EigenCore Multiple Testing Method

Specify a method for adjusting for multiple tests of correlation between the trait variable and each principal component .

For controlling familywise error rate, choose from among the following methods: AdaptiveHolm, AdaptiveHochberg, Bonferroni, Holm, Hommel, Sidak, StepBon, and StepSid. Refer to the documentation of PROC MULTTEST for details and caveats on these methods.

For controlling false discovery rate (which is less restrictive than false positive rate), choose from methods based on FDR (Benjamini and Hochberg, 1995) or pFDR (Storey, 2002, q -values)..

Multiple Testing Method	Definition
None	• Select this option to enable the -log10 ( p-values ) Cutoff field/slider. This selection enables you to specify a -log 10 ( p -value) cutoff directly.
AdaptiveHolm	• Requests adjusted p -values by using the Hochberg and Benjamini (1990) 1 adaptive step-down Bonferroni method.
AdaptiveHochberg	• Requests adjusted p -values by using the Hochberg and Benjamini (1990) 1 adaptive step-up Bonferroni method.
Bonferroni	• Specifies that the Bonferroni adjustments (number of tests p -value) be computed for each test. • Note : These adjustments can be extremely conservative and should be viewed with caution.
Hochberg	• Assumes that p -values are independent and uniformly distributed under their respective null hypotheses, Hochberg (1988) 2 demonstrates that Holm’s step-down adjustments control the familywise error rate even when calculated in step-up fashion. Since the adjusted p -values are uniformly smaller for Hochberg’s method than for Holm’s method, the Hochberg method is more powerful. However, this improved power comes at the cost of having to make the assumption of independence.
Hommel	• Requests adjusted p -values by using the method of Hommel (1988) 3 .
Holm	• See Stepbon , below.
Sidak	• Computes the Šidák adjustment for each test. • Note : These adjustments are slightly less conservative than the Bonferroni adjustments, but they still should be viewed with caution.
StepBon	• Requests adjusted p -values by using the step-down Bonferroni method of Holm (1988).
StepSid	• Requests adjusted p -values by using the Šidák method but in step-down fashion.
AdaptiveFDR	• Requests adjusted p -values by using the Benjamini and Hochberg (2000) 4 adaptive linear step-up method.
Dependent FDR	• Requests adjusted p -values by using the method of Benjamini and Yekateuli (2001) 5 .
FDR	• Requests adjusted p -values by using the linear step-up method of Benjamini and Hochberg (1995) 6 . • These p -values do not control the familywise error rate, but they do control the false discovery rate in some cases.
pFDR	• Computes the " q -values" of Storey (2002) and Storey, Taylor, and Siegmund (2004). PROC MULTTEST treats these " q -values" as adjusted p -values. • The computations depend on selecting a parameter and an estimation method for the false discovery rate.

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1

Hochberg, Y. and Benjamini, Y. (1990). More Powerful Procedures for Multiple Significance Testing. Statistics in Medicine 9: 811–818.

2

Hochberg, Y. (1988). A Sharper Bonferroni Procedure for Multiple Significance Testing. Biometrika 75: 800–803.

3

Hommel, G. (1988). A Comparison of Two Modified Bonferroni Procedures. Biometrika 75: 383–386.

4

Benjamini, Y. and Hochberg, Y. (2000). On the Adaptive Control of the False Discovery Rate in Multiple Testing with Independent Statistics. Journal of Educational and Behavioral Statistics 25: 60–83.

5

Benjamini, Y. and Yekateuli, D. (2001). The Control of the False Discovery Rate in Multiple Testing under Dependency. Annals of Statistics 29: 1165–1188.

6

Benjamini, Y. and Hochberg, Y. (1995). Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing. Journal of the Royal Statistical Society, B 57: 289–300.