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Educational Research. Chapter 7. Sampling. Sample – a portion of the population Population – larger group about which the generalization is made; any well-defined class of people, events, or objects Rationale: select a sample make observations of the sample

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### EducationalResearch

Chapter 7

Sampling

- Sample – a portion of the population
- Population – larger group about which the generalization is made; any well-defined class of people, events, or objects
- Rationale:
- select a sample
- make observations of the sample
- then generalize the findings to the population from which the sample was withdrawn
*In order to generalize, the individuals must be a representative cross-section of the individuals in the population

Sampling cont

Steps in Sampling

- Identify the target population
- Identify the accessible population
- Select a representative sample from the accessible population
- If the sample is representative, fairly safe in generalizing to the accessible population
- Much riskier to generalize to the target population (dependent on the similarity of the accessible population to the target population)

Sampling cont

- Probability Sampling – every element of the population has an equal and independent chance of being chosen
- Nonprobability Sampling – every element of the population does not have an equal and independent chance of being chosen – elements are not chosen by chance
- Types of Probability Sampling
- Simple random
- Stratified and proportional stratified
- Cluster
- Systematic

Probability Sampling

- Simple random sampling – does not absolutely guarantee that the sample will represent the population, but guarantees that any differences between the sample and the population are a function of chance and not the bias of the researcher (the characteristics of a small sample are more likely to differ from population than characteristics of a large sample)
- Steps:
- Define the population
- List all the members of the population
- Assign a distinct identification number
- Use a table of random numbers to choose

Probability Sampling cont

- Stratified sampling – divide the population into subgroups or strata – age or gender – then randomly select a specified number of subjects from each strata
- If interested in studying differences that exist among the strata – select equal amounts of individuals from each stratum
- If interested in the characteristics of the population, select subjects in proportion to the size of the stratum in the population = proportional stratified sampling
- Stratified sampling guarantees representation of defined groups in the population

Probability Sampling cont

- Cluster sampling - the unit chosen is not an individual, but a group of individuals who are naturally together. A common application is the use of intact classrooms
- The clusters included in your study need to be chosen at random from a population of clusters
- Once a cluster is chosen, all members of the cluster must be included in the sample
- If the number of clusters is small, there is a greater likelihood that sampling error is great

Probability Sampling cont

- Systematic sampling – take every Kth case from a list of the population; choices are not independent. Once the first case is chosen the remainder of the cases are automatically determined. If the original list is random (not alphabetical) then sample could be considered a good substitute for a random sample
- Steps:
- Decide how many subjects you need in sample (n)
- Because you know how many in population (N) divide N/n to determine the sampling interval (K)
- Select the first member randomly from the first (K) members of the list and then select every Kth member of the population

Nonprobability Sampling

- Nonprobability sampling – accidental, purposive, quota
- Accidental – involves using the available cases for the study; need to be cautious in interpreting the findings
- Purposive – also know as judgment – sample elements judged to be typical or representative, are chosen from the population
- Quota – involves selecting typical cases from diverse strata of a population; sample is a miniature approximation of the population with respect to the selected characteristics.

Sample Size

- Size of sample is determined by power calculations
- Refer to chart entitled “Sample Sizes” (S) Required for Given Population Sizes (N)
- Most important aspect of the sample is its representativeness

Sampling Error

- Sampling Error - is the difference between the population mean and the sample mean – it is beyond the control of the researcher
- If you draw several samples from the same population and compute the mean of each sample, the means would differ from one another and from the population mean
- If you draw every possible sample mean from the population, compute the mean for each sample – add them and divide by the number of samples – this will equal the population mean

Sampling Error cont.

- This variation among the means is due to sampling error associated with each random sample mean as an estimate of the population mean
- No sample will have a composition exactly like that of the population
- But if well selected and sufficiently large, chances are the sample will closely resemble the population

Sampling Bias

- Sampling bias is nonrandom and the fault of the researcher – for example, if you are interested in parent attitudes toward inclusion – you need to sample all types of parents – parents of children in special education and parents of children in general education
- If you get a small response rate from a survey – you might not be getting responses from people who represent different strata
- Sampling bias effects the validity of the study – all should be done to avoid sampling bias

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