ECOSOC Ad Hoc Advisory Groups on African Countries Emerging from Conflict
Post hoc tests - Wesleyan University hoc tests.pdf · ANOVA. TimetoFatigue 3434.475 3 1144.825...
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Post hoc tests
Transcript of Post hoc tests - Wesleyan University hoc tests.pdf · ANOVA. TimetoFatigue 3434.475 3 1144.825...
Post hoc tests
Placebo
Lucozade
Gatorade
Powerade
Post hoc tests (example)….
Random Assignment My Sample
Time to
Fatigue (min)
Dependent Variable
Independent Variable
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
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.
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
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%.
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
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 =
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
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
Adding post hoc test to ANOVA… SAS
proc anova; class VCAT; Model VCONT=VCAT; means VCAT /duncan; run;
ChiSquare …
White Black NAmer Asian Hispanic Nicotine
dependence
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.
ChiSquare …
White Black NAmer Asian Hispanic Nicotine
dependence
.05/10, so that alpha for each test = 0.005.
Subset data for paired comparisons… SAS
IF ETHRACE2A eq 1 or ETHRACE2A eq 3;
Rate of nicotine dependence by race/ethnicity….
0
5
10
15
20
25
30
35
40
White Black NativeAmerican
Asian Hispanic
% Nicotine
Dependent Lifetime
White Black Nicotine
dependence
White NAmer
Nicotine dependence
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
