# 18 Simple statistical tests

This page demonstrates how to conduct simple statistical tests using base R, rstatix, and gtsummary.

• T-test
• Shapiro-Wilk test
• Wilcoxon rank sum test
• Kruskal-Wallis test
• Chi-squared test
• Correlations between numeric variables

…many other tests can be performed, but we showcase just these common ones and link to further documentation.

• Use base R functions to print a statistical outputs to the R Console
• Use rstatix functions to return results in a data frame, or if you want tests to run by group
• Use gtsummary if you want to quickly print publication-ready tables

## 18.1 Preparation

This code chunk shows the loading of packages required for the analyses. In this handbook we emphasize p_load() from pacman, which installs the package if necessary and loads it for use. You can also load installed packages with library() from base R. See the page on R basics for more information on R packages.

pacman::p_load(
rio,          # File import
here,         # File locator
skimr,        # get overview of data
tidyverse,    # data management + ggplot2 graphics,
gtsummary,    # summary statistics and tests
rstatix,      # statistics
corrr,        # correlation analayis for numeric variables
janitor,      # adding totals and percents to tables
flextable     # converting tables to HTML
)

### Import data

We import the dataset of cases from a simulated Ebola epidemic. If you want to follow along, (as .rds file). Import your data with the import() function from the rio package (it accepts many file types like .xlsx, .rds, .csv - see the Import and export page for details).

# import the linelist
linelist <- import("linelist_cleaned.rds")

The first 50 rows of the linelist are displayed below.

## 18.2base R

You can use base R functions to conduct statistical tests. The commands are relatively simple and results will print to the R Console for simple viewing. However, the outputs are usually lists and so are harder to manipulate if you want to use the results in subsequent operations.

### T-tests

A t-test, also called “Student’s t-Test”, is typically used to determine if there is a significant difference between the means of some numeric variable between two groups. Here we’ll show the syntax to do this test depending on whether the columns are in the same data frame.

Syntax 1: This is the syntax when your numeric and categorical columns are in the same data frame. Provide the numeric column on the left side of the equation and the categorical column on the right side. Specify the dataset to data =. Optionally, set paired = TRUE, and conf.level = (0.95 default), and alternative = (either “two.sided”, “less”, or “greater”). Enter ?t.test for more details.

## compare mean age by outcome group with a t-test
t.test(age_years ~ gender, data = linelist)
##
##  Welch Two Sample t-test
##
## data:  age_years by gender
## t = -21.344, df = 4902.3, p-value < 2.2e-16
## alternative hypothesis: true difference in means between group f and group m is not equal to 0
## 95 percent confidence interval:
##  -7.571920 -6.297975
## sample estimates:
## mean in group f mean in group m
##        12.60207        19.53701

Syntax 2: You can compare two separate numeric vectors using this alternative syntax. For example, if the two columns are in different data sets.

t.test(df1$age_years, df2$age_years)

You can also use a t-test to determine whether a sample mean is significantly different from some specific value. Here we conduct a one-sample t-test with the known/hypothesized population mean as mu =:

### Wilcoxon rank sum test

The Wilcoxon rank sum test, also called the Mann–Whitney U test, is often used to help determine if two numeric samples are from the same distribution when their populations are not normally distributed or have unequal variance.

## compare age distribution by outcome group with a wilcox test
wilcox.test(age_years ~ outcome, data = linelist)
##
##  Wilcoxon rank sum test with continuity correction
##
## data:  age_years by outcome
## W = 2501868, p-value = 0.8308
## alternative hypothesis: true location shift is not equal to 0

### Kruskal-Wallis test

The Kruskal-Wallis test is an extension of the Wilcoxon rank sum test that can be used to test for differences in the distribution of more than two samples. When only two samples are used it gives identical results to the Wilcoxon rank sum test.

## compare age distribution by outcome group with a kruskal-wallis test
kruskal.test(age_years ~ outcome, linelist)
##
##  Kruskal-Wallis rank sum test
##
## data:  age_years by outcome
## Kruskal-Wallis chi-squared = 0.045675, df = 1, p-value = 0.8308

### Chi-squared test

Pearson’s Chi-squared test is used in testing for significant differences between categorical croups.

## compare the proportions in each group with a chi-squared test
chisq.test(linelist$gender, linelist$outcome)
##
##  Pearson's Chi-squared test with Yates' continuity correction
##
## data:  linelist$gender and linelist$outcome
## X-squared = 0.0011841, df = 1, p-value = 0.9725

## 18.3rstatix package

The rstatix package offers the ability to run statistical tests and retrieve results in a “pipe-friendly” framework. The results are automatically in a data frame so that you can perform subsequent operations on the results. It is also easy to group the data being passed into the functions, so that the statistics are run for each group.

### Summary statistics

The function get_summary_stats() is a quick way to return summary statistics. Simply pipe your dataset to this function and provide the columns to analyse. If no columns are specified, the statistics are calculated for all columns.

