Presentation on theme: "SAMPLE DESIGN: HOW MANY WILL BE IN THE SAMPLE—DESCRIPTIVE STUDIES ?"— Presentation transcript:
1 SAMPLE DESIGN: HOW MANY WILL BE IN THE SAMPLE—DESCRIPTIVE STUDIES ? Lu Ann Aday, Ph.D. The University of TexasSchool of Public Health
2 TYPES OF OBJECTIVES DESCRIPTIVE ANALYTICAL Describes Explains Is more exploratoryProfiles characteristics of group(s)Focuses on what?Assumes no hypothesisDoes not require comparisons (between groups or over time)Try to maximize precision of estimatesANALYTICALExplainsIs more explanatoryAnalyzes why group(s) have characteristicsFocuses on why?Assumes an hypothesisRequires comparisons (between groups or over time)Try to maximize power to detect differences, if they exist
3 RELATING SAMPLE SIZE ESTIMATION TO STUDY OBJECTIVES Select the sample size estimation procedure that best matches the study design underlying the respective study objectivesCompute the sample size required to address each objectiveBased on the sample sizes required to address each of the objectives, appropriate sample size adjustments, as well as time and resource constraints, recommend an overall sample sizeDiscuss possible limitations in terms of statistical precision or power in addressing any specific study objective(s), given the recommended sample size
4 CRITERIA: Descriptive Studies Objective:to estimate a parameter, i.e., provide a precise estimate for selected variable(s)Framework:normal sampling distribution
6 NORMAL SAMPLING DISTRIBUTION Sampling Distribution: distribution of estimates, e.g., mean, for all possible simple random samples of a certain size that could be hypothetically drawn from the target populationPopulation Mean: grand mean of all possible simple random samples of a certain size that could be hypothetically drawn from the target population
7 STANDARD ERRORDefinition: average variation of all possible simple random samples of a certain size that could be hypothetically drawn from the target populationFormula:SE = s/n, where,SE = standard error s = sample standard deviation n = sample size = square root (sqrt)
8 CONFIDENCE INTERVALDefinition: range of values in which the population mean is likely to be contained, with a given level of probability, defined by the standard errors of the sampling distributionConfidence Interval Standard Errors (Z)68 %90 %95 %99 %
12 SAMPLE SIZE ESTIMATION: Cross-Sectional (One Group)—Proportion Example:n = Z21-α/2 P (1-P)/d2n = * .50(1-.50)/.052n = 384Note: See Table 7.1B, Aday & Cornelius, 2006, for sample size estimates based on different estimated proportions (P) and levels of desired precision (d).
14 SAMPLE SIZE ESTIMATION: Cross-Sectional (One Group)—Mean Example:n = Z21-α/2 σ2/d2n = * (2.5 2) /1 2n = 24Note: To estimate σ when not known, estimate the inter-quartile range by dividing the possible range of values by 4, e.g., if range is 0-10, then 10/4 = 2.5.
18 SAMPLE SIZE ESTIMATION: Group Comparison (Two Groups)—Mean Example:n = Z21-α/2 [2σ2]/d2n = * [2 * (2.5 2)] /1 2n = 48 (in each group)Note: To estimate σ when not known, estimate the inter-quartile range by dividing the possible range of values by 4, e.g., if range is 0-10, then 10/4 = 2.5.
19 SUMMARY: Steps in Estimating Sample Size – Descriptive Studies 1. Identify the major study variables.2. Determine the types of estimates of study variables, such as means or proportions.3. Select the population or subgroups of interest (based on study objectives and design).4a. Indicate what you expect the population value to be.4b. Estimate the standard deviation of the estimate.
20 SUMMARY: Steps in Estimating Sample Size – Descriptive Studies 5. Decide on a desired level of confidence in the estimate (confidence interval).6. Decide on a tolerable range of error in the estimate (desired precision).7. Compute sample size, based on study assumptions.
21 SAMPLE SIZE ESTIMATION: EXCEL SPREADSHEET See EXCEL file with spreadsheet for computing sample sizes.