Learning by sampling

In many circumstances, there’s simply no feasible way to gather data about everyone in a population.
- For example, the Department of Water & Power (DWP) wants to determine how much water people in Los Angeles use to take a shower. They’ve created a survey to pass out to collect this information.
- Write down two reasons why getting everyone in Los Angeles to fill out the survey would be difficult. Also, write a sentence why the DWP might consider using a sample of households instead.
In this lab, we’ll learn how sampling methods affect how representative a sample is of a population.

Loading a population

In previous labs, we used the cdc data as a sample for young people in the United States.
- In this lab, we’ll consider these survey respondents to be our population.
Load the cdc data into R and fill in the blanks to take a convenience sample of the first 50 people in the data:

s1 <- slice(____, 1:____)

A convenience sample is a sample from a population where we collect data on subjects because they’re easy-to-find.
Using your convenience sample, create a bargraph for the number of people in each grade.
- Do you think the distribution of grade for your sample would look similar when compared to the whole cdc data?
- Which groups of people do you think are over or under represented in your convenience sample? Why?
Create a bargraph for grade using the cdc data.
- Compare the distributions of the cdc data and your convenience sample and write down how they differ.

Fill in the blanks below to create a sample by randomly selecting 50 people in the cdc data, without replacement. Call this new sample s2:

___ <- sample(___, size = ___, replace = ___)

Write a sentence that explains why you think the distribution of grade for this random sample will look more or less similar to the distribution from the whole cdc data.
- Create a bargraph for grade based on this random sample to check your prediction.

Create bargraphs for grade based on each of the following sample sizes: 10, 100, 1,000, 10,000.
- Compare each distribution to that of the population.
How do the distributions change as the size of the sample increases? Why do you think this occurs?
tally() the proportion of grades for your convenience sample and all your random samples.
- Which set of proportions looks most similar to the proportions of the population?

The mean, or proportion, from a random sample might not always be closer to that of the true population when compared to a convenience sample.
However, as sample sizes get larger:
- Random samples will tend to be better estimates for the population.
- With convenience samples, this might not be the case.
Write down a reason why estimates based on convenience samples might not improve even as sample size increases.