Chapter 13: Samples and surveys

STAT 1010 - Fall 2022

Learning outcomes

  • Know basic sampling vocabulary.
  • Understand why randomization is important and describe different sampling methods
  • How to sample in R
  • Know pitfalls related to sampling



  • survey : researchers ask questions of a subset of people who belong to a population.
  • this subset of the population that reserachers ask is called the sample
  • a sample is representative if it seeks to accurately reflect the characteristics of the larger group
  • bias occurs in sampling when samples systematically omit a portion of the population
  • random samples, where each unit has an equal probability of being choosen, are important

Predictive policing

  • Research question - Can police use crime data from disparate sources to anticipate and prevent future crime?
  • population - all crime
  • sample - arrests recorded in police database
  • Is this a random sample?
  • arrests is a surrogate measurement because crime is hard to track

Predictive policing

  • for arrests to occur police must be present
  • some areas are over policed, so have more arrests
  • this algorithm sends police to those areas
  • read more here
  • use census data to predict crime instead of arrests, we may do better


  • sample everyone in the population
  • this is often difficult because some individuals are hard to locate, and these people may have certain characterisitics that distinguish them from the rest of the population
  • Populations move so getting a perfect measure is hard.
  • A census may be more complex than sampling

Landon vs Roosevelt

  • Literary digest - correctly predicted presidential elections from 1916 - 1932 with mock ballots
  • 1936 election
    • 10 million ballots
    • Landon win by landslide with 57%
  • 10 million names and addresses in 1936
  • poor people were unlikely to have phones, so they over sampled the wealthy
  • Gallup predicted a Roosevelt win
  • weighting can be used to correct biased samples



  • tasting is analogous to exploratory analysis
  • stirring helps ensure that the taste is representative because it randomizes
  • if we add ingredients and don’t stir we may get a biased sample
  • if we generalize and decide that it needs more salt, that’s an inference

Sampling frame

  • lists every member of the population of interest
  • can be complex to identify
  • sample from registered voters, but really want people who will vote
  • hypothetical populations are more complex
  • a brewery must sample hops across farmers, and different geographic regions prior to formalizing brewing

Simple random sample

Stratified sampling

Cluster sample


  • Randomly select cases from the population, where there is no implied connection between the points that are selected.

  • Strata are made up of similar observations. We take a simple random sample from each stratum.

  • Clusters are usually not made up of homogeneous observations. We take a simple random sample of clusters, and then sample all observations in that cluster. Usually preferred for economical reasons.

Sampling in R

data %>% 
  slice_sample(n = sample_size)

# Stratified sampling
data %>% 
  group_by(strata) %>% 
  slice_sample(n = size_from_each_strata)

# Cluster sampling
random_cluster <- slice_sample(data$cluster, 
                               n = no_of_clusters)

Not great sampling methods

  • voluntary response
  • convenience sampling - asking friends or families feedback about your product


  • sampling frame match population
  • sampling method
  • rate of nonresponse - how many people did not answer
  • wording of the question - do you like this class
  • interviewer affects - you are more likely to tell Patrick that you do not like this course than me
  • survivor bias - we don’t know how students who did not stay in this class feel about it