Shampoo Comparison Worksheet
Experimental Structure/Elements
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Primary Goal: Compare 2 formulations of shampoo (A vs B) on hair combability
Experimental Units: 16 hair swatches created from human hair clippings
Observational Units: Each swatch measured on 5 occasions (runs) both before and after shampoo
Randomization: Swatches randomized so that 8 receive shampoo A, 8 receive B
Questions:
 How many total measurements obtained? ___________________________________
 How many “true” replications per shampoo? _______________________________
 How many ways to assign the 16 swatches to 8 for A, 8 for B? __________________
Results (Data Averaged over Swatch’s 5 runs):
swatch
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
shampoo
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
period0
180.8
249.4
73.2
136.8
125.8
130.2
158.2
50.0
144.4
153.8
201.6
132.0
90.0
76.0
100.0
88.0
period1
166.4
161.8
70.2
126.6
126.8
97.2
141.4
43.8
173.2
145.2
180.6
136.0
84.0
66.0
154.0
57.0
Period1
Mean
SD
Sh1
116.775
43.377
Sh2
124.500
48.651
PooledSD
Period0
Mean
SD
Sh1
138.050
61.880
Sh2
123.225
42.623
PooledSD
ybar1-2
se(yb1-2)
t-stat
14.825
26.566
0.558
46.090
ybar1-2
se(yb1-2)
t-stat
53.131
 Conduct the 2-sample t-test to determine whether the (Period 1) mean
combabilities differ for the 2 shampoos: H0: AB = 0 HA: AB ≠ 0
Point Estimate:
y A  y B = __________________________________________


Std. Error: SE y A  y B = ____________________________________________
t- Statistic __________________________________________________________
Rejection Region (=0.05): _________________________________________
 Conduct the Analysis of Covariance (Multiple regression) to determine whether
the (Period 1) mean combabilities differ for the 2 shampoos, controlling for preshampoo levels: H0: A = 0 HA: A ≠ 0 for the model: E Y    0  1 X   A A
(X = pre-shampoo score, A=1 if Shampoo A, 0 if shampoo B)
Intercept
shampooA
period0
Coefficients
Standard Error t Stat
P-value
33.90
18.11
1.87
0.0839
-18.63
12.83
0.74
0.13
5.76
0.0001
Adj
Adj
Point Estimate: y A  y B = __________________________________________

Adj
Adj
Std. Error: SE y A  y B
 = ____________________________________________
t- Statistic __________________________________________________________
Rejection Region (=0.05): _________________________________________
 Conduct a “simulated” randomization test to determine whether the (Period 1)
mean combabilities differ for the 2 shampoos: H0: AB = 0 HA: AB ≠ 0
Point Estimate:
y A  y B = __________________________________________
rank(actual)
717
# of abs(Randomization Differences) larger than observed _______________
Observed significance level________________________________