1. MA151 Lecture 2: Sampling methods
Grazyna Badowski
University of Guam

2. Population and sample
Population is the entire collection of subjects of interest in a study. You need to specify clearly the population.
Sample is the smaller group from the population on which the study collects data.

3. Sample
Sample should be representative of population. The distribution of a sample should be similar to the distribution of the population.
A sample that does not represent the population in some important way is said to be biased.
How do you choose a representative sample?

4. Theoretical vs. accessible population
Theoretical population is the population you would like to generalize your results to. And usually it is not the population that will be accessible to you.
Source:

5. Sampling Frame
The listing of the accessible population from which you'll draw your sample is called the sampling frame. Examples: telephone book, voters’ registration, list of students, patients’ registry

6. Probability Sampling Methods
Simple Random Sampling
Stratified Random Sampling
Cluster Sampling
Systematic Sampling
Multistage Sampling

7. Probability Sampling Methods
A probability sampling method is any method of sampling that utilizes some form of random selection. In order to have a random selection method, you must set up some process or procedure that assures that the different units in your population have equal probabilities of being chosen.

8. Simple Random Sampling
Each possible sample of size n has the same chance of being selected.
We need the list of all subjects in the population - sampling frame, and use random numbers to draw sample.
SRS might not get good representation of subgroups in a population.
SRS is simple and easy to explain, it is reasonable to generalize the results. But we might not get goo

9. Stratified Random Sampling
First divide the population into separate groups, called strata, and then select a SRS from each stratum.
Source:

10. Stratified Sampling – cont.
It is useful when the strata are groups that the study will compare. For example, your strata could be ethnicity. The sampling is proportional if the proportions of the sample chosen are the same as those in the entire population.

11. Stratified Random Sampling Advantages
Individual estimates for each stratum.
Can get more accurate estimate of parameter if variable is less variable within each strata than within the whole population.
Can use disproportional sampling when one stratum small. (weights)
Use different interviewers within each strata.

12. Cluster Sampling
The population is divided into groups called clusters, we select a random sample of clusters and measure only those clusters.
Advantage: you only need a list of clusters, instead of a list of all individuals. If each cluster fairly represents the full population, cluster sampling will give us an unbiased sample.

13. Cluster vs. Stratified Sampling
We stratify to ensure that our sample represents different groups in the population; strata are homogeneous, but differ from one another.
Clusters are alike, each heterogeneous and resembling the overall population. We select clusters to make sampling more practical/affordable.
For example, random sample of city blocks and then sample every family on the block.

14. Systematic Sampling
We draw a sample by selecting individuals systematically. For example you might choose every 50th person on a list. You start with randomly selected individual.
Subjects have to be randomly ordered.

15. Multistage Sampling Combined sampling methods.
Example: sampling students in grade schools
1. Stratified sample from national school districts.
2. SRS of schools within districts.
3. SRS of classes within schools.

16. Difficulties in Sampling
Wrong sampling frame.
An SRS from an incomplete sampling frame introduces bias because the individuals included may differ from the ones not in the frame. People in prison, homeless, students, travelers.

17. Difficulties in Sampling
2. Not reaching selected individuals/low response rate. The problem is that those who don’t respond may differ from those who do. It is better to put resources into getting a smaller sample and ensure a high response rate. (revisit)

18. Disasters Voluntary response sample.
viewers’/listeners’ opinions
Convenience sampling: include individuals who are convenient.
streetcorner interview

19. Literary Digest Poll of 1936
In 1936, the Literary Digest, predicted that Landon would beat FDR in that year's election by 57 to 43 percent.  The Digest mailed over 10 million questionnaires to names drawn from lists of automobile and telephone owners, and over 2.3 million people responded . At the same time Gallup sampled only 50,000 people and predicted that Roosevelt would win.  Roosevelt won with 62% of the vote. 
Two mistakes:
sampling frame wrong
Low response rate, only 23%
Telephone lists, club and associations membership

20. Biases in Random Samples
Randomization doesn’t correct for certain problems with sampling
Bias 1: Undercoverage: some groups in the population are left out of the process of choosing the sample
Bias 2: Nonresponse: sampled individuals can not be contacted or do not cooperate
Eg presidential polls
Low response rate: less than 25% of responded
Undercoverage of poorer demographics: sample of voters relied heavily on lists of automobile and telephone owners, which were generally more affluent voters
Well, at least we learned from those mistakes, right?

21. Nonprobability Sampling
Convenience (most available)
Purposive sampling
Quota sampling (setting quotas and then using convenience sampling to obtain those quotas; similar to stratified )
Snowball sampling
the researcher specifies the characteristics of the population of interest and then locates individuals who match those characteristics). For example, you might decide that you want to only include "boys who are in the 7th grade and have been diagnosed with ADHD" in your research study. You would then, try to find 50 students who meet your "inclusion criteria" and include them in your research study.

22. Experimental psychology example
Mostly used convenience samples. Who?
According to Joseph Henrich (Uof B.C.), most undergraduates are WEIRD and not representative of humanity as a whole.
Western, Educated, Industrialized, Rich and Democratic
He found a random American undergraduate is about 4,000 times more likely than an average human being to be the subject of such a study.
He did analysis of leading psychology journals

23. Source: The Economist, May 26th, 2012

24. More Potential Problems with Surveys
Response Bias: respondents may not answer truthfully to survey questions
Illegal or unpopular behavior such as drug usage
Controversial topics such as teen sexual activity
Race or gender of interviewer can influence answers about race or gender-related questions
Respondents often have trouble remembering past events eg. yearly nutrition and health surveys

25. More Potential Problems with Surveys
Wording of questions can be confusing or intentionally lead the respondent
Do you favor a ban on disposable diapers?
It is estimated that disposable diapers account for less than 2% of the trash in today’s landfills. In contrast, beverage containers, third-class mail and yard wastes account for 21% of the trash in landfills. Given this, would it be fair to ban disposable diapers?
Complicated multi-part forms that require lots of skipped questions lead to a drop off in response