Is there an association between gender and self-image? The 2003-2004 National Health & Nuitrition Exam Survey (NHANES) asked participants to describe their own self-image regarding weight. The options were Underweight, About Right, and Overweight. Here is the data, separated by gender.
selfImage = matrix(c(116,274,1175,1469,1730,1112),ncol=2,byrow=T)
colnames(selfImage)=c('Female','Male')
rownames(selfImage)=c('Underweight','About Right','Overweight')
selfImage
## Female Male
## Underweight 116 274
## About Right 1175 1469
## Overweight 1730 1112
You can make either a bar graph or a mosaic plot for this data, and each can be oriented two ways:
par(mfrow=c(2,2))
barplot(selfImage,legend=T)
barplot(t(selfImage),legend=T)
mosaicplot(t(selfImage),color=T,las=1,main="Self-Image vs. Gender")
mosaicplot(selfImage,color=T,las=1,main="Gender vs. Self-Image")
You’ll have to decide which of these plots looks the best.
In order to test the hypotheses:
We use the R command chisq.test()
.
chisq.test(selfImage)
##
## Pearson's Chi-squared test
##
## data: selfImage
## X-squared = 226.58, df = 2, p-value < 2.2e-16
As you can see, the results are very significant, so we can safely conclude that there is a real association between gender and self-image in the population. It appears that women are significantly more likely to view themselves as overweight.