Review of Chi Square

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Richard L. Amdur, PhDChief, Biostatistics, DCVAMC

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region response Frequency| Percent | Row Pct | Col Pct |No |Yes | Total ---------+--------+--------+ A | 60 | 140 | 200 | 10.00 | 23.33 | 33.33 | 30.00 | 70.00 | | 27.91 | 36.36 | ---------+--------+--------+ B | 70 | 130 | 200 | 11.67 | 21.67 | 33.33 | 35.00 | 65.00 | | 32.56 | 33.77 | ---------+--------+--------+ C | 85 | 115 | 200 | 14.17 | 19.17 | 33.33 | 42.50 | 57.50 | | 39.53 | 29.87 | ---------+--------+--------+ Total 215 385 600 35.83 64.17 100.00

Statistic DF Value Prob------------------------------------------------------Chi-Square 2 6.8861 0.0320Phi Coefficient 0.1071

region x response

region response Frequency| Percent | Row Pct | Col Pct |No |Yes | Total ---------+--------+--------+ A | 60 | 140 | 200 | 15.00 | 35.00 | 50.00 | 30.00 | 70.00 | | 46.15 | 51.85 | ---------+--------+--------+ B | 70 | 130 | 200 | 17.50 | 32.50 | 50.00 | 35.00 | 65.00 | | 53.85 | 48.15 | ---------+--------+--------+ Total 130 270 400 32.50 67.50 100.00 Statistic DF Value Prob ------------------------------------------------------ Chi-Square 1 1.1396 0.2857

Phi Coefficient -0.0534

Region (A vs. B) x response

region response Frequency| Percent | Row Pct | Col Pct |No |Yes | Total ---------+--------+--------+ B | 70 | 130 | 200 | 17.50 | 32.50 | 50.00 | 35.00 | 65.00 | | 45.16 | 53.06 | ---------+--------+--------+ C | 85 | 115 | 200 | 21.25 | 28.75 | 50.00 | 42.50 | 57.50 | | 54.84 | 46.94 | ---------+--------+--------+ Total 155 245 400 38.75 61.25 100.00 Statistic DF Value Prob ------------------------------------------------------ Chi-Square 1 2.3700 0.1237

Region (B vs. C) x response

region response Frequency| Percent | Row Pct | Col Pct |No |Yes | Total ---------+--------+--------+ A | 60 | 140 | 200 | 15.00 | 35.00 | 50.00 | 30.00 | 70.00 | | 41.38 | 54.90 | ---------+--------+--------+ C | 85 | 115 | 200 | 21.25 | 28.75 | 50.00 | 42.50 | 57.50 | | 58.62 | 45.10 | ---------+--------+--------+ Total 145 255 400 36.25 63.75 100.00 Statistic DF Value Prob ------------------------------------------------------ Chi-Square 1 6.7613 0.0093

Region (A vs. C) x response

region response Frequency| Percent | Row Pct | Col Pct |No |Yes | Total ---------+--------+--------+ A | 60 | 140 | 200 | 10.00 | 23.33 | 33.33 | 30.00 | 70.00 | | 27.91 | 36.36 | ---------+--------+--------+ B+C | 155 | 245 | 400 | 25.83 | 40.83 | 66.67 | 38.75 | 61.25 | | 72.09 | 63.64 | ---------+--------+--------+ Total 215 385 600 35.83 64.17 100.00 Statistic DF Value Prob ------------------------------------------------------ Chi-Square 1 4.4397 0.0351

Region (A vs. B+C) x response

region response Frequency| Percent | Row Pct | Col Pct |No |Yes | Total ---------+--------+--------+ A+B | 130 | 270 | 400 | 21.67 | 45.00 | 66.67 | 32.50 | 67.50 | | 60.47 | 70.13 | ---------+--------+--------+ C | 85 | 115 | 200 | 14.17 | 19.17 | 33.33 | 42.50 | 57.50 | | 39.53 | 29.87 | ---------+--------+--------+ Total 215 385 600 35.83 64.17 100.00 Statistic DF Value Prob ------------------------------------------------------ Chi-Square 1 5.7989 0.0160

Region (A+B vs. C) x response

Number of subjects responding Yes or No in each region

response

region | No | Yes | Total----------+------+--------+--------A+B | 130 | 270 | 400----------+------+--------+--------C | 85 | 115 | 200----------+------+--------+--------Total 215 385 600

Odds Ratio for a Yes Response in Region C

OR (C=yes) = (115/85)/(270/130) = 0.65

95% Confidence interval is 0.46 – 0.92

The odds of saying “yes” are 35% lower in C than in the other regions.

The Relative Risk of saying “yes” in Region C is 0.85, compared to Regions A&B

[RR = (115/200)/(270/400)

Response

Region N Y Total % yesOR vs

Region C

A 60 140 200 70% a 1.72

B 70 130 200 65% a,b 1.37

C 85 115 200 58% b reference

Total 215 385 600 64%

For % yes, rows that do not share a superscipt are significantly different (p<.05).

How to compute a 2x2 chi-squarehttp://graphpad.com/quickcalcs/contingency1.cfm

When there are more than 2 rows or columns:

r×c Contingency Table: How many rows? columns?

You are about to enter your data for a chi-square contingency table analysis. For this to make sense you should have a table of data (at least 2x2; maximum: 9x9).

Number of rows:

Number of columns:

You must have data for each box in the table: no blanks allowed!

http://www.physics.csbsju.edu/stats/contingency_NROW_NCOLUMN_form.html

Submit

Data Entry: 3 × 2 Contingency Table

Your data have been doubly sorted into one of the 2 "treatments" (A, B, ...) and into one of the 3 "outcomes" (1, 2, ...). In the below table you are to enter the number of data items that fit into a particular (treatment,outcome) pair e.g., (B1 or A2). Enter your data in the below set of boxes and then click on the Calculate Now button when data entry is complete. Leave no empty boxes! All entries should be whole numbers!

Calculate Now Clear All

r × c Contingency Table: Results

The results of a contingency table X2 statistical test performed at 12:53 on 19-DEC-2010

data: contingency table A B 1 60 140 200 2 70 130 200 3 85 115 200

215 385 600

expected: contingency table A B

4 71.7 128. 5 71.7 128. 3 71.7 128.

chi-square = 6.89 degrees of freedom = 2probability = 0.032

Review of Chi Square

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