Wednesday, May 30, 2007

sampling: final and initial sample size determination

Chapter 12

The statistical approaches to determining sample size are based on confidence intervals. These approaches may involve the estimation of the mean or proportion. When estimating the mean, determination of sample size using a confidence interval approach requires a specification of precision level, confidence level, and population standard deviation. In the case of proportion, the precision level, confidence level, and an estimate of the population proportion must be specified. The sample size determined statistically represents the final or net sample size that must be achieved. In order to achieve this final sample size, a much greater number of potential respondents have to be contacted to account for reduction in response due to incidence rates and completion rates.

Non-response error arises when some of the potential respondents included in the sample did not respond. The primary causes of low response rates are refusals and not-at-homes. Refusal rates may be reduced by prior notification, motivating the respondents, incentives, proper questionnaire design and administration, and follow-up. The percentage of not-at-homes can be substantially reduced by callbacks. Adjustments for non-response can be made by subsampling non-respondents, replacement, substitution, subjective estimates, trend analysis, weighting, and imputation.

The statistical estimation of sample size is even more complicated in international marketing research, as the population variance may differ from one country to the next. A preliminary estimation of population variance for the purpose of determining the sample size also has ethical ramifications. The Internet and computers can assist in determining the sample size and adjusting it to a count for expected incidence and completion rates.

Sampling distribution -- the distribution of the values of a sample statistic computed for each possible sample that could be drawn from the target population under a specified sampling plan
statistical inference -- the process of generalizing the sample results to the population results
normal distribution -- a basis for classical statistical inference that is bell shaped and symmetrical and appearance. Its measures of central tendency are all identical
standard error -- the standard deviation of the sampling distribution of the mean or proportion
z values -- the number of standard errors in point is away from the mean
incidence rate -- the rate of occurrence of persons eligible to participate in a study expressed as a percentage
completion rate -- the percentage of qualified respondents to complete the interview. It enables researchers to take into account anticipated refusals by people who qualify
substitution -- a procedure that substitutes for nonrespondents other elements from the sampling frame that are expected to respond
trend analysis -- a method of adjusting for nonrespondents in which the researcher tries to discern a trend between early and late respondents. This trend is projected to nonrespondents to estimate their characteristic of interest
weighting -- statistical procedure that attempts to account for non-response by assigning differential weight to the data depending on the response rate
imputation -- a method to adjust for non-response by assigning to characteristic of interest to the nonrespondents based on the similarity of the variables available for both nonrespondents and respondents