The notes for the topics on this page can be found in the lecture 8 folder on Canvas.
To conduct a chi-squared test or Fisher’s exact test in R you can use the CrossTable() function from the descr package. CrossTable() isn’t set up to directly account for weighted cell counts. If you only have summary data you can first use xtabs() to build the contigency table and then use the %>% operator to ‘pipe’ the table into CrossTable(); the below examples illustrate this. For more help, type ?CrossTable in the R console. For further help, please watch the video example.
vietnam <- tibble(
service = c(rep("yes", 2), rep("no", 2)),
sleep = c(rep(c("yes", "no"), 2)),
count = c(173, 160, 599, 851)
)
vietnam <- vietnam %>%
mutate(service = as_factor(service),
sleep = as_factor(sleep))To conduct a chi-squared test, set the chisq argument to TRUE.
library(descr)
xtabs(count ~ service + sleep, data = vietnam) %>%
CrossTable(expected = TRUE, chisq = TRUE)## Cell Contents
## |-------------------------|
## | N |
## | Expected N |
## | Chi-square contribution |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
## ================================
## sleep
## service yes no Total
## --------------------------------
## yes 173 160 333
## 144.2 188.8
## 5.760 4.398
## 0.520 0.480 0.187
## 0.224 0.158
## 0.097 0.090
## --------------------------------
## no 599 851 1450
## 627.8 822.2
## 1.323 1.010
## 0.413 0.587 0.813
## 0.776 0.842
## 0.336 0.477
## --------------------------------
## Total 772 1011 1783
## 0.433 0.567
## ================================
##
## Statistics for All Table Factors
##
## Pearson's Chi-squared test
## ------------------------------------------------------------
## Chi^2 = 12.49136 d.f. = 1 p = 0.000409
##
## Pearson's Chi-squared test with Yates' continuity correction
## ------------------------------------------------------------
## Chi^2 = 12.06166 d.f. = 1 p = 0.000515To conduct a Fisher’s exact test, set the fisher argument to TRUE
xtabs(count ~ service + sleep, data = vietnam) %>%
CrossTable(fisher = TRUE)## Cell Contents
## |-------------------------|
## | N |
## | Chi-square contribution |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
## ================================
## sleep
## service yes no Total
## --------------------------------
## yes 173 160 333
## 5.760 4.398
## 0.520 0.480 0.187
## 0.224 0.158
## 0.097 0.090
## --------------------------------
## no 599 851 1450
## 1.323 1.010
## 0.413 0.587 0.813
## 0.776 0.842
## 0.336 0.477
## --------------------------------
## Total 772 1011 1783
## 0.433 0.567
## ================================
##
##
## Fisher's Exact Test for Count Data
## ------------------------------------------------------------
## Sample estimate odds ratio: 1.535716
##
## Alternative hypothesis: true odds ratio is not equal to 1
## p = 0.000466
## 95% confidence interval: 1.200679 1.965386
##
## Alternative hypothesis: true odds ratio is less than 1
## p = 1
## 95%s confidence interval: % 0 1.890994
##
## Alternative hypothesis: true odds ratio is greater than 1
## p = 0.000269
## 95%s confidence interval: % 1.247644 InfTo conduct a chi-squared test or Fisher’s exact test in SAS use the frequency procedure. The following code will produce return results for both a chi-squared test and a Fisher’s exact test. The syntax is:
proc freq data = <dataset>;
table <row variable>*<column variable> / chisq expected;
weight <weighting variable if summary data>;
run; data vietnam;
input service $ sleep $ count;
cards;
yes yes 173
yes no 160
no yes 599
no no 851
;
run;
title 'Chi-squared test example';
proc freq data = vietnam order = data;
table service*sleep / relrisk chisq expected;
weight count;
run; ## Chi-squared test example
##
## The FREQ Procedure
##
## Table of service by sleep
##
## service sleep
##
## Frequency|
## Expected |
## Percent |
## Row Pct |
## Col Pct |yes |no | Total
## ---------+--------+--------+
## yes | 173 | 160 | 333
## | 144.18 | 188.82 |
## | 9.70 | 8.97 | 18.68
## | 51.95 | 48.05 |
## | 22.41 | 15.83 |
## ---------+--------+--------+
## no | 599 | 851 | 1450
## | 627.82 | 822.18 |
## | 33.60 | 47.73 | 81.32
## | 41.31 | 58.69 |
## | 77.59 | 84.17 |
## ---------+--------+--------+
## Total 772 1011 1783
## 43.30 56.70 100.00
##
##
## Statistics for Table of service by sleep
##
## Statistic DF Value Prob
## ------------------------------------------------------
## Chi-Square 1 12.4914 0.0004
## Likelihood Ratio Chi-Square 1 12.3936 0.0004
## Continuity Adj. Chi-Square 1 12.0617 0.0005
## Mantel-Haenszel Chi-Square 1 12.4843 0.0004
## Phi Coefficient 0.0837
## Contingency Coefficient 0.0834
## Cramer's V 0.0837
##
##
## Fisher's Exact Test
## ----------------------------------
## Cell (1,1) Frequency (F) 173
## Left-sided Pr <= F 0.9998
## Right-sided Pr >= F 0.0003
##
## Table Probability (P) <.0001
## Two-sided Pr <= P 0.0005
##
##
## Odds Ratio and Relative Risks
##
## Statistic Value 95% Confidence Limits
## ------------------------------------------------------------------
## Odds Ratio 1.5361 1.2095 1.9509
## Relative Risk (Column 1) 1.2576 1.1152 1.4181
## Relative Risk (Column 2) 0.8187 0.7263 0.9228
##
## Sample Size = 1783