Question

Compounds in the saliva, hair and urine of pets may potentially trigger asthma in some patients. To test this hypothesis, some researchers conducted a study. As test subjects, they used 8 families, 4 of which had a pet in their home and 4 did not. They measured respiratory flow of each family member, as this is known to decrease in patients with asthma. Recent research has shown body weight to correlate with asthma in children, and sex, age, and height are also known to affect respiratory flow measures. Therefore, the researchers measured and included these covariates in their model to control for any confounding effects that they may have had before testing their treatment of interest (whether the home had pets). The analysis conducted by the researchers is presented below. They concluded that pets in the family do not influence respiratory flow.

> attach(pets.data)

> pets.data

resp.flow body.weight treatment sex age height family

1 266          41     pet   F 13    130 Smith

2 400          95     pet    M 37    190   Smith

3 369          81     pet    F 36    180   Smith

4 365          78     pet    M 42    185   Wilson

5 351          75     pet    M 35    192   Wilson

6 334          62     pet    F 41    170   Taylor

...

13 391          78         no pet   M 41    180 Singh

14 340          62        no pet   F 27    177 Singh

15 337          55         no pet   F 34    185 Singh

16 389          87         no pet   M 27    172 Campbell

17 376          78         no pet   F 33    167 Campbell

18 338          57         no pet   F 47    155 Li

19 337          62         no pet   M 50    172 Li

20 359          69         no pet   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 6626.9 6626.9 209.6419 8.117e-10 ***

age          1 10264.8 10264.8 324.7247 4.396e-11 ***

height       1 8346.9 8346.9 264.0536 1.758e-10 ***

body.weight 1 5786.0 5786.0 183.0373 1.978e-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 three aspects of the design and/or analysis of this study that reduce your confidence in the conclusion that pets dont influence respiratory flow.    

b) List four assumptions of the model used in this analysis.

c) If the assumptions aren’t met, what are three approaches you can take to analyse the data?

d) Which variable in their analysis explained the most variance in respiratory flow?

e) In the ANOVA table below, which letters (A-E) represent numbers that would NOT change if the sample size of people increased?                      (1 mark)

Response: resp.flow

Df Sum Sq Mean Sq F value Pr(>F)   

Treatment    A            B             C            D                      E   

sex 1 6626.9 6626.9 209.6419 8.117e-10 ***

age 1 10264.8 10264.8 324.7247 4.396e-11 ***

height 1 8346.9 8346.9 264.0536 1.758e-10 ***

body.weight 1 5786.0 5786.0 183.0373 1.978e-09 ***

Residuals   14   442.6    31.6                      

       

Answer 1

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