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Confidence intervals and sample size

Confidence intervals and sample size. Thore Egeland May 21, UUS. Confidence intervals. Cumming, Fidler and Vaux , JCB 2007. Confidence intervals and sample size. Idea: As sample size increases, the confidence intervals get shorter. If we require confidence interval to be shorter

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Confidence intervals and sample size

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  1. Confidence intervals and sample size ThoreEgeland May 21, UUS

  2. Confidence intervals Cumming, Fidler and Vaux , JCB 2007

  3. Confidence intervals and sample size Idea: As sample size increases, the confidence intervals get shorter. If we require confidence interval to be shorter than a prescribed limit, required sample size n can be calculated.

  4. Example 1 Exemplifying formulae Data: 28.7, 38.7,52.6 M=(28.7+38.7+52.6)/3=40 Interpretation?

  5. Example 2 Reuired sample size Based on a previous study, our best guess for the mean M is 40 and standard deviation SD 7. How large must n be for the confidence interval to be (39,41). Answer: If we require (38,42), n=49 Generally, if sample size is made 4 times larger (4*49=196), the SE is halved and the length of the confidence interval is similarly halved

  6. General comment • Previous calculations are based on continuous data. Some modifications needed for next example.

  7. Example 3 Binomial data Assume 2*n alleles are genotyped. The frequency of a mutation is assumed to be 1 of 150 or 0.67% . What sample size n is required for a confidence interval from 0.41% to 0.92%?

  8. Databases and sample size Example 4: 540 Portuguesian mtDNA samples, of which 162 are singletons The coverage is C=1-162/540=0.58 (Good 1953 crediting Turing) The probability that the next sample is not in the database is 1-0.58=0.42

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