Compounds in the saliva, hair andurine of pets may potentially trigger asthma in some patients. Totest this hypothesis, some researchers conducted a study. As testsubjects, they used 8 families, 4 of which had a pet in their homeand 4 did not. They measured respiratory flow of each familymember, as this is known to decrease in patients with asthma.Recent research has shown body weight to correlate with asthma inchildren, and sex, age, and height are also known to affectrespiratory flow measures. Therefore, the researchers measured andincluded these covariates in their model to control for anyconfounding effects that they may have had before testing theirtreatment of interest (whether the home had pets). The analysisconducted by the researchers is presented below. They concludedthat pets in the family do not influence respiratory flow.
>attach(pets.data)
> pets.data
resp.flow body.weight treatment sexage height family
1266 41 pet F 13 130Smith
2400 95 pet M 37 190 Smith
3369 81 pet F 36 180 Smith
4365 78 pet M 42 185 Wilson
5351 75 pet M 35 192 Wilson
6334 62 pet F 41 170 Taylor
...
13391 78 nopet M 41 180 Singh
14340 62 no pet F27 177 Singh
15337 55 nopet F 34 185 Singh
16389 87 nopet M 27 172 Campbell
17376 78 nopet F 33 167 Campbell
18338 57 nopet F 47 155 Li
19337 62 nopet M 50 172 Li
20359 69 nopet M 18 173 Li
>model<-lm(resp.flow~treatment+sex+age+height+body.weight)
>anova(model)
Analysis of Variance Table
Response: resp.flow
Df Sum Sq Mean Sq F value Pr(>F)
Treatment 1 1.8 1.8 0.0569 0.8149
sex 1 6626.96626.9 209.6419 8.117e-10 ***
age 1 10264.810264.8 324.7247 4.396e-11 ***
height 1 8346.9 8346.9 264.05361.758e-10 ***
body.weight 1 5786.0 5786.0 183.03731.978e-09 ***
Residuals 14 442.6 31.6
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Signif. codes: 0 '***' 0.001 '**'0.01 '*' 0.05 '.' 0.1 ' ' 1
a) Identify threeaspects of the design and/or analysis of this study that reduceyour confidence in the conclusion that pets dont influencerespiratory flow.
b) List fourassumptions of the model used in this analysis.
c) If the assumptions aren’t met,what are three approaches you can take to analysethe data?
d) Which variable in their analysisexplained the most variance in respiratory flow?
e) In the ANOVA table below, which letters (A-E) representnumbers that would NOT change if the sample size of peopleincreased? (1 mark)
Response: resp.flow
Df Sum Sq Mean Sq F valuePr(>F)
Treatment A B C D E
sex 1 6626.9 6626.9 209.64198.117e-10 ***
age 1 10264.8 10264.8 324.72474.396e-11 ***
height 1 8346.9 8346.9 264.05361.758e-10 ***
body.weight 1 5786.0 5786.0 183.03731.978e-09 ***
Residuals 14 442.6 31.6
