Browsers and JavaScript

Microsoft Internet Explorer, Netscape Navigator, Opera, Firefox, and Safari can all do this page, provided that their JavaScript is turned on. Some lesser-known browsers can do this page too. If JavaScript is not turned on, there will be a diagnostic at the top of this page when this page is loaded.

The user is respectfully warned that the data and formulas typed into this page will be picked up by JavaScript, so the data and formulas must follow the grammatical rules of JavaScript. In particular, an integer with a leading zero will be understood to be in base 8. A decimal-pointed number with an unnecessary leading zero on the left of the point may be regarded as wrong. To top.

Get Holmed p-values

The famous Bonferroni correction for multiple inference is never more powerful than the Holm (1979) correction. The latter can be used in every case where the former can be used. I have not seen Holm’s paper, but I have read Levin (1996) and Aickin and Gensler (1996). They are easy to read, and it is easy to write a program from their description, so I did. Following Aickin and Gensler, I say that p-values corrected by the method of Holm have been “Holmed.” I respectfully invite the reader to select and copy the array of p-values

[ .01 , .017 , .04 ]

to the clipboard, to move to the upper text area of the present page, to clear that text area with the “Clear” button if necessary, to paste into that area, and to click on the “Get Holmed p-values” button. The array of corrected p-values will appear in the lower text area. It is [ 0.03 , 0.034 , 0.04 ]. If somebody is using a 5% test boundary, then all three hypotheses are rejected. On the other hand, if the Bonferroni correction were used, then the array of corrected values would be [ .03 , .051 , .12 ], and only one of the hypotheses would be rejected.

The reader sees that these arrays are sorted into ascending order. This is not necessary. They could just as well be in descending order. That is, if the raw p-value array is

[ .04 , .017 , .01 ]

then the resulting array of “Holmed” values is

[ 0.04 , 0.034 , 0.03 ]

That is, the user may use any order she pleases, any order which seems to follow naturally from the design of her experiment, and my program will follow her order. The program does first sort into ascending order to prepare to do the Holm algorithm, but after the algorithm is finished the program changes the order back to what it was.

Any mistakes which I may have made are my own. They are not Holm’s, Aickin’s, or Gensler’s. To top.

Run a JavaScript program

While building this page I needed a way to run little JavaScript programs, so I constructed the “Run a JavaScript program” button. When I was done I left the button so users can practice JavaScript programming with it. If a program is in the upper text area, the button will run it. Here is a trivial example:

var x=[];
for( var j=0;j<10;j++ )x[j]=j;
x;

The user is respectfully invited. To top.

Insert commas

It may be that the user is bringing in data copied from other web pages, or from files, and is pasting the data from the clipboard to the upper text area. In that case the numbers are perhaps separated by blanks or tabulation characters or the like instead of by commas. The “Insert commas” button changes such other separators to commas. Then blanks are placed on the left and right of each comma. Then a blank is placed on the inside of each square bracket. These blanks are for easier reading by humans. The button does not always guess rightly what is expected of it, so the user is respectfully asked to look at the button’s work to make sure everything is as desired. It is a good idea to type the left and right square brackets before clicking the “Insert commas” button. To top.

Bibliography

Aickin, M. and Gensler, H. (1996) Adjusting for Multiple Testing When Reporting Research Results: The Bonferroni vs Holm Methods, American Journal of Public Health, Volume 86 Number 5, pages 726-728. This article is also available on the Web at http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=1380484&blobtype=pdf

Holm, S. (1979) A simple sequentially rejective multiple test procedure, Scandinavian Journal of Statistics, Volume 6, pages 65-70.

Levin, B. (1996) Annotation: On the Holm, Simes, and Hochberg Multiple Test Procedures, American Journal of Public Health, Volume 86 Number 5, pages 628-629. This article is also available on the Web at http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=1380467&blobtype=pdf

To top.

License, revision date, and e-mail address

This file, including the programs, is in the public domain. The date of this revision is 6 March 2012. Criticism both constructive and destructive comes to me, Harold Kaplan,

       at     dot        
smtw2gh  gmail   com