1 / 20

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

hailey
Télécharger la présentation

Sample Size Determination

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related