Confidence Intervals

Another important statistical concept is that of confidence intervals. Confidence intervals are useful for determining the precision of a point estimate. Typically a

The Bonferroni correction

Carlo Emilio Bonferroni was an Italian mathematician that lived from

1892-1960 who developed theories for simultaneous statistical analysis. The Bonferroni correction is a multiple-comparison correction used when several independent statistical tests are being performed simultaneously. While a given alpha value (e.g., 0.05) may be appropriate for each individual comparison, it is probably not sufficient for the set of all comparisons. Thus, the alpha value needs to be lowered to account for the number of comparisons being performed.

The Bonferroni correction lowers the significance level for the entire set of n comparisons by dividing n into the alpha value for each comparison. The adjusted significance level becomes:

Thus, a set of 10 comparisons would lower the alpha value from 0.05 to 0.005 (0.05/10) so only p-values below 0.005 would be considered statistically significant rather than the conventional p < 0.05.

In the analysis of genetic data for Hardy-Weinberg equilibrium, application of the Bonferroni correction almost always removes the stigma of a locus being below the 5% threshold level. Essentially applying the Bonferroni correction means that the more sources of data being tested (e.g., more STR loci), the less sensitive the testing regime becomes since the p-value threshold has been lowered.

Sources: Perneger, T.V. (1998) What's wrong with Bonferroni adjustments.

British Medical Journal, 316, 1236-1238. Weir, B.S. (1996) Genetic Data Analysis II, Multiple Tests, pp. 133-135.

95% confidence interval is computed reflecting the probability that in 95% of the samples tested, the interval should contain the actual value measured. A 95% confidence interval effectively is the sample average plus or minus two standard deviations. A confidence interval around some value n is a function of the frequency of the observation (p) and the number of individuals or items sampled in a population (n).

For 90% confidence intervals, z005 = 1.645 and for 95% confidence intervals,

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