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Sample Size

NTR 629 - Week 4B. Sample Size. Sample Size. Sample Size = The number of elements in the obtained sample. When determining sample size, consider: Central Limit Theorem Importance of Precision and Reliability Power Analysis. 1. Central Limit Theorem (CLT).

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Sample Size

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  1. NTR 629 - Week 4B Sample Size

  2. Sample Size • Sample Size = The number of elements in the obtained sample. • When determining sample size, consider: • Central Limit Theorem • Importance of Precision and Reliability • Power Analysis

  3. 1. Central Limit Theorem (CLT) • CLT says that under most distributions (normal or not), as sample size increases, distribution of means will tend towards the normal distribution. • With sample sizes of at least 30 per variable (or group if that is the variable) the sample means will approximate the population mean. The small sample sizes of 2 and 5 (above) do not approximate the mean, whereas the sample of 100 (below) does, and is much closer to a ‘normal’ (bell shaped) distribution. See also: http://www.wadsworth.com/psychology_d/templates/student_resources/workshops/stat_workshp/cnt_lim_therm/cnt_lim_therm_20.html

  4. 2. Precision and Reliability Precision = how close the statistic of the sample matches that of the study population. Determine precision based on: • Amount of error allowed, or the size of Standard Error (SE) or Standard Error. Larger sample sizes decrease SE. • Confidence Interval (CI) • How confident are you that you would achieve similar results if you repeated the study? • 95% of means for each subjects lies within +/- 1.96 sd of the mean. • The +/- 2.58 value reflects 99% of cases. Example Likert scale response GRAPH : Trochim, William M. The Research Methods Knowledge Base, 2nd Edition. Internet WWW page, at URL: <http://www.socialresearchmethods.net/kb/> (version current as of July 16, 2012).

  5. 3. Power Analysis • Power analysis allows the researcher to determine how many subjects are needed to give the hypothesis a chance of being accepted (assuming the hypothesis is true). Must consider: • Type I error (alpha, ) • Type II error (beta, ) • Effect size • Directionality of the Hypothesis

  6. Power Analysis Considerations • Power = The probability of rejecting the null hypothesis when false (i.e., arriving at the correct conclusions). • Formula: 1-… or in this example, an 80% probability of detecting existing relationship. Type I and type II errors are inversely related. • If  (or ) level set at .05, researchers want to be 95% certain they will not commit a type I error. • Set  (for type II error) at four times the  value. • Example: If  set at .05, then  would be .20. Interpretation: There is a 20% probability that one will fail to uncover an existing relationship.

  7. Power Analysis Considerations Effect Size Directionality of Hypothesis One-tailed test used if certain about direction (e.g., increase, decrease) of the effect. The two-tailed hypothesis (null hypothesis) examines differences in both directions. It is used if the researcher is uncertain about the effect of the independent variable on the dependent variable. • The size or magnitude of a difference. • Target having at least a ‘medium’ effect size. • Many fields not require reporting of effect size in journals. • Refer to course handout ‘Using Statistics’, page 15, for the interpretation of effect sizes for various statistical tests.

  8. Power Analysis Computation • Refer to Power Analysis Tables as guide. • If the standard deviations in population are known, can compute sample size needed • Online (free) Sample Size Calculators: • http://www.surveysystem.com/sscalc.htm • http://www.nss.gov.au/nss/home.nsf/pages/Sample+Size+Calculator+Description?OpenDocument • Power Analysis Tables of Points to allow for 95% margin of error for various survey sample sizes • http://research-advisors.com/tools/SampleSize.htm

  9. Sample Size Rules of Thumb • Another consideration is nature of study (impacts statistics). The recommended minimum number of subjects are as follows for the following types of studies: • 100 for a Descriptive Study • 50 for a Correlational Study • 30 in each group for Experimental and Causal-Comparative Study • The use of 15 subjects per group should likely be replicated

  10. Determinants of Sample Size • Increase sample size: • When homogeneous sampling units. • For greater precision. • When want higher statistical significance and/ or power • When predict small differences between groups (want larger effect size) • If high attrition expected • If subsamples (thus smaller group size N for analyses) • If numerous variables are being explored • When numerous confounding variables are present • If dependent variable is expected to vary greatly • Mail surveys - Increase sample size by 40-50% • Use of less reliable and valid instrumentation (e.g., essay vs. validated Likert scale) • Balance with need for more resources to increase sample size (financial, time, manage participants)

  11. External Validity a.k.a. Generalizability • External Validity refers to the extent that the results of a study can be generalized from a sample to a population. • Population generalizabilityis the degree to which a sample represents the population of interest. • Obtaining a representative sample becomes very important • Ecological generalizabilityrefers to the extent to which the results of a study can be generalized to conditions or settings other than those that prevailed in the study.

  12. Nonsampling Errors • Nonsampling Errors • An inadequate sampling frame • Nonresponse from participants • Field errors • Response errors • Coding and data entry error

  13. NTR 629 - Week 4C Recruitment Methods

  14. Recruitment • Goals of recruitment: • Recruit participants that represent the target population • Recruit an adequate number of participants to meet the recommended sample size requirements for study • Pre-Screening Guidelines: http://healthcare.partners.org/phsirb/prescreen.htm • Recruitment Guidelines: http://healthcare.partners.org/phsirb/recruit.htm • The Response Rate is the percent of eligible subjects who agree to participate in the study.

  15. Attrition Nonresponse Dropouts Dropouts = withdrawal after the start or unavailable for required follow-up. Count in the initial response rate, but do not count in the sample size (N) for results. If a percentage of dropouts are anticipated, a researcher should increase the sample size at the start of the study to account for this. • Compromises validity and distorts findings. Reduce nonresponse by: • Multiple methods to make contact • Several points of contact • Providing information materials • Less invasive procedures • Less time consuming and/or less visits • Incentives (e.g., gas $) • Bilingual staff

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