Sampling Methods & Survey Design Cheat Sheet

Key Facts

• In a simple random sample of size $n$ from a population of size $N$, every possible group of $n$ individuals has the same chance of being selected.
• The sampling fraction is $\frac{n}{N}$, where $n$ is the sample size and $N$ is the population size.
• In stratified random sampling, split the population into similar groups called strata, then take a random sample from each stratum.
• In cluster sampling, split the population into mixed groups called clusters, randomly choose some clusters, and survey everyone or many people inside those clusters.
• In systematic sampling, choose a random starting point and then select every $k$th person, where $k \approx \frac{N}{n}$.
• The response rate is $\frac{\text{number of responses}}{\text{number contacted}} \times 100\%$.
• For a sample proportion $\hat{p}$, an approximate margin of error is $2\sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}$ for a rough $95\%$ confidence estimate.
• Larger random samples usually reduce sampling variability because the standard error for a proportion is $\sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}$.

Vocabulary

Population

The entire group of individuals or items that a study wants to learn about.

Sample

A smaller group selected from the population to provide data for a study.

Simple Random Sample

A sample chosen so that every possible group of size $n$ has an equal chance of being selected.

Stratum

A subgroup of the population whose members share an important characteristic, such as grade level or age group.

Bias

A systematic problem in data collection that makes results consistently favor some outcomes over others.

Margin of Error

An estimate of how far a sample statistic, such as $\hat{p}$, may be from the true population value.