post hoc tests - wesleyan university hoc tests.pdf · anova. timetofatigue 3434.475 3 1144.825...
TRANSCRIPT
![Page 1: Post hoc tests - Wesleyan University hoc tests.pdf · ANOVA. TimetoFatigue 3434.475 3 1144.825 6.364 .001 6476.500 36 179.903 9910.975 39 Between Groups Within Groups Total Sum of](https://reader034.vdocuments.us/reader034/viewer/2022042316/5f054c437e708231d41244c2/html5/thumbnails/1.jpg)
Post hoc tests
![Page 2: Post hoc tests - Wesleyan University hoc tests.pdf · ANOVA. TimetoFatigue 3434.475 3 1144.825 6.364 .001 6476.500 36 179.903 9910.975 39 Between Groups Within Groups Total Sum of](https://reader034.vdocuments.us/reader034/viewer/2022042316/5f054c437e708231d41244c2/html5/thumbnails/2.jpg)
Placebo
Lucozade
Gatorade
Powerade
Post hoc tests (example)….
Random Assignment My Sample
Time to
Fatigue (min)
Dependent Variable
Independent Variable
![Page 3: Post hoc tests - Wesleyan University hoc tests.pdf · ANOVA. TimetoFatigue 3434.475 3 1144.825 6.364 .001 6476.500 36 179.903 9910.975 39 Between Groups Within Groups Total Sum of](https://reader034.vdocuments.us/reader034/viewer/2022042316/5f054c437e708231d41244c2/html5/thumbnails/3.jpg)
ANOVA Hypotheses
The Null hypothesis for ANOVA is that the means for all groups are equal:
The Alternative hypothesis for ANOVA is that at least two of the means are not equal.
koH µµµµ ==== ....: 321
![Page 4: Post hoc tests - Wesleyan University hoc tests.pdf · ANOVA. TimetoFatigue 3434.475 3 1144.825 6.364 .001 6476.500 36 179.903 9910.975 39 Between Groups Within Groups Total Sum of](https://reader034.vdocuments.us/reader034/viewer/2022042316/5f054c437e708231d41244c2/html5/thumbnails/4.jpg)
ANOVA
TimetoFatigue
3434.475 3 1144.825 6.364 .0016476.500 36 179.9039910.975 39
Between GroupsWithin GroupsTotal
Sum ofSquares df Mean Square F Sig.
![Page 5: Post hoc tests - Wesleyan University hoc tests.pdf · ANOVA. TimetoFatigue 3434.475 3 1144.825 6.364 .001 6476.500 36 179.903 9910.975 39 Between Groups Within Groups Total Sum of](https://reader034.vdocuments.us/reader034/viewer/2022042316/5f054c437e708231d41244c2/html5/thumbnails/5.jpg)
Tim
e to
Fat
igue
(min
)
0
20
40
60
80
100
120 PlaceboLGIHGIGlucose
Thomas et al. (1991)
*
*P <0.05 vs. Placebo, HGI & Glucose
Placebo Lucozade Gatorade Powerade
Placebo Lucozade Gatorade Powerade
![Page 6: Post hoc tests - Wesleyan University hoc tests.pdf · ANOVA. TimetoFatigue 3434.475 3 1144.825 6.364 .001 6476.500 36 179.903 9910.975 39 Between Groups Within Groups Total Sum of](https://reader034.vdocuments.us/reader034/viewer/2022042316/5f054c437e708231d41244c2/html5/thumbnails/6.jpg)
Why not multiple Anovas? i.e. Placebo vs Lucozade Placebo vs Gatorade Placebo vs Powerade Lucozade vs Gatorade Lucozade vs Powerade Gatorade vs Powerade
We accept ‘significance’ and reject the null hypothesis at P≤0.05 (i.e. a 5% chance that we are wrong)
Performing multiple tests therefore means that our overall chance of committing a type I error is >5%.
![Page 7: Post hoc tests - Wesleyan University hoc tests.pdf · ANOVA. TimetoFatigue 3434.475 3 1144.825 6.364 .001 6476.500 36 179.903 9910.975 39 Between Groups Within Groups Total Sum of](https://reader034.vdocuments.us/reader034/viewer/2022042316/5f054c437e708231d41244c2/html5/thumbnails/7.jpg)
Inflated Type I Error and Pairwise Comparisons
# Tests Comparison α Familywise α
1 .05 .05
3 .05 .14
6 .05 .26
10 .05 .40
15 .05 .54
![Page 8: Post hoc tests - Wesleyan University hoc tests.pdf · ANOVA. TimetoFatigue 3434.475 3 1144.825 6.364 .001 6476.500 36 179.903 9910.975 39 Between Groups Within Groups Total Sum of](https://reader034.vdocuments.us/reader034/viewer/2022042316/5f054c437e708231d41244c2/html5/thumbnails/8.jpg)
Determining Error Rates
Two Important Error Rates (Alpha): Per-Comparison: Probability of Type I Error for
each specific comparison Family-Wise: Overall Type I Error probability
Type I Error Rate for Multiple Tests:
where c = # of comparisons
cPCFW ) - (1 -1 αα =
![Page 9: Post hoc tests - Wesleyan University hoc tests.pdf · ANOVA. TimetoFatigue 3434.475 3 1144.825 6.364 .001 6476.500 36 179.903 9910.975 39 Between Groups Within Groups Total Sum of](https://reader034.vdocuments.us/reader034/viewer/2022042316/5f054c437e708231d41244c2/html5/thumbnails/9.jpg)
