Lab 2: Descriptive statistics and estimation

With solutions

Author

Your Name Here

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# load datasets
load('data/famuss.RData')
load('data/nhanes.RData')
load('data/temps2.RData')

Descriptive statistics

The FAMuSS study recruited young adults to examine how genetic variation affects muscle strength gains from resistance training. We’ll use this dataset throughout.

Histograms

How old were participants when they enrolled in FAMuSS?

For numeric variables, hist() bins observations into intervals to show the shape of the distribution. The breaks argument controls the number of bins.

# extract age variable
age <- famuss$age

# default histogram
hist(age)

# more bins — finer detail
hist(age, breaks = 20)

# fewer bins — broader shape
hist(age, breaks = 5)

CautionYour turn 1 [L3]

How much did participants’ nondominant arm strength change over the course of the training program — was there consistent improvement?

Extract ndrm.ch (percent change in nondominant arm strength) from famuss and construct a histogram. Tinker with the breaks argument to find a setting that captures the shape well. Is the distribution skewed or symmetric?

# extract ndrm.ch variable
ndrm.ch <- famuss$ndrm.ch

# construct histogram
hist(ndrm.ch, breaks = 20)

The distribution is right-skewed. Around 20 breaks captures the shape well.

Summary statistics

Beyond shape, we often want a few numbers to summarize where the distribution is centered and how spread out it is. summary() returns the five-number summary plus the mean in one call.

# five-number summary + mean for age
summary(age)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
   17.0    20.0    22.0    24.4    27.0    40.0
CautionYour turn 2 [L3]

Compute summary statistics for ndrm.ch using summary(). Store the result as ndrm.summary.

What is the best way to characterize the typical percent change in strength? (Hint: look at your histogram from Your turn 1.)

# five-number summary + mean for ndrm.ch
ndrm.summary <- summary(ndrm.ch)
ndrm.summary
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
   0.00   30.00   45.50   53.29   66.70  250.00

The distribution is right-skewed, so the median is the better measure of center. The median percent change in nondominant arm strength was about 15%.

Estimating a population mean

The goal here shifts from describing a sample to making inferences about a broader population. The NHANES survey is designed to be representative of the U.S. adult population.

What is the mean total cholesterol level among U.S. adults?

t.test() computes a point estimate and standard error for a population mean in one step.

# extract total cholesterol
totchol <- nhanes$totchol

# run one-sample t-test — stores the full result
totchol.tt <- t.test(totchol)

# point estimate (sample mean)
totchol.tt$estimate
mean of x 
 5.042938 
# standard error
totchol.tt$stderr
[1] 0.01906042

Interpreted as a point estimate of the population mean:

Mean total cholesterol of U.S. adults is estimated to be 5.04 mmol/L (SE 0.019).

CautionYour turn 3 [L4]

It’s long been claimed that normal human body temperature is 98.6°F — but is that accurate?

The temps dataset comes from a study that set out to answer exactly this question. Use t.test() on body temperature (body.temp) and store the result as bodytemp.tt. Print the point estimate and standard error. Write a one-sentence interpretation of the point estimate.

# extract body temperature
bodytemp <- temps$body.temp

# run t-test
bodytemp.tt <- t.test(bodytemp)

# point estimate and standard error
bodytemp.tt$estimate
mean of x 
 98.24923 
bodytemp.tt$stderr
[1] 0.06430442

Mean body temperature is estimated to be 98.25°F (SE 0.064).

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