1. Sampling
Population: The overall group to which the research findings are intended to apply
Sampling frame: A list that contains every “element” or member of the population
Sample: A subset of population “elements” or members
Once they’re in a sample each population member or “element” is called a “case”
Why do we sample?
To describe characteristics of a population, or test a hypotheses when measuring each member is too expensive or impractical
To test a hypotheses using inferential (probability) statistics

2. Sampling error Statistic
A mathematical description of any characteristic that can be measured; say, the mean (arithmetic average)
A mathematical way to describe the interplay between two or more characteristics; say, the correlation coefficient (r)
Summary statistic: A statistic that gives an overall measure; say, the mean
Population parameter
A statistic of the population; say, the mean
Sample statistic
Same, of a sample
Sampling error: Unintended differences between a population parameter and a sample statistic
Inevitable result of sampling
Try it out in class! Get population parameter for mean age. Sample, then compare.
These differences, or errors, decrease as the size of the sample increases
Rule of thumb
For populations of moderate size (up to 500 or so) sample size should be at least 30; for larger populations sample size should be larger

3. Sampling accuracy
Samples should accurately reflect, or represent , the population from which they are drawn
If a sample is representative, then we can generalize (apply, infer) our findings from the sample to the population
That’s why we’re studying “inferential statistics”
Warning: We can never generalize to other populations
There are various sampling techniques
Probability sampling: Each element or “case” in the population has exactly the same chance to be selected for the sample
“Gold standard” to which all sampling techniques aspire
If the sampling frame is 5, the first element’s probability of being selected is 1/5 (.20) on the first draw

4. Sample with or without replacement?
Sampling with replacement
Return each element to the population before drawing the next
This keeps the probability of being drawn the same but makes it possible to redraw the same element
If the sampling frame (population size) is 5, on the second and subsequent draws the probability of being drawn remains 1/5 (.20)
Sampling without replacement: During selection, drawn elements are not returned to the population
If the sampling frame (population size) is 5, on the second draw, each remaining element’s probability of being drawn is ¼ (.25). On the final draw it’s 1/1 (1.0)
In social science research sampling without replacement is by far the most common
Most sampling frames are sufficiently large so that as elements are drawn changes in the probability of being drawn are vey small

5. Probability sampling exercises
Every element has an equal chance of being selected
Data from
Jay’s correctional center
Sheba Wachtel, warden

6. Simple random sampling
Population: 200 inmates Mean sentence: 2.94 years
Draw a sample of 30 and compare the population parameter and sample statistic.
How much error is there?
A population “distribution”

7. Stratified random sampling
Divide population into strata (categories), then randomly sample from each
In proportionate sampling the number of elements drawn from each stratum is proportionate to that stratum’s representation in the population
Problem: if some strata have few elements their sample size may become unacceptably small unless we take very large samples from other strata
Property crimes: Mean sentence : 2.88
Violent crimes: 50 Mean sentence: 3.12
Draw proportionate samples and compare their statistics to the population.
How much error is there?

8. Using descriptive statistics to answer simple research questions
Does the gender of patrol officers affect cynicism?
Is there more likely to be a personal relationship between suspect and victim in violent crimes or in crimes against property?
Can training reduce officer cynicism?

9. Does the gender of patrol officers affect cynicism?
Stratified proportionate random sampling
Does the gender of patrol officers affect cynicism?
Sin City 200 patrol officers
150 male (75 %)
50 female (25 %)
randomly select 30 officers
expect 22.5 males
expect 7.5 females
Compare average cynicism scores
Is there a problem? (Hint: how many females in the sample?

10. Disproportionate sampling
Draw the same number of elements from all strata, at least thirty (30) regardless of a strata’s representation in the population
You are then free to compare the summary statistic, say, mean, between the strata
Keep in mind that you can’t combine the cases from these strata into a single sample, then use a characteristic, say, the mean, to represent the population
Why? Because the statistic will be skewed or biased in the direction of the strata that were oversampled

11. Sin City 200 patrol officers
Stratified disproportionate random sampling
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 scores
Note: don’t combine these into a single sample!

12. Sampling exercise - Sin City
Is there more likely to be a personal relationship between suspects and victims 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. Use proportionate and disproportionate techniques. Which is better? Why?

13. randomly select 30 cases (15% of the population)
Stratified proportionate random sampling
Is there more likely to be a personal relationship between suspect and victim in violent crimes or in crimes against property?
Sin City 200 crimes in 2004
50 violent (25 %)
150 property (75 %)
randomly select 30 cases (15% of the population)
(expect 7.5 violent – 25%)
(expect 22.5 property – 75%)
Compare proportions of these cases where suspects knew the victim

14. randomly select 30 cases from each category
Stratified disproportionate random sampling
Sin City 200 crimes in 2003
50 violent (25 %)
150 property (75 %)
randomly select 30 cases from each category
30 property
30 violent
Compare proportions within each where suspect and victim were acquainted
(Note: cannot combine results)

15. Jay’s cynicism reduction program
Does Jay’s goofy training program reduce officer 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?

16. Does Jay’s goofy training program reduce officer cynicism?
Stratified disproportionate random sampling
Does Jay’s goofy training program reduce officer cynicism?
population:
200 patrol officers
150 males (75%)
50 females (25%)
CONTROL
GROUP
Randomly Assign
25 Officers
CONTROL GROUP
EXPERIMENTAL
For each group, pre-measure dependent variable officer cynicism
Apply the intervention (adjust the value of independent variable – Jay’s program.)
NO YES YES NO
For each group, post-measure dependent variable officer cynicism
Compare within-group changes – what do they tell us?

17. Quasi-probability sampling
Systematic sampling
Randomly select first element, then choose every 5th, 10th, etc. depending on the size of the sampling frame (number of cases or elements in the population)
Problem: Sampling list that is ordered in a particular way could result in a non-representative sample
Cluster sampling
Method
Divide population into equal-sized groups (clusters) chosen on the basis of a neutral characteristic
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 not be so and affect outcomes!
Since not everyone in the population has an equal chance of being selected, there may be considerable sampling error

18. Non-probability sampling
Accidental sample
Subjects who happen to be encountered by researchers
Example – observer ride-alongs 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
Issues
Can your findings be “generalized” or projected to a larger population?
Are your findings valid only for those actually included in your samples?