1. Describe sampling techniques.
   • Understand key terms
   • Describe how to collect data using a random sample
   • Understand the differences between simple random, stratified, cluster, and systematic sampling.

How do we get samples?

• We want a sample that represents our population.
• Representative samples reflect the relevant characteristics of our population.
• In general, we get representative samples by selecting our samples at random and with an adequate sample size.

A non-representative sample is said to be biased.

Ex: A sample of chihuahuas to represent all dogs.

These can be a result of convenience sampling, choosing a sample based on ease.

Common sources of bias in our daily lives:

• Anecdotal evidence is data based on personal experience or observation.
  • Typically this consists of only one or two observations and is NOT representative of the population.
• Availability bias is your brain’s tendency to think that examples of things that come readily to mind are more representative than is actually the case.

• We avoid bias by taking random samples.
• One type of random sample is a simple random sample.
  • We can think of this as “raffle sampling”, like drawing names out of a hat.
  • Each case (or each possible sample) has an equal chance of being selected.
  • Knowing that A is selected doesn’t tell us anything about whether B is selected.
• Instead of literally drawing from a hat, we usually use a random number generator from a computer.

• In a stratified sample, we break the population down into groups called strata
  • Strata are based on characteristics we think might be relevant to our study.
  • Individuals or items within a strata should be fairly similar to each other.
  • We then take a random sample from each strata.
    • This ensures we have representation from each group.

• A local politician believes men and women will vote differently on an upcoming ballot measure.
• She goes into the community and randomly samples 50 men and 50 women to ask for their thoughts on the ballot measure.

We can also use stratified sampling to make sure that the proportion of items in each group in the population matches the proportions in our sample.

• A local high school is 29% freshmen, 27% sophomores, 24% juniors and 19% seniors.
• They want to collect a sample of 100 students using class level as strata.
• Since some class levels have more students than others, they set their strata to match:
  • 29 freshmen (29% of their sample), 27 sophomores, 24 juniors, and 19 seniors.

This approach to stratified sampling can also help us ensure that small strata are adequately represented in our study.

• Suppose we are doing some drug development research for a particular disease and know that a very small part of our population develops an especially severe form of the disease.
  • In order to make sure those individuals are represented in our sample, we could treat disease severity as strata.
  • Motivation: in a simple random sample, we might miss those individuals entirely!

• In a cluster sample, we break the population into clusters.
  • Each cluster is similar to the population (and so the clusters are all similar to each other).
  • We then take a random sample of clusters and measure all items or individuals within each of those randomly selected clusters.

• An airline wants to survey people who take its international flights from the United States to Asia.
• They randomly select 10 of these flights and give the survey to every individual on each of those 10 flights.

• A farmer wants to know something about the plants in their fields.
• They randomly select 5 of their fields and examine all of the plants in each field.

The potential downside to cluster sampling is that there may be factors that make clusters meaningfully different from one other.

• Say our airline randomly samples flights to Asia.
  • It’s likely the people going to Vietnam are different from the people going to the Philippines who are different from the people going to India.
  • That is, not every flight to Asia is representative of the entire population of individuals who fly to Asia.

• In a systematic sample, we choose some starting point in our population and then collect every \(k\)th observation.

1. If I have a list of student ID numbers for every student at Sacramento State, I could generate a sample of students by selecting every 100th number.
2. Suppose we want to examine some machine part coming off on an assembly line. We collect a sample by pulling every 20th part off of the assembly line for additional testing.

One potential issue with systematic sampling is that there may be some pattern in the data.

• Suppose a machine on an assembly line is oiled after producing 20 components, and its performance degrades steadily after it is oiled.
• If we select every 20 components, we match this periodicity and fail to capture a representative sample of components.