Question

1. Explain why Repeated Measures ANOVA applies in this problem. Use Mauchley’s sphericity test in STATISTICA OR R to determine if the homogeneity of variance assumption is met. Use a 0.05 level of significance.

A study reported in the Journal of the American Medical Association investigated the cardiac demands of heavy snow shoveling. Ten healthy men underwent exercise testing with a treadmill and a cycle ergometer modified for arm cranking. The men then cleared two tracts of heavy, wet snow by using a lightweight plastic snow shovel and an electric snow thrower. Each subject’s composite score consisting of heart rate blood pressure, oxygen uptake, and perceived exertion during snow removal were compared with the values obtained during treadmill and arm-crank ergometer testing. The data below gives the heart rates in beats per minute for each of the 10 subjects.

Subject	Treadmill	Arm-Crank Ergometer	Snow Shovel	Snow Thrower
1	177	205	180	98
2	151	177	164	120
3	184	166	167	111
4	161	152	173	122
5	192	142	179	151
6	193	172	205	158
7	164	191	156	117
8	207	170	160	123
9	177	181	175	127
10	174	154	191	109

Subject	Count	Sum	Average	Variance
1	4	660	165	2152.667
2	4	612	153	596.6667
3	4	628	157	1008.667
4	4	608	152	474
5	4	664	166	548.6667
6	4	728	182	442
7	4	628	157	935.3333
8	4	660	165	1192.667
9	4	660	165	648
10	4	628	157	1252.667
Activity
Treadmill	10	1780	178	281.1111
Arm-Crank Ergometer	10	1710	171	356.6667
Snow Shovel	10	1750	175	219.1111
Snow Thrower	10	1236	123.6	336.9333

Answer 1

> install.packages("car" )

> Data = read.table ("E:/Documents/Exercise.txt", header = TRUE)

> attach (Data)

> Data

> DatMatrix = as.matrix (Data, rownames.force = NA)

> DatMatrix

> results = Anova (DatModel, idata = data.frame(design), idesign = ~design, type = "III")

> summary (results, multivariate = FALSE)

Test statistic and p-value will be obtained and if p-value > α, so the data appears to satisfy sphericity.