COB 191 Chapter 7

Sampling

Selecting a subset of a population to make inferences about the whole

Reasons for sampling

Less time consuming less costly less cumbersome more practical than a census

Nonprobability sample

Items chosen without regard to probability of selection

Probability sample

Items chosen based on known probabilities

Simple random sample

Every individual has an equal chance of being selected

Sampling with replacement

Selected items are returned to the population before next draw

Sampling without replacement

Selected items are not returned to the population

Systematic sample

Select every kth individual after a random start

k value in systematic sampling

k equals population size divided by sample size

Stratified sample

Population divided into strata and random samples taken from each

Cluster sample

Population divided into clusters and random clusters are selected

Convenience sample

Sample chosen based on ease of access

Judgment sample

Sample chosen based on researcher’s expertise

Quota sample

Sample reflects population proportions but is non-random

Coverage error

Some groups excluded from the sampling frame

Nonresponse error

Differences between respondents and non-respondents

Sampling error

Variation between different samples

Measurement error

Error due to poor question design or data collection

Sampling distribution

Distribution of a statistic from all possible samples of a given size

Sampling distribution of the mean

Distribution of sample means

Sampling distribution of the proportion

Distribution of sample proportions

Population mean (μ)

Average of the population

Sample mean (x̄)

Average of a sample

Standard error of the mean

Standard deviation of the sampling distribution of the mean

Standard error formula (mean)

Population standard deviation divided by square root of sample size

Central Limit Theorem

Sample means become approximately normal as sample size increases

Normal distribution condition CLT

n greater than or equal to 30 if population not normal

Unbiased estimator

Sample mean equals population mean on average

Z-score for sample mean

Measures how far sample mean is from population mean in standard errors

Sample proportion (p̂)

Proportion of successes in a sample

Population proportion (p)

True proportion in the population

Standard error of proportion

Square root of p times 1 minus p divided by n

Normality condition for proportion

np greater than or equal to 5 and n(1-p) greater than or equal to 5

Z-score for sample proportion

Measures how far sample proportion is from population proportion

Larger sample size effect

Reduces standard error and variability

Cluster sampling advantage

More cost effective

Stratified sampling advantage

Better representation of population

Simple random disadvantage

May not represent population characteristics well