Definitions Population: the entire group to which we wish to project our findings Sample: the subgroup that is actually measured Unit of analysis: that which “contains” the variables under study Case: single occurrence of a unit of analysis Coding: assigning a measurement to a variable

Sampling Population: Every member, “case” or element of the group to which your findings are intended to apply –Sampling frame: A list that contains each element Sample: A subset of “cases” or elements selected from a population

Sampling error Differences between the characteristics of the sample and the population Decreases as size of sample increases Rule of thumb: number of cases in the smallest group or subgroup to be separately measured, tested or compared should be at least 30

Representative sampling Selecting members so that characteristics of the sample accurately reflect the characteristics of the population –Purpose: To be able to generalize from the sample to the population –Limitation: Can only generalize to the population from which the sample was drawn

Probability sampling Each element or “case” in the population has an equal chance to be selected and become a part of the sample. –If the sampling frame is 5 and we draw two from a hat, each element’s probability of being selected is 2/5 (.20) on the first draw. Sampling with replacement: During selection, drawn elements are returned to the population. This keeps the probability of any element being drawn the same but makes duplicate draws possible. –On the second draw, each remaining element’s probability of being drawn is 1/5 (.20).

Sampling without replacement: During selection, drawn elements are not returned to the population –On the second draw, each remaining element’s probability of being drawn is ¼ (.25). Sampling without replacement is most common since most sampling frames are sufficiently large so that as elements are drawn, changes in probability are small

Probability sampling techniques Simple random sampling: Each element and combination of elements has the same chance of being selected Bring out the chips!

Stratified random sampling: Divide population into categories (strata) and randomly sample within each –Proportionate: Number of elements in each category is proportionate to that category’s representation in the population.

Does the cynicism of female and male patrol officers differ? Sin City 200 patrol officers 150 male (75 %)50 female (25 %) randomly select 30 officers expect 22.5 malesexpect 7.5 females Compare average cynicism score within each strata Is there a problem? Stratified proportionate random sampling

Disproportionate sampling: Randomly drawing a disproportionate number of elements from a specific strata whose overall representation is low.

Does the cynicism of female and male patrol officers differ? Sin City 200 patrol officers 150 male (75 %)50 female (25 %) randomly select 30 cases from each category 30 males 30 females Compare average cynicism score for each strata (Note: cannot combine results to get department score) Stratified disproportionate random sampling

Sampling exercise, Sin City Research question: Is there more likely to be a personal relationship between suspect and victim in violent crimes or in crimes against property? You have full access to crime data for “Sin City” in These statistics show there were 200 crimes, of which 75 percent were property crimes and 25 percent were violent crimes. For each crime, you know whether the victim and the suspect were acquainted (yes/no). 1. Identify the population. 2. How would you sample? 3. Would you stratify? How? 4. Do it two ways – using proportionate and disproportionate techniques. Which is better? Why?

Is there more likely to be a personal relationship between suspect and victim in violent crimes or crimes against property? Sin City 200 crimes in violent (25 %)150 property (75 %) (expect 7.5 violent – 25%)(expect 22.5 property – 75%) randomly select 30 cases (15% of the population) Compare proportions of these cases where suspects knew the victim Stratified proportionate random sampling

Is there more likely to be a personal relationship between suspect and victim in violent crimes or crimes against property? Sin City 200 crimes in violent (25 %)150 property (75 %) randomly select 30 cases from each category 30 violent 30 property Compare proportions within each where suspect and victim were acquainted (Note: cannot combine results) Stratified disproportionate random sampling

Jay’s cynicism reduction program Hypothesis: Training reduces cynicism The Anywhere Police Department has 200 patrol officers, of which 150 are males and 50 are females. Jay wants to conduct an experiment using control groups to test his program. 1. Identify the population. 2. How would you sample? 3. Would you stratify? How? 4. Is it better to use proportionate or disproportionate techniques. Why?

population: 200 patrol officers 150 males (75%)50 females (25%) Apply the intervention (adjust the value of independent variable – Jay’s program.) NO YES YES NO CONTROL GROUP Randomly Assign 25 Officers CONTROL GROUP Randomly Assign 25 Officers EXPERIMENTAL GROUP Randomly Assign 25 Officers EXPERIMENTAL GROUP Randomly Assign 25 Officers For each group, pre-measure dependent variable officer cynicism Stratified disproportionate random assignment Does Jay’s Cynicism reduction program work? Hypothesis: Training reduces cynicism For each group, post-measure dependent variable officer cynicism Compare within-group changes – do they support the hypothesis?

Systematic sampling: Randomly select first element, then choose every 5 th, 10 th, etc. depending on the size of the frame. –Problem: Sampling list that is ordered in a particular way could result in a non-representative sample Cluster sampling: Divide population into equal-sized groups (clusters) chosen on the basis of a neutral characteristic, then draw a random sample of clusters. The study sample contains every element of the chosen clusters. –Often done to study public opinion (city divided into blocks) –Rule of equally-sized clusters usually violated –The “neutral” characteristic may wind up being an extraneous variable and affect outcomes! –Since not everyone in the population has an equal chance of being selected, there will be sampling error Quasi-probability sampling

Nonprobability sampling Accidental sample: Subjects who happen to be encountered by researchers –Example – observer ridealongs in police cars Quota sample: Elements are included in proportion to their known representation in the population Purposive/“convenience” sample: Researcher uses best judgment to select elements that typify the population –Example: Interview all burglars arrested during the past month