topic Re: Wilcoxon rank sum test (NPAR1WAY) and c-statistic (LOGISTIC) , test result comparison in Statistical Procedures

Wilcoxon rank sum test (NPAR1WAY) and c-statistic (LOGISTIC) , test result comparison

LAYMAN_YO — Thu, 05 Dec 2019 06:23:02 GMT

Th Mann-Whitney (WMW) chi-square statistic is

X2 =[ R1-E(R1)]/se(R1)] * [ R1-E(R1)]/se(R1)]

The WMW U formulation is based on a U statistic instead of a rank sum, but hose two quantities differ only by a constant,

that is U1= n1*n2 + n1*(n1+n2)/2 - R1

and the WMW chi-square test statistic may be expressed as:

X2=[ U1-E(U1)]/se(U1)] * [ U1-E(U1)]/se(U1)]

The general null hypothesis of the WMW test is p''=Pr(X1 >X2 ) + 1/2 * Pr(X1=X2) =.5

U1/n1/n2 = p''_hat

So, the chi-square statistic might be expressed as:

X2={ [ p''_hat -E(p''_hat)] / se(U1)/n1/n2] } * { [ p''_hat -E(p''_hat)] / se(U1)/n1/n2] }

which directly shows that the WMW procdeure is a test of

p''=Pr(X1 >X2 ) + 1/2 * Pr(X1=X2) = 0.5.

--------------------------------------------------------

I tried to compare the test result using NPAR1WAY and LOGISTIC procedures.

data roc;
input arm z ;
cards;
1 1
1 1
1 1
1 2
2 1
2 2
2 3
2 3
;
run;

proc npar1way data=roc wilcoxon;
class arm;
var z;
exact wilcoxon;
run;

Wilcoxon Two-Sample Test

13.0000 -1.4031 0.0803 0.1606 0.1017 0.2033 0.1286 0.2571
Z includes a continuity correction of 0.5.

Kruskal-Wallis Test
Chi-Square DF Pr > ChiSq
2.4306 1 0.1190

proc logistic data=roc;
model arm=z/ scale=none
clparm=wald
clodds=pl
rsquare;
roc ; roccontrast;
run;

ROC Association Statistics

Mann-Whitney

ROC Model Area Standard 95% Wald

Error Confidence Limits
Model 0.8125 0.1614 0.4962 1.0000
ROC1 0.5000 0 0.5000 0.5000

ROC Contrast Test Results
Contrast DF Chi-Square Pr > ChiSq
Reference = Model 1 3.7500 0.0528

p'' = 0.8125

I could not get find any same chi-square values.

What is wrong with the idea?

Re: Wilcoxon rank sum test (NPAR1WAY) and c-statistic (LOGISTIC) , test result comparison

Ksharp — Thu, 05 Dec 2019 11:34:11 GMT

Better post it at Stat forum and calling @StatDave

Re: Wilcoxon rank sum test (NPAR1WAY) and c-statistic (LOGISTIC) , test result comparison

PaigeMiller — Thu, 05 Dec 2019 11:47:22 GMT

You will not find the same chi-squared tests. LOGISTIC and NPAR1WAY do different tests, using different assumptions and different algorithms. It's perfectly normal to show different results.

Re: Wilcoxon rank sum test (NPAR1WAY) and c-statistic (LOGISTIC) , test result comparison

LAYMAN_YO — Fri, 06 Dec 2019 05:03:55 GMT

The null hypothesis for WMW is Pr(X1>X2) + 1/2 * Pr(X1=X2)=0.5

I think that for AUC is the same.

How different are test statistics for both tests?

Could you tell me in a more specific formula?

Re: Wilcoxon rank sum test (NPAR1WAY) and c-statistic (LOGISTIC) , test result comparison

PaigeMiller — Fri, 06 Dec 2019 00:20:40 GMT

"LOGISTIC and NPAR1WAY do different tests, using different assumptions and different algorithms."

It doesn't matter that the null hypotheses are the same.

Re: Wilcoxon rank sum test (NPAR1WAY) and c-statistic (LOGISTIC) , test result comparison

StatDave — Fri, 06 Dec 2019 16:20:15 GMT

Formulas for the test and and confidence interval in ROC analysis are given in the Details:Receiver Operating Characteristic Curves section of the PROC LOGISTIC documentation. A reference to a paper by DeLong et. al. is also provided which describes the connection to the Mann-Whitney U statistic which might be what you need to look over.