R vs SAS One Sample T-Test

Summary

Goal

The goal of this comparison is to evaluate whether one sample 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

One sample t-test
Lognormal one sample t-test

Technical implementations

SAS: PROC TTEST with and without the DIST=LOGNORMAL option
R: stats::t.test() 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 One Sample t-test and Lognormal One Sample t-test Sample Data

We use a simulated sample data containing one numeric variable, score. The same data are used for the R and SAS examples.

read <- tibble::tribble(
  ~score, ~count,
  40, 2, 47, 2, 52, 2, 26, 1, 19, 2,
  25, 2, 35, 4, 39, 1, 26, 1, 48, 1,
  14, 2, 22, 1, 42, 1, 34, 2, 33, 2,
  18, 1, 15, 1, 29, 1, 41, 2, 44, 1,
  51, 1, 43, 1, 27, 2, 46, 2, 28, 1,
  49, 1, 31, 1, 28, 1, 54, 1, 45, 1
)

SAS:

data read;
    input score count @@;
    datalines;
40 2 47 2 52 2 26 1 19 2
25 2 35 4 39 1 26 1 48 1
14 2 22 1 42 1 34 2 33 2
18 1 15 1 29 1 41 2 44 1
51 1 43 1 27 2 46 2 28 1
49 1 31 1 28 1 54 1 45 1
;
run;

One Sample t-test Comparison

The following table shows the types of One Sample 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
One sample t-test, normal data	Yes	Yes	Yes	In Base R, use `mu` parameter on `t.test()` function to set null hypothesis value
One sample t-test, lognormal data	Yes	Yes	Yes	Apply natural log transformation, perform `stats::t.test()` on the log-transformed data, and exponentiate the mean and 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	43	43	43	Yes
t value	2.8727	2.8727	2.87	Yes
p value	0.006297	0.006297	0.0063	Yes
Mean	34.8636	34.8636	34.8636	Yes
Lower 95% CL Mean	31.44930	31.44930	31.44930	Yes
Upper 95% CL Mean	38.27797	38.27797	38.2780	Yes

Lognormal Data

Lognormal one sample t-tests can be performed in R by applying a natural log transformation to the data, performing stats::t.test() on the log-transformed values, and exponentiating the resulting mean and confidence limits. Comparison of the example data produced equivalent results to 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	43	43	43	Yes	Calculated on log-transformed data
t value	1.6373	1.6373	1.64	Yes	Calculated on log-transformed data
p value	0.1089	0.1089	0.1089	Yes	Calculated on log-transformed data
Geometric Mean	32.84336	32.84336	32.8434	Yes	Back-transformed mean
Lower 95% CL Mean	29.3770	29.3770	29.3770	Yes	Back-transformed lower confidence limit
Upper 95% CL Mean	36.7187	36.7187	36.7187	Yes	Back-transformed upper confidence limit

Summary and Recommendation

For normal data, the R one sample 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 one sample t-test, R does not provide a dedicated lognormal option in stats::t.test() or procs::proc_ttest(). However, lognormal data can be analyzed by applying a natural log transformation to the data, performing the t-test on the log-transformed values, and exponentiating the resulting mean and confidence limits. Comparison of the example data showed equivalent results to SAS PROC TTEST using the DIST=LOGNORMAL option.

Also note that neither t.test() or proc_ttest() supports the “freq” option that is utilized on examples from the SAS documentation. Therefore, this option has been removed from this comparison. In R, the “freq” functionality could be performed by manipulating the data prior to sending to the t-test function.

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 One Sample analysis documentation: https://documentation.sas.com/doc/en/pgmsascdc/9.4_3.4/statug/statug_ttest_syntax09.htm