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DrLynTaylor merged 3 commits into from
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Update 2-sample t-test QMD to include image png file. #595

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27 changes: 15 additions & 12 deletions Comp/r-sas_ttest_1Sample.qmd
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Expand Up @@ -46,7 +46,7 @@ library(procs) # proc_ttest()

## Data

### Lognormal One Sample t-test
### 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.

Expand Down Expand Up @@ -104,11 +104,14 @@ The following table shows the types of One Sample t-test analysis, the capabilit

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 | 29 | 29 | 29 | Yes | |
| t value | 2.364306 | 2.364306 | 2.364306 | Yes | |
| p value | 0.0249741 | 0.0249741 | 0.0249741 | Yes | |
| Statistic | t.test() | proc_ttest() | PROC TTEST | Match | Notes |
|--------------------|----------|--------------|------------|-------|-------|
| 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}

Expand All @@ -118,12 +121,12 @@ Here is a table of comparison values between `t.test()`, `proc_ttest()`, and SAS

| Statistic | t.test() | proc_ttest() | PROC TTEST | Match | Notes |
|------------|------------|------------|------------|------------|------------|
| Degrees of Freedom | 29 | 29 | 29 | Yes | Calculated on log-transformed data |
| t value | 1.351675 | 1.351675 | 1.351675 | Yes | Calculated on log-transformed data |
| p value | 0.1869289 | 0.1869289 | 0.1869289 | Yes | Calculated on log-transformed data |
| Geometric Mean | 32.91447 | 32.91447 | 32.91447 | Yes | Back-transformed mean |
| Lower 95% CL Mean | 28.60623 | 28.60622 | 28.60623 | Yes | Back-transformed lower confidence limit |
| Upper 95% CL Mean | 37.87155 | 37.87155 | 37.87155 | Yes | Back-transformed upper confidence limit |
| 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

Expand Down
155 changes: 125 additions & 30 deletions Comp/r-sas_ttest_2Sample.qmd
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---
title: "R vs SAS Two Sample T-Test"
title: "R vs SAS Two-Sample T-Test"
---

```{r}
#| label: setup
```{r setup}
#| include: false
knitr::opts_chunk$set(echo = TRUE)
```

# Summary

## Goal

The goal of this comparison is to evaluate whether two-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

::::::: columns
:::: {.column width="45%"}
::: {.callout-note appearance="minimal" collapse="false"}
## Methodologies

Two-sample t-test

Lognormal two-sample t-test
:::
::::

:::: {.column width="55%"}
::: {.callout-note appearance="minimal" collapse="false"}
## 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

```{r load-packages}
#| output: false
#| message: false
library(tibble) # for example data
library(stats) # t.test()
library(procs) # proc_ttest()
```

## Data

### Normal two-sample t-test and Lognormal two-sample t-test Sample Data

We use a simulated two-sample dataset containing weight gain measurements for two treatment groups. 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.

R:

```{r}
d1 <- tibble::tribble(
~trt_grp, ~WtGain,
"placebo", 94, "placebo", 12, "placebo", 26, "placebo", 89,
"placebo", 88, "placebo", 96, "placebo", 85, "placebo", 130,
"placebo", 75, "placebo", 54, "placebo", 112, "placebo", 69,
"placebo", 104, "placebo", 95, "placebo", 53, "placebo", 21,
"treatment", 45, "treatment", 62, "treatment", 96, "treatment", 128,
"treatment", 120, "treatment", 99, "treatment", 28, "treatment", 50,
"treatment", 109, "treatment", 115, "treatment", 39, "treatment", 96,
"treatment", 87, "treatment", 100, "treatment", 76, "treatment", 80
)
```

SAS:

``` sas
data d1;
length trt_grp $ 9;
input trt_grp $ WtGain @@;
datalines;
placebo 94 placebo 12 placebo 26 placebo 89
placebo 88 placebo 96 placebo 85 placebo 130
placebo 75 placebo 54 placebo 112 placebo 69
placebo 104 placebo 95 placebo 53 placebo 21
treatment 45 treatment 62 treatment 96 treatment 128
treatment 120 treatment 99 treatment 28 treatment 50
treatment 109 treatment 115 treatment 39 treatment 96
treatment 87 treatment 100 treatment 76 treatment 80
;

