Data 606 - Lab 3

Questions to answer:

1. Make a histogram of men’s heights and a histogram of women’s heights. How would you compare the various aspects of the two distributions?

hist(mdims$hgt)

hist(fdims$hgt)

Distributions look roughly normal. Average height higher for men. Spread is about the same for each.

2. Based on the this plot, does it appear that the data follow a nearly normal distribution?

Yes

3. Make a normal probability plot of sim_norm. Do all of the points fall on the line? How does this plot compare to the probability plot for the real data?

sim_norm <- rnorm(n = length(fdims$hgt), mean = fhgtmean, sd = fhgtsd)
qqnorm(sim_norm)
qqline(sim_norm)

Except at the tail ends, the simulated points do fall on the line.

4. Does the normal probability plot for fdims$hgt look similar to the plots created for the simulated data? That is, do plots provide evidence that the female heights are nearly normal?

Yes.

5. Using the same technique, determine whether or not female weights appear to come from a normal distribution.

I think ‘male’ might have been meant here?

mhgtmean <- mean(mdims$hgt)
mhgtsd   <- sd(mdims$hgt)

sim_norm <- rnorm(n = length(mdims$hgt), mean = mhgtmean, sd = mhgtsd)
qqnorm(sim_norm)
qqline(sim_norm)

qqnormsim(mdims$hgt)

These also appear to be normally distributed.

6. Write out two probability questions that you would like to answer; one regarding female heights and one regarding female weights. Calculate the those probabilities using both the theoretical normal distribution as well as the empirical distribution (four probabilities in all). Which variable, height or weight, had a closer agreement between the two methods?

1. What is the probability that a woman is taller than 160 cm?
2. What is the probability that a woman weighs less than 65 Kg?

1 - pnorm(q = 160, mean = fhgtmean, sd = fhgtsd)

## [1] 0.7717061

sum(fdims$hgt > 160) / length(fdims$hgt)

## [1] 0.7307692

fwgtmean <- mean(fdims$wgt)
fwgtsd   <- sd(fdims$wgt)

pnorm(q = 65, mean = fwgtmean, sd = fwgtsd)

## [1] 0.6763603

sum(fdims$wgt < 65) / length(fdims$wgt)

## [1] 0.7384615

Weight had a slightly closer agreement.

qqnorm(fdims$che.di)
qqline(fdims$che.di)

On Your Own

• Now let’s consider some of the other variables in the body dimensions data set. Using the figures at the end of the exercises, match the histogram to its normal probability plot. All of the variables have been standardized (first subtract the mean, then divide by the standard deviation), so the units won’t be of any help. If you are uncertain based on these figures, generate the plots in R to check.

  a. The histogram for female biiliac (pelvic) diameter (bii.di) belongs to normal probability plot letter B.

  b. The histogram for female elbow diameter (elb.di) belongs to normal probability plot letter C.

  c. The histogram for general age (age) belongs to normal probability plot letter A.

  d. The histogram for female chest depth (che.de) belongs to normal probability plot letter D.

• Note that normal probability plots C and D have a slight stepwise pattern.
  Why do you think this is the case?

  Not sure… Continuous variables being rounded?

• As you can see, normal probability plots can be used both to assess normality and visualize skewness. Make a normal probability plot for female knee diameter (kne.di). Based on this normal probability plot, is this variable left skewed, symmetric, or right skewed? Use a histogram to confirm your findings.

qqnorm(fdims$kne.di)
qqline(fdims$kne.di)

Looks right-skewed.