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### Chapter Fifteen

Sampling and Sample Size

Sampling

- A sample represents a microcosm of the population you wish to study
- If the sample is representative of the population from which it is drawn, the researcher can have confidence in concluding that the results are generalizable to the entire population studied

The Rationale of Sampling

- Save time & money and yet get an accurate description of a population
- Poorly selected samples may misrepresent the population
- Literary Digest example Landon vs Roosevelt. George Gallop establishes his name by indicating reservations

Key Distinctions

- Population: the entire group one wishes to describe; it could be the student body at St. FXU, the province, the state, the country
- Sampling frame: the list from which a sample is selected
- Sample: those units (individuals) selected for a study
- Response rate: percentage of successfully contacted respondents who participate

Probability Sampling Techniques

- Simple random sample: each unit in the population has a equal chance of being selected.
- Process:
- number units
- table of random numbers or computer (SPSS) will do selection
- replacement units selected using the same process

Probability Sampling Cont.

- Systematic Sample: here the process is to give everyone an equal chance but process a little different.
- Process
- list, map, diagram as appropriate
- divide sample required into number on list to determine skip interval or sample interval
- random numbers used to begin randomly then every kth number selected

Probability Sampling Cont.

- Stratified Sample: sometimes to ensure an adequate representation of sub-groups, we use stratified samples, which provide random samples within sub-groups. For example:
- study of nursing graduates from different classes
- members of early, middle, late adolescent age group

Probability Sampling Cont. Note that within SPSS it is possible to weight cases to return the sample so it can represent the larger population

- Stratified Sampling proceed by:
- determine sample size needed for sub-groups
- obtain list for each sub-group
- using either simple random or systematic sampling select respondents

Probability Sampling Cont.

- Multi-Stage Area Sample: these are used when doing large populations such as states, provinces, or a whole country
- identify primary sampling units: select sample
- identify sub-units within selected units (city blocks, square kilometers etc.)
- identify households within sub-units: select sample
- within household select respondents

Non-Probability Sampling

- Non-probability samples do not provide an equal or a known chance of being selected
- Quota Sample: the parallel here is the stratified sample; a quota sample requires that a certain number be selected in each category--usually done on a first-come first included basis. Sampling stops when enough are included in each category

Non-Probability Sampling Cont.

- Convenience Sampling: purely convenience used to choose participants. Examples include using all those in attendance at a meeting/class; interviewing people in a mall clinic or doctor’s office

Non-Probability Sampling

- Snowball Sampling: also known as “referral sampling”.
- Used on hard to locategroups that one cannot obtain a list of the individuals who possess the attributes or phenomenon you wish to study; e.g. blind, those with some sort of disability, “closet” homosexuals, etc

Non-Probability Sampling

- Purposive sampling: uses the researcher’s knowledge of the population to hand pick the cases to be included
- common in qualitative studies
- useful when you are interested in understanding the experiences of certain segments of a population
- limitation is inability to assess representativeness of participants in relation to the population

Non-Probability Sampling

- Expert Sampling: a type of purposive sampling using the Delphi technique
- Researcher handpicks a group of participants because of their expertise in the study phenomenon
- A means to achieve experts’ consensus on an issue

Qualitative Sampling Techniques

- Interested in samples of participants who can share their interpretation of the experience with others
- Goal is understanding the meaning of the participants’ experience
- Typically not interested in generalizing their results
- Typically do not use probability sampling

Sample Size Determination

- Decide on confidence level--usually 95% level selected; this means that you will be 95% confident that the sample will be within a given range; 19 out of 20 times sample will be within a given range
- Choose major variable and key on that
- Determine precision needed: how precise do you need the estimate to be?

Non-Probability Sampling

- Compute sample size:
2

Reqd. Sample = Confidence limit * sd pop

Accuracy

Non-Probability Sampling

- Are there sufficient cases?
- Adjust Sample for Time and Cost factors
- Sample size and accuracy: to double accuracy you quadruple sample size

Power Analysis & Sample Size

- Power is the ability to detect real differences among variables
- Power consists of 4 elements: alpha or significance level, sample size, effect size, power
- If any 3 are known the fourth can be found using the power analysis formula

Elements of Power

- Alpha refers to the probability of making a Type I error (.05 or .01)
- Beta refers to the probability of making a Type II error
- Power of a statistical test = (1-beta) = 1-.20=.80 The standard for power is .80
- Effect Size is the strength of the relationship among the study variables

Determining Effect Size

- Literature Review (meta-analysis)
- Pilot Study
- Dummy Table Analysis
- Estimate on the Basis of Clinical Experience or Previous Research

Determining Sample Size

- Estimate the population effect size
- Review the literature to see if prior studies report the effect of the intervention
- Consult a table of sample size requirements in a statistic text to determine the # of participants per group for various effect sizes, powers & alpha or significant levels
- If no previous research is available estimate the effect size based on experience, intuitive knowledge, & literature

By Convention Effect Size in a 2-group Test of Means

- .20 for small effects
- .50 for medium effects
- .80 for large effects
- Most nursing studies can not expect effect sizes in excess of .50
- .20 to .40 effect size is a realistic expectation for nursing studies

Other Sampling Issues

- Sample size & accuracy - to double accuracy sample size must be quadrupled
- Sample size & confidence limits - to move from 95% to 99% multiply sample size by 1.73
- Impact of refusals
- Confirming representativeness

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