Post Hoc Tests Bonferroni procedure Duncan Multiple range test Dunnett’s multiple comparison test Newman-Keuls test Scheffe’s test Tukey’s HSD (honestly significant difference) test Fisher’s LSD (Least Significant Difference)
Holm t-test Sidak
![Page 10: Post hoc tests - Wesleyan University hoc tests.pdf · ANOVA. TimetoFatigue 3434.475 3 1144.825 6.364 .001 6476.500 36 179.903 9910.975 39 Between Groups Within Groups Total Sum of](https://reader034.vdocuments.us/reader034/viewer/2022042316/5f054c437e708231d41244c2/html5/thumbnails/10.jpg)
Tim
e to
Fat
igue
(min
)
0
20
40
60
80
100
120 PlaceboLGIHGIGlucose
Thomas et al. (1991)
*
*P <0.05 vs. Placebo, HGI & Glucose
Placebo Lucozade Gatorade Powerade
Placebo Lucozade Gatorade Powerade
A
Placebo Lucozade Gatorade Powerade
Placebo Lucozade Gatorade Powerade
B B
A, B
![Page 11: Post hoc tests - Wesleyan University hoc tests.pdf · ANOVA. TimetoFatigue 3434.475 3 1144.825 6.364 .001 6476.500 36 179.903 9910.975 39 Between Groups Within Groups Total Sum of](https://reader034.vdocuments.us/reader034/viewer/2022042316/5f054c437e708231d41244c2/html5/thumbnails/11.jpg)
Adding post hoc test to ANOVA… SAS
proc anova; class VCAT; Model VCONT=VCAT; means VCAT /duncan; run;
![Page 12: Post hoc tests - Wesleyan University hoc tests.pdf · ANOVA. TimetoFatigue 3434.475 3 1144.825 6.364 .001 6476.500 36 179.903 9910.975 39 Between Groups Within Groups Total Sum of](https://reader034.vdocuments.us/reader034/viewer/2022042316/5f054c437e708231d41244c2/html5/thumbnails/12.jpg)
ChiSquare …
White Black NAmer Asian Hispanic Nicotine
dependence
![Page 13: Post hoc tests - Wesleyan University hoc tests.pdf · ANOVA. TimetoFatigue 3434.475 3 1144.825 6.364 .001 6476.500 36 179.903 9910.975 39 Between Groups Within Groups Total Sum of](https://reader034.vdocuments.us/reader034/viewer/2022042316/5f054c437e708231d41244c2/html5/thumbnails/13.jpg)
Bonferroni post hoc test … A conservative adjustment (Bonferroni adjustment) is to
divide 0.05/c (number of comparisons).
3 comparisons is 0.05/3, so that alpha for each test = 0.017.
![Page 14: Post hoc tests - Wesleyan University hoc tests.pdf · ANOVA. TimetoFatigue 3434.475 3 1144.825 6.364 .001 6476.500 36 179.903 9910.975 39 Between Groups Within Groups Total Sum of](https://reader034.vdocuments.us/reader034/viewer/2022042316/5f054c437e708231d41244c2/html5/thumbnails/14.jpg)
ChiSquare …
White Black NAmer Asian Hispanic Nicotine
dependence
.05/10, so that alpha for each test = 0.005.
![Page 15: Post hoc tests - Wesleyan University hoc tests.pdf · ANOVA. TimetoFatigue 3434.475 3 1144.825 6.364 .001 6476.500 36 179.903 9910.975 39 Between Groups Within Groups Total Sum of](https://reader034.vdocuments.us/reader034/viewer/2022042316/5f054c437e708231d41244c2/html5/thumbnails/15.jpg)
Subset data for paired comparisons… SAS
IF ETHRACE2A eq 1 or ETHRACE2A eq 3;
![Page 16: Post hoc tests - Wesleyan University hoc tests.pdf · ANOVA. TimetoFatigue 3434.475 3 1144.825 6.364 .001 6476.500 36 179.903 9910.975 39 Between Groups Within Groups Total Sum of](https://reader034.vdocuments.us/reader034/viewer/2022042316/5f054c437e708231d41244c2/html5/thumbnails/16.jpg)
Rate of nicotine dependence by race/ethnicity….
0
5
10
15
20
25
30
35
40
White Black NativeAmerican
Asian Hispanic
% Nicotine
Dependent Lifetime
![Page 17: Post hoc tests - Wesleyan University hoc tests.pdf · ANOVA. TimetoFatigue 3434.475 3 1144.825 6.364 .001 6476.500 36 179.903 9910.975 39 Between Groups Within Groups Total Sum of](https://reader034.vdocuments.us/reader034/viewer/2022042316/5f054c437e708231d41244c2/html5/thumbnails/17.jpg)
White Black Nicotine
dependence
![Page 18: Post hoc tests - Wesleyan University hoc tests.pdf · ANOVA. TimetoFatigue 3434.475 3 1144.825 6.364 .001 6476.500 36 179.903 9910.975 39 Between Groups Within Groups Total Sum of](https://reader034.vdocuments.us/reader034/viewer/2022042316/5f054c437e708231d41244c2/html5/thumbnails/18.jpg)
White NAmer
Nicotine dependence
![Page 19: Post hoc tests - Wesleyan University hoc tests.pdf · ANOVA. TimetoFatigue 3434.475 3 1144.825 6.364 .001 6476.500 36 179.903 9910.975 39 Between Groups Within Groups Total Sum of](https://reader034.vdocuments.us/reader034/viewer/2022042316/5f054c437e708231d41244c2/html5/thumbnails/19.jpg)
Rate of nicotine dependence by race/ethnicity….
0
5
10
15
20
25
30
35
40
White Black NativeAmerican
Asian Hispanic
% Nicotine
Dependent Lifetime
A,B
B
C
C
C