[Data] Malformation: X = Alcohol consumption (values are the assigned scores) and Y = Status (Absent/Present)
[Specification]
The trend option works only for tables with two rows or two columns. The trend test is also called “Cochran-Armitage Trend Test” for \(I \times 2\) tables.
The cmh1 gives “Cochran-Mantel-Haenszel Statistics”.
[Code and Output]
data Malformation;
input alcohol present $ count @@;
datalines;
0 no 17066 0 yes 48
0.5 no 14464 0.5 yes 38
1.5 no 788 1.5 yes 5
4 no 126 4 yes 1
7 no 37 7 yes 1
;
proc freq data=Malformation;
weight count;
tables alcohol*present / trend measures cmh1;
run; The FREQ Procedure
Table of alcohol by present
alcohol present
Frequency|
Percent |
Row Pct |
Col Pct |no |yes | Total
---------+--------+--------+
0 | 17066 | 48 | 17114
| 52.39 | 0.15 | 52.54
| 99.72 | 0.28 |
| 52.54 | 51.61 |
---------+--------+--------+
0.5 | 14464 | 38 | 14502
| 44.40 | 0.12 | 44.52
| 99.74 | 0.26 |
| 44.53 | 40.86 |
---------+--------+--------+
1.5 | 788 | 5 | 793
| 2.42 | 0.02 | 2.43
| 99.37 | 0.63 |
| 2.43 | 5.38 |
---------+--------+--------+
4 | 126 | 1 | 127
| 0.39 | 0.00 | 0.39
| 99.21 | 0.79 |
| 0.39 | 1.08 |
---------+--------+--------+
7 | 37 | 1 | 38
| 0.11 | 0.00 | 0.12
| 97.37 | 2.63 |
| 0.11 | 1.08 |
---------+--------+--------+
Total 32481 93 32574
99.71 0.29 100.00
Statistics for Table of alcohol by present
Statistic Value ASE
------------------------------------------------------
Gamma 0.0571 0.1010
Kendall's Tau-b 0.0032 0.0058
Stuart's Tau-c 0.0004 0.0006
Somers' D C|R 0.0003 0.0006
Somers' D R|C 0.0311 0.0556
Pearson Correlation 0.0142 0.0106
Spearman Correlation 0.0033 0.0059
Lambda Asymmetric C|R 0.0000 0.0000
Lambda Asymmetric R|C 0.0000 0.0000
Lambda Symmetric 0.0000 0.0000
Uncertainty Coefficient C|R 0.0049 0.0048
Uncertainty Coefficient R|C 0.0001 0.0001
Uncertainty Coefficient Symmetric 0.0002 0.0002
Cochran-Armitage Trend Test
---------------------------
Statistic (Z) -2.5632
One-sided Pr < Z 0.0052
Two-sided Pr > |Z| 0.0104
Sample Size = 32574
Summary Statistics for alcohol by present
Cochran-Mantel-Haenszel Statistics (Based on Table Scores)
Statistic Alternative Hypothesis DF Value Prob
---------------------------------------------------------------
1 Nonzero Correlation 1 6.5699 0.0104
Total Sample Size = 32574[Result]
The output statistics is on the normal scale Statistic (Z). We can obtain the \(M^2\) test statistic by \(M^2 = (-2.5632)^2=6.57\).
The correlation is \(r=0.0142\). We can also get the \(M^2\) test statistic by \(M^2=(n-1)r^2 = (32574-1)\times (0.0142)^2 = 6.568\).