R vs SAS Paired T-Test

Summary

Goal

The goal of this comparison is to evaluate whether paired t-tests produce equivalent results in R and SAS for both normal and lognormal data. For normal data, results from stats::t.test(), procs::proc_ttest(), and SAS PROC TTEST are compared directly. For lognormal data, results from a log-transformation / back-transformation approach in R are compared with SAS PROC TTEST using the DIST=LOGNORMAL option.

Scope

Methodologies

Paired t-test

Lognormal paired t-test

Technical implementations

SAS: PROC TTEST with and without the DIST=LOGNORMAL option

R: stats::t.test(paired = TRUE) and log-transformation / back-transformation approach for lognormal data

Prerequisites

R packages

library(tibble) # for example data
library(stats) # t.test()
library(procs) # proc_ttest()

Data

Normal Paired t-test and Lognormal Paired t-test Sample Data

We use a simulated paired dataset containing systolic blood pressure measurements before and after treatment. The same data are used in the R and SAS examples to compare the log-transformation / back-transformation approach in R with SAS PROC TTEST using the DIST=LOGNORMAL option.

pressure <- tibble::tribble(
  ~SBPbefore, ~SBPafter,
  120, 128,
  124, 131,
  130, 131,
  118, 127,
  140, 132,
  128, 125,
  140, 141,
  135, 137,
  126, 118,
  130, 132,
  126, 129,
  127, 135
)

SAS:

data pressure;
    input SBPbefore SBPafter @@;
    datalines;
120 128 124 131 130 131 118 127
140 132 128 125 140 141 135 137
126 118 130 132 126 129 127 135
;
run;

Paired t-test Comparison

The following table shows the types of Paired t-test analysis, the capabilities of each language, and whether or not the results from each language match.

Analysis	Supported in R	Supported in SAS	Results Match	Notes
Paired t-test, normal data	Yes	Yes	Yes	In Base R, use `paired = TRUE` on `t.test()` function
Paired t-test, lognormal data	Yes	Yes	Yes	Apply a natural log transformation to both paired measurements, perform the paired t-test on the log-transformed data, and exponentiate the mean difference and the confidence limits.

Comparison Results

Normal Data

Here is a table of comparison values between t.test(), proc_ttest(), and SAS PROC TTEST:

Statistic	t.test()	proc_ttest()	PROC TTEST	Match
Degrees of Freedom	11	11	11	Yes
t value	-1.089648	-1.089648	-1.09	Yes
p value	0.2992	0.2992	0.2992	Yes
Mean Difference	-1.8333	-1.8333	-1.8333	Yes
Lower 95% CL Mean Difference	-5.5365	-5.5365	-5.5365	Yes
Upper 95% CL Mean Difference	1.8698	1.8698	1.8698	Yes

Lognormal Data

For lognormal paired data, a paired t-test can be performed in R by applying a natural log transformation to both paired measurements and conducting the analysis on the log-transformed values. The resulting mean difference and confidence limits can then be exponentiated to obtain a geometric mean ratio and corresponding confidence limits. The table below compares results from stats::t.test(), procs::proc_ttest(), and SAS PROC TTEST with the DIST=LOGNORMAL option.

Here is a table of comparison values between t.test(), proc_ttest(), and SAS PROC TTEST:

Statistic	t.test()	proc_ttest()	PROC TTEST	Match	Notes
Degrees of Freedom	11	11	11	Yes
t value	-1.094185	-1.094185	-1.09	Yes
p value	0.2973	0.2973	0.2973	Yes
Geometric Mean Ratio	0.9856	0.9856	0.9856	Yes	Back-transformed mean difference
Lower 95% CL Mean Ratio	0.9572	0.9572	0.9572	Yes	Back-transformed lower confidence limit
Upper 95% CL Mean Ratio	1.0148	1.0148	1.0148	Yes	Back-transformed upper confidence limit

Summary and Recommendation

For normal data, the R paired t-test capabilities are comparable to SAS. Comparison between SAS and R show identical results for the datasets tried. The procs package proc_ttest() function is very similar to SAS in the syntax and output produced. proc_ttest() also supports by groups, where t.test() does not.

For the lognormal version of the paired t-test, equivalent results can be obtained in R by applying a natural log transformation to the paired measurements, performing the paired t-test on the transformed data, and exponentiating the resulting estimates and confidence limits. Comparison with SAS PROC TTEST using the DIST=LOGNORMAL option showed that the results matched after back-transformation. Therefore, a separate package is not required for this analysis.

References

R t.test() documentation: https://www.rdocumentation.org/packages/stats/versions/3.6.2/topics/t.test

R proc_ttest() documentation: https://procs.r-sassy.org/reference/proc_ttest.html

SAS PROC TTEST Paired analysis documentation: https://documentation.sas.com/doc/en/pgmsascdc/9.4_3.4/statug/statug_ttest_syntax08.htm