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Sample Size Determination

Sample Size Determination. Everything You Ever Wanted to Know About Sampling Distributions--And More!. Sampling Distribution. A frequency distribution of all the means obtained from all the samples of a given size Example: $$ spent on CD’s at Best Buy Daffy $34.00 Donald $72.00

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Sample Size Determination

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  1. Sample Size Determination Everything You Ever Wanted to Know About Sampling Distributions--And More!

  2. Sampling Distribution • A frequency distribution of all the means obtained from all the samples of a given size • Example: $$ spent on CD’s at Best Buy • Daffy $34.00 • Donald $72.00 • Sylvester $36.00 • Tweetie Bird $40.00 • All samples of n=2

  3. Your Turn: • Develop a sampling distribution using n=2 • Calculate the population mean CAR A B C D E Expected 3 4 5 0 1 Life

  4. Sampling Distributions • The distribution of sample means is skinnier than the distribution of elements • Why? • The distribution is normal • The sampling distribution mean equals the population mean

  5. Standard Error • The variability in the sampling distribution • Tells you how reliable your estimate of the population mean is • If this is big (good or bad) • If this is small (good or bad) • WHY?

  6. Standard Error Sxstandard deviation square root of the sample size As the samples size gets bigger, the standard error gets __________

  7. Confidence Intervals • CI= Xbar +/- z (standard error) • Where: • z= _____ for 68% confidence • z= _____ for 95% confidence • z= _____ for 99.7% confidence • (again think Chebychev) • What confidence level should you use?

  8. Develop a Confidence Interval • Estimate the average number of trips to the beach taken by undergrad students during their 4-6 year career • xbar = 5 • SD = 1.5 • 95% Confidence Level • n=100

  9. So, • There is a 95% chance that if all undergrad students were sampled regarding the number of beach trips that the findings would differ from our results by no more than ____ in either direction.

  10. or, maybe better, • If I were to conduct this study 100 times, then I would get _____ different confidence intervals. If I have a 95% confidence interval then ____ of the 100 CI’s will contain the true population mean (mu) and ____ will not. • I sure hope that the confidence interval I got is one of the 95 that contains mu!

  11. Probably the easiest interpretation: • If you have a 95% Confidence Interval - there is a 95% chance that the CI will contain Mu – there is a 5% chance that it won’t.

  12. Confidence Interval Issues • Reliability (Z) • how often we are correct – how often mu falls within the range • Precision • how wide the confidence interval is • The smaller the n, the _____ the CI • Given a particular n, the CI will be _______ when we increase the reliability

  13. Factors that Influence n • Precision (H) • how skinny must your CI be in order to be able to take action on the results? • I will go to a new water park in the area. • DWN PWN Maybe PW DW • I will pay _____ for a musical card. • I will pay _____ for a motorcycle.

  14. More Factors That Influence n • Confidence level (z) • Population SD • Time, money and personnel

  15. Sample Size for Interval or Ratio Data Z2 n= H2 * s2 Where: z= 1, 1.96, or 3 H= precision (+/-) H s2= variance (or standard deviation squared)

  16. Example: Average Number of Books Bought Per Semester • H=0.25 • s=1.5 • Confidence = 95%

  17. Sample Size for Nominal or Ordinal Data Z2 n = H2 * (P) (Q) Where: Z= 1, 1.96, or 3 H= a percentage (e.g., 0.03--NOT 3) P = initial estimate of the population proportion Q= (1-P)

  18. n for Proportion of Students Who Read the News Paper • Do you read the newsl paper? • 1. YES • 2. NO • Estimate that 60% read the news paper • Want a 99 % CI • Want a +/- 3% precision

  19. The Final Sample Size • Compute n for all nominal, interval and ratio questions • most conservative • limited resources

  20. Non-statistical Approaches to Sample Size (n) • All you can afford method: • subtract costs from budget • figure out cost per interview • divide leftover budget by cost per interview • Rules of thumb

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