Sampling Sampling Distributions

Sample is subset of population used to infer something about the population. Probability – know the likelihood of selection Nonprobability – likelihood unknown

Random sampling: each member of population has an equal and independent chance of being selected. Equal – no bias of one person chosen rather than another Independent – choice of one person does not influence choice of next

RANDOM and HAPHAZARD are NOT the same thing. True random sampling is a very systematic structured selection

Simple random Define population List members of population Assign numbers to each member Random selection (eg random number table) If you have the whole population this works

Systematic sampling Select every kth value but have random start point Population list in random order Does not have equal chance of selection

Stratified random selection If some characteristic of the population needs to considered – eg gender, religion Need a profile of the population Know proportions in each category and select sample to match BUT must use random selection

Cluster sampling Units of individual selection at random Eg dorm, clinic, school Not independent Bias possible

Nonprobability sampling Convenience – very common Quota – selects profile but not random selection – first 10 sign up…

Other samples Matched – precision match (eg twins) Range – categorize then assign Cohort samples – common in development studies

Two factors count Random selection Size of sample

Landon vs FDR (1936) Digest Predict election Gallup Predict Digest Gallup predict election Result 43% 10 million surveys (2.4 m) 44% % 50,000 62% FDR

When a selection procedure is biased taking a large sample does not help. It just repeats the same mistake over and over.

Sampling Distribution of Means The distribution of sample means is the collection of all the possible random samples of a particular size (n) that can be obtained from a population. in probability terms we have all possible outcomes and can determine the probability of any one outcome the sample means clump around the population mean (as you would expect if the samples are representing the population)

Central limit theorem states: For any population with mean μ (mu) and standard deviation σ (sigma), the distribution of the sample means for a sample size n will approach a normal distribution with a mean μ and standard deviation of σ/√n (standard error) as n approaches infinity.

What does it mean? for any population the distribution of sample means will approach normal ( the original population does not need to be normal) the distribution of sample means rapidly approaches n>30 gives a good approximation weblink

Standard Error The difference between one sample mean and the population mean. σ/√n What influences standard error? Population standard deviation – the closer your sample is clustered around the mean the closer it will be to estimating the population mean. Sample size – generally the larger the sample the more representative.

Histogram consistent Tues Stroop Time (seconds) frequency Mean = 19.6

N=2 One sample Mean = samples Mean = samples Mean =19.97

N=4 One sample Mean = samples Mean = samples Mean =19.56