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

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)

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

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

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

:where

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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

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)

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)