H0: The population is Normal Xi ~ N(i, i), unknown parameters, i=1…k
Response variable is in continuous scale
• •
Not rej. H0
Lilliefors’ test Shapiro-Wilk test (better)
H0: The k Normal populations are homoscedastic 12 = 22 = … = k2 = 2 • •
Reject H0
Transform the data
Not rej. H0
H0: The k samples come from identical populations •
Kruskal-Wallis test
H0: The k Normal populations have the same mean 1 = 2 = … = k =
• •
Brown-Forsythe test Welch’s test Reject H0
Reject H0
MULTIPLE COMPARISON TESTS H0: Two populations have the same mean i = j (ij) • • •
Tukey's HSD test / TukeyKramer test (better) Hochberg (GF2) Scheffé’s test
H0: Two populations have the same median μi = μj (ij) Hodges-Lehmann test for independent samples Dwass-Steel-Critchlow-Fligner test (Steel-Dwass All Pairs in JMP software)
•
[email protected]
ANOVA
NONPARAMETRIC MULTIPLE COMPARISON TESTS Reject H0
• •
Ana Cristina Costa
•
Reject H0
H0: The k populations have the same scale parameter • Siegel-Tukey test or Ansari-Bradley test • Conover’s Squared Ranks test • Levene’s test using the median
Reject H0
Bartlett’s test Levene’s test (better)
Not rej. H0
H0: The k Normal and homoscedastic populations have the same mean 1 = 2 = … = k =
• •
Nemenyi test (or Nemenyi-Damico-Wolfe-Dunn test) Conover-Inman test Wilcoxon-Mann-Whitney test (a.k.a. MannWhitney U test) with the Bonferroni correction
One-way ANOVA process and nonparametric counterparts (I) © 2017
H0: The population is Normal Xi ~ N(i, i), unknown parameters, i=1…k
Response variable is in metric scale
• •
Not rej. H0
Lilliefors’ test Shapiro-Wilk test (better)
• •
Reject H0
(Multiple) Correspondence Analysis Reject H0
Response variable is in ordinal scale
H0: The k populations have the same scale parameter • Siegel-Tukey test or Ansari-Bradley test • Conover’s Squared Ranks test • Levene’s test using the median
H0: The k samples come from identical populations Kruskal-Wallis test
Bartlett’s test Levene’s test (better)
H0: The k Normal populations have the same mean 1 = 2 = … = k =
• •
Brown-Forsythe test Welch’s test Reject H0
ANOVA Reject H0
MULTIPLE COMPARISON TESTS H0: Two populations have the same mean i = j (ij) • • •
Tukey's HSD test / TukeyKramer test (better) Hochberg (GF2) Scheffé’s test
H0: Two populations have the same median μi = μj (ij) Hodges-Lehmann test for independent samples Dwass-Steel-Critchlow-Fligner test (Steel-Dwass All Pairs in JMP software)
•
[email protected]
•
NONPARAMETRIC MULTIPLE COMPARISON TESTS Reject H0
• •
Ana Cristina Costa
Not rej. H0
H0: The k Normal and homoscedastic populations have the same mean 1 = 2 = … = k =
Reject H0
Not rej. H0
•
H0: The k Normal populations are homoscedastic 12 = 22 = … = k2 = 2
• •
Nemenyi test (or Nemenyi-Damico-Wolfe-Dunn test) Conover-Inman test Wilcoxon-Mann-Whitney test (a.k.a. MannWhitney U test) with the Bonferroni correction
One-way ANOVA process and nonparametric counterparts (II) © 2017
