case1802 {Sleuth3}

Vitamin C and the Common Cold

Description

In a randomized experiment, researchers assigned 407 volunteers to receive 1,000 mg of Vitamin C daily throughout the cold season and 411 to receive a placebo. A physician interviewed the volunteers at the end of the study to determine whether or not they had suffered any colds during the study period.

Usage

case1802

Format

A data frame with 2 observations on the following 3 variables.

Treatment

a factor with levels "Placebo" and "VitC"

Cold

the number of who got colds

NoCold

the number that did not get any colds

Source

Ramsey, F.L. and Schafer, D.W. (2013). The Statistical Sleuth: A Course in Methods of Data Analysis (3rd ed), Cenage Learning.

References

Anderson, T.W., Reid, D.B.W. and Beaton, G. H. (1972). Vitamin C and the Common Cold, Canadian Medial Association Journal 107: 503–508.

Examples

str(case1802)
attach(case1802) 

library(MASS)        
## INFERENCE (4 methods)
myTable <- cbind(Cold,NoCold)
row.names(myTable) <- c("Placebo","Vitamin C")
myTable
prop.test(myTable, alternative="greater") # Compare 2 binomial proportions 
# Alternative: pop prop. of first column (cold) in larger in first row (placebo)    
prop.test(myTable, alternative="greater", correct=TRUE)   
prop.test(myTable,correct=TRUE) # Use 2-sided alternative to get CI    
chisq.test(myTable)   # Chi-square test
fisher.test(myTable, alternative="greater")
fisher.test(myTable) #  2-sided alternative to get CI for odds ratio
myGlm1  <- glm(myTable ~ Treatment, family=binomial) # logistic reg (Ch 21)
summary(myGlm1)
beta    <- myGlm1$coef
1 - exp(beta[2])  # 0.3474911
1 - exp(confint(myGlm1,2)) # 0.53365918 0.09042098
# Interpretation: The odds of getting a cold are 35% less on Vitamin C than 
# Placebo (95% confidence interval: 9% to 53% less).

detach(case1802)