Sample surveys Example: Questionnaire about eating habits. I
A subgroup of a large population is questioned on a set of topics.
I
No intervention or manipulation of the respondents, simply asked to answer some questions.
Randomized experiments Measures the effect of manipulating the environment in some way. Example: Placebo vs aspirin against heart attack. I
Randomized experiment = manipulation is assigned to participants on a random basis.
I
Explanatory variable = the feature being manipulated.
I
Response variable = outcome of interest.
I
Randomization helps to make the groups approximately equal in all respects except for the explanatory variable.
Observational studies Example: Effect of marijuana on college grades. I
Manipulation occurs naturally, not imposed.
I
Cant assume the explanatory variable is the only one responsible for any observed differences in the response variable.
I
Case-control study attempts to include an appropriate control group.
I
Sometimes results more readily extend to the real world than in an experiment no artificial manipulation.
Meta-analyses Example: Multiple studies on effect of a drug. I
Quantitative review of a collection of studies all done on a similar topic.
I
Combining information can lead to emergence of patterns or effects not readily seen in the individual studies.
I
More on meta-analyses in Chapter 25.
Case studies Example: Cancer miracles. I
In-depth examination of one or a small number of individuals.
I
Descriptive and do not require statistical methods.
I
Generally cant be extended to any person or situation other than the one studied.
Example I
Observational study http://www.ncbi.nlm.nih.gov/pubmed/10376617
I
Observational case-control study http://www.biomedcentral.com/1471-2458/1/2
I
Case study http://www.time.com/time/health/article/ 0,8599,1721109,00.html
Definitions I
Unit: single individual or object to be measured e.g. person
I
Population: entire collection of units e.g. everyone in the world
I
Sample: collection of units we actually measure e.g. 100 students
I
Sampling frame: list of units from which we choose sample e.g. phone book
I
Sample survey: measurements taken e.g. questionnaire
I
Census: survey of everyone
Why is sampling good? I
Margin of error
I
Sampling may destroy units
I
Speed
I
Accuracy
Margin of error We ask 1500 people whether they prefer strawberry or chocolate icecream. The results say 80% prefer chocolate. How sure can we be? I
When we have a sample of n people,
I
randomly from the whole population,
I
the population is much larger than the sample,
I
we ask a question/measurement with only 2 options
I
we get an estimate of s%,
Then we can be pretty sure (about 95% sure) that the true percentage is between s − √1n and s + √1n . The quantity √1n is called the margin of error.
Sampling may destroy units Examples: Firecrackers, blood samples.
Speed Asking 1500 people is much quicker than everyone!
Accuracy Few interviewers are trained uniformly well.
Sampling methods I
Simple random sampling
I
Stratified random sampling
I
Cluster sampling
I
Systematic sampling
I
Random dialing
I
Multistage sampling
Simple random sampling Everyone in the population available. Select some of them according to a probability sampling plan. Example: There are 6 of you and you need to decide who has to clean the toilet. How would you decide randomly? How about if you were 20? In general, use random numbers. Need to make sure people do what they have to!
Stratified random sampling Divide population in strata and do simple random sampling within each stratum. Advantages: I
Have individual estimates for each stratum.
I
If variable measured gives more consistent values within each strata than within population, can get more accurate estimates of population values.
I
If strata are geographically separated, may be cheaper to sample them separately.
I
May use different interviewers within each strata.
Cluster sampling Divide population into groups (clusters), take a random sample of clusters and measure only the selected clusters. Advantages: I
need only a list of clusters, not a list of all individual units.
Example: Sample students living in a dorm at a college. The college has 30 dorms, each dorm has 6 floors. The total 180 floors form the clusters. Take a random sample of floors and measure everyone on those floors.
Systematic sampling Divide population list into as many consecutive segments as you need, randomly choose a starting point in the first segment, then sample at that same point in each segment. Example: I
List of 5000 names, want a sample of 100.
I
Divide the list into 100 consecutive segments of 50.
I
Randomly choose a starting point in the first 50 names.
I
Then sample every 50th name after that.
Random dialing Results in a sample that approximates a simple random sample of all households in the U.S. that have telephones. Procedure: I
List all possible exchanges (area code + next 3 digits).
I
Use white pages to approximate proportion of all households in country that have each exchange.
I
Use computer to generate a sample with approximately the same proportions.
I
Repeat above to sample banks (next 2 digits)
I
Computer randomly generates last two digits to complete the phone number.
Multistage sampling Sampling plan that uses a combination of sampling methods in various stages. Example: I
Stratify by region of the country; then
I
stratify by urban, suburban, and rural; then
I
choose a random sample of communities within those strata.
I
Divide those communities into city blocks or fixed areas, as clusters, and sample some of those.
I
Everyone on the block or within fixed area may then be sampled.
