how to find significance between any two numbers in chi square

[Kyra]

Hi,

I run a chi-square test. My codes are below:

proc format;
value $category 
'' =''
'Agree'='Agree1'
'Disagree'= 'Disagree1'
'Neither agree or disagree'='Neither agree or disagree1'
'Strongly agree'= 'Agree1'
'Strongly disagree'= 'Disagree1'
;

proc freq data=red.survey2;
tables My_compensation_should_be_augmen*Program__select_one_ /chisq exact ;
format     My_compensation_should_be_augmen $category.  ;
run;

I received following output:

Table of My_compensation_should_be_augmen by Program__select_one_
My_compensation_should_be_augmen(My compensation should be augmented due to the associated risks)	Program__select_one_(Program: select one#)
Frequency Percent Row Pct Col Pct	Anesthesia	Emergency Medicine	General Surgery	Total
Agree1	28 19.05 32.56 49.12	24 16.33 27.91 82.76	34 23.13 39.53 55.74	86 58.50
Disagree1	12 8.16 54.55 21.05	1 0.68 4.55 3.45	9 6.12 40.91 14.75	22 14.97
Neither agree or disagree1	17 11.56 43.59 29.82	4 2.72 10.26 13.79	18 12.24 46.15 29.51	39 26.53
Total	57 38.78	29 19.73	61 41.50	147 100.00
Frequency Missing = 4

Statistic	DF	Value	Prob
Chi-Square	4	10.0471	0.0396
Likelihood Ratio Chi-Square	4	11.1415	0.0250
Mantel-Haenszel Chi-Square	1	0.1559	0.6929
Phi Coefficient		0.2614
Contingency Coefficient		0.2529
Cramer's V		0.1849

I get a p-value of 0.0396.

This shows me that My_compensation_should_be_augmen is significantly different by the program.

However, it does not give me  what is specifically different here significantly.

I want to say something like respondents who agreed were significantly higher in Emergency Medicine than Anesthesia or may be respondents who agreed were significantly higher in Emergency Medicine than Anesthesia and Surgery. I am not sure which statement is correct.

How can i do that?

Thanks,

[Rick_SAS]

When you perform a two-way frequency analysis, the syntax

tables X*Y / chisq;

performs a chi-square test for association between X and Y. The null hypothesis is that X and Y are independent. If the p-value is small, you reject the null hypothesis and conclude that there is an association between X and Y. See the section "Pearson Chi-Square Test for Two-Way Tables" in the PROC FREQ documentation.

[Kyra]

Thank you for the reply. How can I study which two numbers are statistically different in the Chi square analysis which is making two variables associated.

Thanks,

[Rick_SAS · Accepted solution]

There might be more than two numbers. It is the sum of the squared deviations that is important.

But to answer the spirit of your question, read the article "Color cells in a mosaic plot by deviation from independence," which shows how to create a mosaic plot in PROC FREQ that color-codes each cell according to the deviation from independence. 

tables X*Y / norow cellchi2 expected stdres crosslist
                           missing plots=MosaicPlot(colorstat=StdRes);

[Kyra]

Thank you very much!

[SteveDenham]

A couple of things to note.  You have 2 cells out of 9 where the counts are less than 5. Beware of using the standard chi squared test.  Your code calls for the exact option, so looking at the exact test results should inform you as to your next step.  Assuming you have identified that at least one column has a different association with the response variables than another.  You get 2 chances to test this, so you need to clearly identify what question you are trying to answer.  One way might be to ask: "Is anesthesia different from general surgery" and "Is EM different from general surgery". In this case, you have identified general surgery as a reference category. So you run follow-up analyses where you subset the data to include only anesthesia and general surgery in the first case and only EM and general surgery in the second case. Those are your 2 chances to test under the reference scenario.  Another scenario might be to test 1)Is the collapsed incidence of anesthesia and EM different from general surgery and 2)Is anesthesia different from EM?  What you shouldn't do is the all possible comparisons of anesthesia vs. general surgery, EM vs. general surgery, and anesthesia vs. EM.

So how do you go about this? The reference scenario can be done in two separate PROC FREQ calls, using a where= clause in the data= option to select the two columns of interest in each case. The second scenario involves some DATA step preprocessing to collapse the observations in two categories to a single category and then comparing the "collapsed" column to the third in one PROC FREQ call, and comparing the two categories involved in the collapse in a second PROC FREQ call.

SteveDenham