In a study of patient confidentiality, a large number of pediatricians was surve

Question

In a study of patient confidentiality, a large number of pediatricians was surveyed. Each pediatrician was given a “fable” about a female patient less than 18 years old.

There were sixteen different fables, the combinations of the factors complaint (C: 1—drug problem, 2—venereal disease), age (A:1—14 years, 2—17 years), the length of time the pediatrician had known the family (L: 1—less than 1 year, 2—more than 5 years), and the maturity of patient (M: 1—immature for age, 2—mature for age).

The response at each combination of factor levels is the fraction of doctors who would keep confidentiality and not inform the patient’s parents (data modeled on Moses 1987). Analyze these data to determine which factors influence the pediatrician’s decision:

Data for R: data <- read.table("http://www.stat.umn.edu/~corbett/classes/5303/RDataFiles/pr10.7",
header=TRUE)

C A L M Response C A L M Response .578 -786 622 .755 814 902 869 902 1 445 1 1 2.624 1 2.360 1 2 2493 1 2 .513 1 2 1 2.693 1 2 2 534 1 2 2 2.675

Explanation / Answer

> data <- read.table("http://www.stat.umn.edu/~corbett/classes/5303/RDataFiles/pr10.7",
+ header=TRUE)
> attach(data)
> data
complaint age timeknown maturity y
1 1 1 1 1 0.445
2 1 1 1 2 0.624
3 1 1 2 1 0.360
4 1 1 2 2 0.493
5 1 2 1 1 0.513
6 1 2 1 2 0.693
7 1 2 2 1 0.534
8 1 2 2 2 0.675
9 2 1 1 1 0.578
10 2 1 1 2 0.786
11 2 1 2 1 0.622
12 2 1 2 2 0.755
13 2 2 1 1 0.814
14 2 2 1 2 0.902
15 2 2 2 1 0.869
16 2 2 2 2 0.902
> class(complaint)
[1] "integer"
> complaint=as.factor(complaint)
> age=as.factor(age)
> timeknown=as.factor(timeknown)
> maturity=as.factor(maturity)
> model=lm(y~complaint+age+timeknown+maturity)
> summary(model)

Call:
lm(formula = y ~ complaint + age + timeknown + maturity)

Residuals:
Min 1Q Median 3Q Max
-0.063687 -0.028156 -0.004750 0.009938 0.090562

Coefficients:
Estimate Std. Error t value Pr(>|t|)   
(Intercept) 0.40531 0.02724 14.882 1.24e-08 ***
complaint2 0.23638 0.02436 9.703 9.98e-07 ***
age2 0.15488 0.02436 6.358 5.39e-05 ***
timeknown2 -0.01812 0.02436 -0.744 0.472448   
maturity2 0.13688 0.02436 5.619 0.000156 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.04872 on 11 degrees of freedom
Multiple R-squared: 0.9381, Adjusted R-squared: 0.9156
F-statistic: 41.67 on 4 and 11 DF, p-value: 1.393e-06

As per p-values (<0.05), three factors : complaint, age and maturity are significant in determining pediatrician's decision since p-value < 0.05 implies we reject the null hypothesis of no significance.

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