene's test. i have school project that make an app for QUEST algorithm. after do chi square or anova f test, sometimes i have to do levene's test. if you don't mind help me with an example

Answer 1

Question #28401give me an exampe to perform levene's test. i have school project that make an app for QUEST algorithm. after do chi square or anova f test, sometimes i have to do levene's test. if you don't mind help me with an example Solution. Levene's test is used to test if $k$ samples have equal variances. Equal variances across samples is called homogeneity of variance. Suppose that your big sample $Y = (Y_{1,\cdot},\ldots ,Y_{k,cdot})$ is divided into $k$ "small" samples $Y_{i,\cdot},1\leq i\leq k$ . Leven's test tests whether r.v.s inside small groups possess the same variance. Statistic of the test is

$$W = \frac {(N - k) \sum_ {i = 1} ^ {k} N _ {i} (\overline {{Z _ {i , \cdot}}} - \overline {{Z _ {\cdot , \cdot}}}) ^ {2}}{(k - 1) \sum_ {i = 1} ^ {k} \sum_ {j = 1} ^ {N _ {i}} (Z _ {i , j} - \overline {{Z _ {i , \cdot}}}) ^ {2}}$$

here $Z_{i,j} = |Y_{i,j} - \overline{Y_{i,\cdot}}|$ , $\overline{Y_{i,\cdot}}$ is the mean of the i-th group. Respectively, $\overline{Z_{i,\cdot}}$ are the group means of $Z_{i,j}$ , $\overline{Y_{i,\cdot}}$ is the mean of the all $Z_{i,j}$ , $N, N_i$ are respectively the size of the big and small samples. After calculating this statistics you should compare it with $F_{a,k-1,N-k}$ (take $\alpha = 0.05$ for instance) quantile of Fisher distribution with $k-1$ and $N-k$ degrees of freedom. If $W > F_{a,k-1,N-k}$ , then the null hypothesis is rejected, that is the variance inside the small samples differs. Otherwise, we accept the null hypothesis.