Confidence intervals and sample size

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Confidence intervals and sample size

• Thore Egeland
• May 21, UUS

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Confidence intervals
Cumming, Fidler and Vaux , JCB 2007
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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.
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Example 1 Exemplifying formulae Data 28.7,
38.7,52.6 M(28.738.752.6)/340
Interpretation?
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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), n49 Generally, if
sample size is made 4 times larger (449196),
the SE is halved and the length of the
confidence interval is similarly halved
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General comment

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

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Example 3 Binomial data
Assume 2n 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?
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Databases and sample size
Example 4 540 Portuguesian mtDNA samples, of
which 162 are singletons The coverage is
C1-162/5400.58 (Good 1953 crediting Turing) The
probability that the next sample is not in the
database is 1-0.580.42
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