run;
```

# Two Sample t-test Comparison

The following table shows the types of Two 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 |
| Analysis | Supported in R | Supported in SAS | Results Match | Notes |
|---------------|---------------|---------------|---------------|---------------|
| Two sample Student's t-test | [Yes](../R/ttest_2Sample.html#baseS) | [Yes](../SAS/ttest_2Sample.html#sas) | [Yes](#student) | In Base R, use `t.test()` function with `paired = FALSE` and `var.equal = TRUE`|
| Two sample Welch's t-test | [Yes](../R/ttest_2Sample.html#baseW) | [Yes](../SAS/ttest_2Sample.html#sas) | [Yes](#welch) | In Base R, use `t.test()` function with `paired = FALSE` and `var.equal = FALSE` |
| Two sample Student's t-test | [Yes](../R/ttest_2Sample.html#baseS) | [Yes](../SAS/ttest_2Sample.html#sas) | [Yes](#student) | In Base R, use `t.test()` function with `paired = FALSE` and `var.equal = TRUE` |
| Two sample Welch's t-test | [Yes](../R/ttest_2Sample.html#baseW) | [Yes](../SAS/ttest_2Sample_W.html#sas) | [Yes](#welch) | In Base R, use `t.test()` function with `paired = FALSE` and `var.equal = FALSE` |
| Two sample Lognormal t-test | [Yes](../R/ttest_2Sample.html#baseWlog) | [Yes](../SAS/ttest_2Sample_lognormal.html#sas) | [Yes](#lognormal) | |

## Comparison Results

### Student's T-Test {#student}

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 | 30 | 30 | 30 | Yes | |
| t value | -0.6969002 | -0.6969002 | -0.6969002 | Yes | |
| p value | 0.4912306 | 0.4912306 | 0.4912306 | Yes | |

| Statistic | t.test() | proc_ttest() | PROC TTEST | Match | Notes |
|------------|------------|------------|------------|------------|------------|
| Degrees of Freedom | 30 | 30 | 30 | Yes | |
| t value | -0.6969 | -0.70 | -0.70 | Yes | |
| p value | 0.4912 | 0.4912 | 0.4912 | Yes | |
| Mean Difference | -7.9375 | -7.9375 | -7.9375 | Yes | |
| Lower 95% CL Mean Difference | -31.1984 | -31.1984 | -31.1984 | Yes | |
| Upper 95% CL Mean Difference | 15.3234 | 15.3234 | 15.3234 | Yes | |

### Welch's T-Test {#welch}

In the Welch T-test the variance and effective degrees of freedom are calculated using Satterthwaite method.

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

Example with fairly equal variances:
| Statistic | t.test() | proc_ttest() | PROC TTEST | Match | Notes |
|--------------------|-----------|--------------|------------|-------|-------|
| Degrees of Freedom | 29.69359 | 29.69359 | 29.69359 | Yes | |
| t value | -0.6969002 | -0.6969002 | -0.6969002 | Yes | |
| p value | 0.4912856 | 0.4912856 | 0.4912856 | Yes | |
Example with unequal variances:

| Statistic | t.test() | proc_ttest() | PROC TTEST | Match | Notes |
|------------|------------|------------|------------|------------|------------|
| Degrees of Freedom | 29.694 | 29.694 | 29.694 | Yes | |
| t value | -0.6969 | -0.70 | -0.70 | Yes | |
| p value | 0.4913 | 0.4913 | 0.4913 | Yes | |
| Mean Difference | -7.9375 | -7.9375 | -7.9375 | Yes | |
| Lower 95% CL Mean Difference | -31.2085 | -31.2085 | -31.2085 | Yes | |
| Upper 95% CL Mean Difference | 15.3335 | 15.3335 | 15.3335 | Yes | |

Example with unequal variances:
| Statistic | t.test() | proc_ttest() | PROC TTEST | Match | Notes |
|--------------------|-----------|--------------|------------|-------|-------|
| Degrees of Freedom | 18.137 | 18.137 | 18.137 | Yes | |
| t value | -1.54 | -1.54 | -1.54 | Yes | |
| p value | 0.1413 | 0.1413 | 0.1413 | Yes | |
### Lognormal Data {#lognormal}

For lognormal data for two independent groups, a two-sample t-test can be performed in R by applying a natural log transformation to the measurements in each group 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 | 30 | 30 | 30 | Yes | |
| t value | -0.8763 | -0.88 | -0.88 | Yes | |
| p value | 0.3878 | 0.3878 | 0.3878 | Yes | |
| Geometric Mean Ratio | 0.8381 | 0.8381 | 0.8381 | Yes | Back-transformed mean difference |
| Lower 95% CL Mean Ratio | 0.5553 | 0.5553 | 0.5553 | Yes | Back-transformed lower confidence limit |
| Upper 95% CL Mean Ratio | 1.265 | 1.2649 | 1.2649 | Yes | Back-transformed upper confidence limit |

# Summary and Recommendation

For the Student's T-Test, the R two sample `t.test()` and **procs** `proc_ttest()` capabilities are comparable to SAS.
Comparison between SAS and R show identical results for the datasets tried.
For the Student's T-Test, the R two-sample `t.test()` and **procs** `proc_ttest()` 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. The `proc_ttest()` also supports by groups, where `t.test()` does not.

Likewise, for the Welch's T-Test, the R two sample `t.test()` and **procs** `proc_ttest()` capabilities are comparable to SAS.
Comparison between SAS and R show identical results for the datasets tried.
Likewise, for the Welch's T-Test, the R two-sample `t.test()` and **procs** `proc_ttest()` capabilities are comparable to SAS. Comparison between SAS and R show identical results for the datasets tried.

For the lognormal version of the two-sample t-test, equivalent results can be obtained in R by applying a natural log transformation to the measurements in each group, performing the two-sample 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` Two Sample analysis documentation: <https://documentation.sas.com/doc/en/pgmsascdc/9.4_3.4/statug/statug_ttest_examples01.htm>
SAS `PROC TTEST` Two-Sample analysis documentation: <https://documentation.sas.com/doc/en/pgmsascdc/9.4_3.4/statug/statug_ttest_examples01.htm>
31 changes: 17 additions & 14 deletions Comp/r-sas_ttest_Paired.qmd
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Expand Up @@ -46,7 +46,7 @@ library(procs) # proc_ttest()

## Data

### Lognormal One Sample t-test
### 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.

Expand Down Expand Up @@ -97,21 +97,24 @@ library(procs)
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](../R/ttest_Paired.html#normal) | [Yes](../SAS/ttest_Paired.html#normal) | [Yes](#normal) | In Base R, use `paired = TRUE` on `t.test()` function |
| Paired t-test, lognormal data | [Yes](../R/ttest_Paired.html#lognormal) | [Yes](../SAS/ttest_Paired.html#lognormal) | [NA](#lognormal) | 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. |
| Paired t-test, lognormal data | [Yes](../R/ttest_Paired.html#lognormal) | [Yes](../SAS/ttest_Paired.html#lognormal) | [Yes](#lognormal) | 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 {#normal}

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 | -1.089648 | -1.089648 | -1.089648 | Yes | |
| p value | 0.2992 | 0.2992 | 0.2992 | Yes | |
| Statistic | t.test() | proc_ttest() | PROC TTEST | Match | Notes |
|-----------------|-----------|-----------|-----------|-----------|-----------|
| 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 {#lognormal}

Expand All @@ -120,13 +123,13 @@ For lognormal paired data, a paired t-test can be performed in R by applying a n
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 | 1.094185 | Yes | |
| p value | 0.2972 | 0.2992 | 0.2972 | Yes | |
| Geometric Mean Ratio | 1.0146204 | 1.0146204 | 1.0146204 | Yes | Back-transformed mean difference |
| Lower 95% CL Mean Ratio | 0.98542 | 0.98542 | 0.98542 | Yes | Back-transformed lower confidence limit |
| Upper 95% CL Mean Ratio | 1.04468 | 1.04468 | 1.04468 | Yes | Back-transformed upper confidence limit |
| 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

Expand Down
31 changes: 26 additions & 5 deletions R/ttest_2Sample.qmd
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Expand Up @@ -77,7 +77,6 @@ stats::t.test(d1p$WtGain, d1t$WtGain, var.equal = FALSE, paired = FALSE)

