wek 6 - case selection: large-n and evolution of random sampling - poli 110

what is average error?

• average absolute value of how far off a poll is from the true value (ie: vote)

what is bias?

• prejudice in favor of or against one thing, person, or group compared with another, usually in a way considered to be unfair.

  • polling average vs true value (ie: vote)

what is sampling?

• all of these (quite accurate) estimates are based on samples which are subsets of units of observation taken from a population of interest

  • ie: % of all US voters intending to vote DJT in 2020

• researchers do not care about simple statistics in and of themselves, rather they care about populations

• as with in the more general case of hypothesis testing, we want to make an inference about a broader population parameter from the more limited information provided by a sample statistic

  • how good inference is depends on the sample that was chosen

what is a sampling error? → equation with example

population parameter = sample statistic (what we find in our sample) + random sampling error (uncertainty introduced by the sampling process) + systematic sampling error (biases in how units are sampled from the population

what is systematic sampling error?

• large sample sizes are great, but they are meaningless if the same is not representative of the population of interest

what is a sampling frame?

• list or quasi list of units composing a population from which the sample is selected

what is quota sampling?

• choosing subjects based on knowledge of the characteristics of the population being sampled

  • selects ppl such that the sample will match the population on a set of relevant characteristics

    • urban v rural, female v men etc

what is probability sampling?

• involves the selection of a random sample from a list containing the names of everyone in the population being sampled

  • randomly picking a selection from a list

• the key property of probability sampling (for our purposes) is that, because each unit has an equal probability of selection, the sample…

  • is representative of the broader population in expectation

  • will bring about increasingly precise estimations of population parameter as sample size increases

can you define random sampling error?

• random sampling error = variation component → how much variation in the population being measured/sample size component → size of sample

  • larger sample size → reduces marginal room for error

• ppl are happy with 3-4% margin of error → thats why most surveys are done with 1500 ppl

what is “in-fact representativeness”

• a given sample yields exactly the population parameter of interest

what is “in expectation representativeness”?

• sampling distribution centres on the population parameter

what is a confidence interval?

• knowledge of the sampling distribution allows us to quantify uncertain around an estimate due to random sampling error

  • ie: as of a probability survey of 3000 canadians conducted in feb 2024, trudeaus favourability was 24% (estimate) +/- 2.0 (margin of error → p) , 19/20 times

what are some questions to ask based on confidence intervals?

• what happens if we increase sample size?

• what if we want to be 99% instead of 95% certain?

• what if we want to be 50% instead of 95% certain?

how is measurement error and sampling error similar?

• both start with data we generate will imperfectly map onto the truth we want to understand

• errors can be generated by both random and systematic processes

  • systematic biases: measurement bias v systematic sampling error

  • randomness: random measurement error v random sampling error

• in both cases, randomness leads to imprecise estimate that are nevertheless accurate in expectation

• in both cases, systematic biases lead to estimates that are consistently high or low, versuses the truth

how is measurement error and sampling error different?

• they are different in the sense that the source of error varies

  • with measurement, error occurs as function of response to a measurement that is consistently applied across units of observation

  • with sampling, error occurs because some units of observation are more likely to be sampled than others