The notes for the topics on this page can be found in the lectures 9 folders on Canvas.
To conduct a likelihood ratio test on a 2 x 2 table in R you can use GTest() from the DescTools package. To conduct a 2-sample test of proportions you can use prop_test() from the catfun package. For both functions you can provide a frequency table as the main argument as seen in the examples below.
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))library(DescTools)
xtabs(count ~ service + sleep, data = vietnam) %>%
GTest()##
## Log likelihood ratio (G-test) test of independence without
## correction
##
## data: .
## G = 12.394, X-squared df = 1, p-value = 0.0004308library(catfun)
xtabs(count ~ service + sleep, data = vietnam) %>%
prop_test()## Observed proportions:
## * 0.5195
## * 0.4131
## ----------------------------------------
## Confidence interval method: wald
## Confidence intervals:
## Lower bound Upper bound
## 1 0.4658578 0.5731813
## 2 0.3877595 0.4384474
## ----------------------------------------
## 2 sample test for equality of proportions
## Chi-squared: 12.49136
## p-value: 0.00041To conduct a likelihood ratio test for a frequency table and a two-sample test of proportions in SAS you use the frequency procedure. To indicate that you want SAS to return a likelihood ratio test you specify the chisq argument in the options of the table statement. To indicate you want SAS to return a two-sample test of proportions you can specify riskdiff(equal var = null) in the options of the table statement.
data vietnam;
input service $ sleep $ count;
cards;
yes yes 173
yes no 160
no yes 599
no no 851
;
run;
proc freq data = vietnam order = data;
table service*sleep / relrisk chisq expected;
weight count;
run; ## 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 = 1783data vietnam;
input service $ sleep $ count;
cards;
yes yes 173
yes no 160
no yes 599
no no 851
;
run;
proc freq data = vietnam order = data;
table service*sleep / expected riskdiff(equal var = null);
weight count;
run; ## 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
##
## Column 1 Risk Estimates
##
## (Asymptotic) 95% (Exact) 95%
## Risk ASE Confidence Limits Confidence Limits
## -----------------------------------------------------------------------------
## Row 1 0.5195 0.0274 0.4659 0.5732 0.4644 0.5743
## Row 2 0.4131 0.0129 0.3878 0.4384 0.3876 0.4389
## Total 0.4330 0.0117 0.4100 0.4560 0.4098 0.4564
##
## Difference 0.1064 0.0303 0.0471 0.1658
##
## Difference is (Row 1 - Row 2)
##
##
## Proportion (Risk) Difference Test
## H0: P1 - P2 = 0 Wald Method
##
## Proportion Difference 0.1064
## ASE (H0) 0.0301
## Z 3.5343
## One-sided Pr > Z 0.0002
## Two-sided Pr > |Z| 0.0004
##
## Column 1 (sleep = yes)
##
##
## Column 2 Risk Estimates
##
## (Asymptotic) 95% (Exact) 95%
## Risk ASE Confidence Limits Confidence Limits
## -----------------------------------------------------------------------------
## Row 1 0.4805 0.0274 0.4268 0.5341 0.4257 0.5356
## Row 2 0.5869 0.0129 0.5616 0.6122 0.5611 0.6124
## Total 0.5670 0.0117 0.5440 0.5900 0.5436 0.5902
##
## Difference -0.1064 0.0303 -0.1658 -0.0471
##
## Difference is (Row 1 - Row 2)
##
## Sample Size = 1783