```


## Procs Package

### Student's T-Test and Welch's T-Test {#procs}
Expand Down Expand Up @@ -105,7 +104,6 @@ Viewer Output:
knitr::include_graphics("../images/ttest/twosample_rtest1.png")
```


## Example with unequal variances

```{r}
Expand Down Expand Up @@ -140,8 +138,6 @@ Viewer Output:
knitr::include_graphics("../images/ttest/twosample_rtest2.png")
```



::: {.callout-note collapse="true" title="Session Info"}
```{r}
#| echo: false
Expand All @@ -154,4 +150,29 @@ si <- sessioninfo::session_info(c(
))
si
```
:::
:::

## Lognormal Data {#lognormal}

The Base R `t.test()` function does not have an option for lognormal data. Likewise, the **procs** `proc_ttest()` function also does not have an option for lognormal data.

Although Base R `t.test()` does not include a lognormal option, lognormal data can be analyzed by applying a natural log transformation to the data, performing a two-sample t-test on the log-transformed data, and exponentiating the group means and confidence limits. The back-transformed difference is interpreted as a ratio of geometric means. The standard deviation is not back-transformed.

The following example applies a natural log transformation, performs the two-sample t-test on the log-transformed data, and exponentiates the mean and confidence limits.

```{r}
# Apply natural log transformation to outcome variable
d1$log_WtGain <- log(d1$WtGain)

# Perform two-sample t-test on log-transformed data
tt <- t.test(log_WtGain ~ trt_grp, data = d1)

# Back-transform log means using exponential function
gm <- tapply(d1$WtGain, d1$trt_grp, function(x) exp(mean(log(x))))

# Back-transform confidence interval limits
ci <- exp(tt$conf.int)

# Extract p-value from t-test result
p_value <- tt$p.value
```
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