repeated measures anova rogaine for hair growth in women v.h. price and e. menefee (1990)....
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![Page 1: Repeated Measures ANOVA Rogaine for Hair Growth in Women V.H. Price and E. Menefee (1990). “Quantitative Estimation of Hair Growth I. Androgenic Alopecia](https://reader036.vdocuments.site/reader036/viewer/2022082820/56649f425503460f94c61788/html5/thumbnails/1.jpg)
Repeated Measures ANOVA
Rogaine for Hair Growth in Women
V.H. Price and E. Menefee (1990). “Quantitative Estimation of Hair Growth I. Androgenic Alopecia in Women: Effect of Minoxidil,” The journal of Investigative Dermatology, Vol.95, pp.683-687
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Data Description
• Subjects: 8 Women with Androgenetic Alopecia
• Treatments: Minoxidil (Rogaine) and Placebo (4 Women per treatment)
• Time Periods: Measurements made Pre-treatment (0 weeks), 8, 16, 24, and 32 weeks (will only consider post-treatment measures)
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DataTrt Subject Week0 Week8 Week16 Week24 Week321 1 216 290 340 275 2941 2 130 146 206 220 2091 3 206 193 218 223 2261 4 106 130 144 150 1730 5 142 154 145 160 1480 6 178 161 170 194 1690 7 189 219 197 218 2030 8 180 185 223 201 182
Trt\Week 8 16 24 32 OverallRogaine 189.75 227 217 225.5 214.8125Placebo 179.75 183.75 193.25 175.5 183.0625Overall 184.75 205.375 205.125 200.5 198.9375
Subject Trt Average1 Rogaine 299.752 Rogaine 195.253 Rogaine 2154 Rogaine 149.255 Placebo 151.756 Placebo 173.57 Placebo 209.258 Placebo 197.75
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Mean Hair Growth versus Week by Treatment
150
160
170
180
190
200
210
220
230
240
0 5 10 15 20 25 30 35
Week
Ha
ir G
row
th
Rogaine
Placebo
Overall
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Statistical Model
error term Random
Time and Trt between n Interactio )(
4,3,2,1 period time ofEffect
4,3,2,1 ent hin treatm woman wit ofEffect
2,1Trt ofEffect
GrowthHair Mean Overall
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Sums of Squares
n)Subtractio(By 13.5233
:18)3(6)(df n)Interactio t)Subject(Tr x (Time Squares of Sum Error2
75.2004)94.19850.20006.1835.175(...)94.19875.18481.21475.189(4
:3)1(3)(df Squares of Sumn Interactio Timex Treatment
63.2267)94.19850.200()94.19813.205()94.19838.205()94.19875.184()4(2
:31)-4(df Squares of Sum Time
88.55475
)06.18375.197(...)06.18375.151()81.21425.149(...)81.21475.299(4
:6)1)-2(4(df Squares of SumTreatment thin Subject Wi
5.8064)94.19806.183()94.19381.214()4(4
:1)1-2(df Squares of SumTreatment
88.73045)94.198182(...)94.198290(
31)1-2(4)(4)(df Squares of Sum Total
2
22
2222
2222
)(
22
22
Error
TrtsxTime
Time
TrtsSubjects
TRTS
SS
SS
SS
SS
SS
TSS
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ANOVA Table/F-TestsSource df SS MS F P-valueTreatments 1 8064.50 8064.50 0.87 0.3864Subject(Trts) 6 55475.88 9245.98Time 3 2267.63 755.88 2.60 0.0839TrtxTime 3 2004.75 668.25 2.30 0.1120Error2 18 5233.13 290.73Total 31 73045.88
Note: We cannot conclude any treatment or time effects or interaction at the 0.05 significance level. The subject-to-subject variation is very large, which makes finding a treatment effect very difficult in this setting (and very few subjects as well)
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Post-Hoc comparisons*
21.63 than moreby differ means timeNo 26.25)4(2
)73.290(2963.2
963.273.2905.20013.20538.20575.184
:s)Comparison (6 Means Time Comparing
94.114,44.5119.8375.31)4(4
)9246(2447.206.18381.214
447.26924606.18381.214
Placebo) - Rogaine :Comparison (1 Treatments Comparing
18),62/(05.24..3..2..1..
6,2/05.)(
Time
xError
TrtSubjectsPR
B
tMSYYYY
tdfMSYY
* Bonferroni’s method for illustration only (no significant effects found from Analysis of Variance)