Combination of p-Values

combine(PValues, <:PValueCombination)

Combine p-values

Examples

julia> pvals = PValues([0.01, 0.02, 0.3, 0.5]);

julia> combine(pvals, Fisher())
0.007616871850449092

julia> combine(pvals, Stouffer())
0.00709832618126593

See also

PValueCombinations:

Fisher Logit Stouffer Tippett Simes Wilkinson Minimum

Fisher's p-value combination

Examples

julia> pvals = PValues([0.01, 0.02, 0.3, 0.5]);

julia> combine(pvals, Fisher())
0.007616871850449092

References

Fisher, R.A. (1925). Statistical methods for research workers (Genesis Publishing Pvt Ltd).

Logit p-value combination

Examples

julia> pvals = PValues([0.01, 0.02, 0.3, 0.5]);

julia> combine(pvals, Logit())
0.006434494635148462

References

Mudholkar, G.S., and George, E.O. (1977). The Logit Statistic for Combining Probabilities - An Overview (Rochester University NY, Dept of Statistics).

Stouffer's p-value combination

Examples

julia> pvals = PValues([0.01, 0.02, 0.3, 0.5]);

julia> combine(pvals, Stouffer())
0.00709832618126593

julia> weights = [1.0, 2.0, 0.4, 1.5];

julia> combine(pvals, weights, Stouffer())
0.007331653763696742

References

Stouffer, S.A. (1949). The American soldier. Vol. 1: Adjustment during army life (Princeton University Press).

Liptak, T. (1958). On the combination of independent tests. Magyar Tud Akad Mat Kutato Int Kozl 3, 171–197.

Tippett's p-value combination

Examples

julia> pvals = PValues([0.01, 0.02, 0.3, 0.5]);

julia> combine(pvals, Tippett())
0.039403990000000055

References

Tippett, L.H.C. (1931). The Methods of Statistics. An introduction mainly for workers in the biological sciences.

Simes's p-value combination

Examples

julia> pvals = PValues([0.01, 0.02, 0.3, 0.5]);

julia> combine(pvals, Simes())
0.04

References

Simes, R.J. (1986). An improved Bonferroni procedure for multiple tests of significance. Biometrika 73, 751–754.

Wilkinson's p-value combination

Examples

julia> pv = PValues([0.01, 0.02, 0.3, 0.5]);

julia> combine(pv, Wilkinson(1))  # combination with rank 1
0.03940399000000003

julia> combine(pv, Wilkinson(4))  # combination with rank 4
0.0625

References

Wilkinson, B. (1951). A statistical consideration in psychological research. Psychological Bulletin 48, 156.

Minimum of adjusted p-value combination

Examples

julia> pv = PValues([0.01, 0.02, 0.3, 0.5]);

julia> combine(pv, Minimum(BenjaminiHochberg()))
0.04

julia> combine(pv, Minimum(ForwardStop()))
0.01005033585350145