By default, a full range of summary statistics are returned: n, max, min, median, 25%ile, 75%ile, IQR, median absolute deviation (mad), mean, standard deviation, standard error, and a confidence interval of the mean.

linelist %>%
rstatix::get_summary_stats(age, temp)
## # A tibble: 2 x 13
##   variable     n   min   max median    q1    q3   iqr    mad  mean     sd    se    ci
##   <chr>    <dbl> <dbl> <dbl>  <dbl> <dbl> <dbl> <dbl>  <dbl> <dbl>  <dbl> <dbl> <dbl>
## 1 age       5802   0    84     13     6    23      17 11.9    16.1 12.6   0.166 0.325
## 2 temp      5739  35.2  40.8   38.8  38.2  39.2     1  0.741  38.6  0.977 0.013 0.025

You can specify a subset of summary statistics to return by providing one of the following values to type =: “full”, “common”, “robust”, “five_number”, “mean_sd”, “mean_se”, “mean_ci”, “median_iqr”, “median_mad”, “quantile”, “mean”, “median”, “min”, “max”.

It can be used with grouped data as well, such that a row is returned for each grouping-variable:

linelist %>%
group_by(hospital) %>%
rstatix::get_summary_stats(age, temp, type = "common")
## # A tibble: 12 x 11
##    hospital          variable     n   min   max median   iqr  mean     sd    se    ci
##    <chr>             <chr>    <dbl> <dbl> <dbl>  <dbl> <dbl> <dbl>  <dbl> <dbl> <dbl>
##  1 Central Hospital  age        445   0    58     12    15    15.7 12.5   0.591 1.16
##  2 Central Hospital  temp       450  35.2  40.4   38.8   1    38.5  0.964 0.045 0.089
##  3 Military Hospital age        884   0    72     14    18    16.1 12.4   0.417 0.818
##  4 Military Hospital temp       873  35.3  40.5   38.8   1    38.6  0.952 0.032 0.063
##  5 Missing           age       1441   0    76     13    17    16.0 12.9   0.339 0.665
##  6 Missing           temp      1431  35.8  40.6   38.9   1    38.6  0.97  0.026 0.05
##  7 Other             age        873   0    69     13    17    16.0 12.5   0.422 0.828
##  8 Other             temp       862  35.7  40.8   38.8   1.1  38.5  1.01  0.034 0.067
##  9 Port Hospital     age       1739   0    68     14    18    16.3 12.7   0.305 0.598
## 10 Port Hospital     temp      1713  35.5  40.6   38.8   1.1  38.6  0.981 0.024 0.046
## 11 St. Mark's Mater~ age        420   0    84     12    15    15.7 12.4   0.606 1.19
## 12 St. Mark's Mater~ temp       410  35.9  40.6   38.8   1.1  38.5  0.983 0.049 0.095

You can also use rstatix to conduct statistical tests:

### T-test

Use a formula syntax to specify the numeric and categorical columns:

linelist %>%
t_test(age_years ~ gender)
## # A tibble: 1 x 10
## * <chr>     <chr>  <chr>  <int> <int>     <dbl> <dbl>    <dbl>    <dbl> <chr>
## 1 age_years f      m       2807  2803     -21.3 4902. 9.89e-97 9.89e-97 ****

Or use ~ 1 and specify mu = for a one-sample T-test. This can also be done by group.

linelist %>%
t_test(age_years ~ 1, mu = 30)
## # A tibble: 1 x 7
##   .y.       group1 group2         n statistic    df     p
## * <chr>     <chr>  <chr>      <int>     <dbl> <dbl> <dbl>
## 1 age_years 1      null model  5888     -84.2  5801     0

If applicable, the statistical tests can be done by group, as shown below:

linelist %>%
group_by(gender) %>%
t_test(age_years ~ 1, mu = 18)
## # A tibble: 3 x 8
##   gender .y.       group1 group2         n statistic    df         p
## * <chr>  <chr>     <chr>  <chr>      <int>     <dbl> <dbl>     <dbl>
## 1 f      age_years 1      null model  2807    -29.8   2806 7.52e-170
## 2 m      age_years 1      null model  2803      5.70  2802 1.34e-  8
## 3 <NA>   age_years 1      null model   278     -3.80   191 1.96e-  4

### Shapiro-Wilk test

As stated above, sample size must be between 3 and 5000.

linelist %>%
head(500) %>%            # first 500 rows of case linelist, for example only
shapiro_test(age_years)
## # A tibble: 1 x 3
##   variable  statistic        p
##   <chr>         <dbl>    <dbl>
## 1 age_years     0.917 6.67e-16

### Wilcoxon rank sum test

linelist %>%
wilcox_test(age_years ~ gender)
## # A tibble: 1 x 9
## * <chr>     <chr>  <chr>  <int> <int>     <dbl>    <dbl>    <dbl> <chr>
## 1 age_years f      m       2807  2803   2829274 3.47e-74 3.47e-74 ****

### Kruskal-Wallis test

Also known as the Mann-Whitney U test.

linelist %>%
kruskal_test(age_years ~ outcome)
## # A tibble: 1 x 6
##   .y.           n statistic    df     p method
## * <chr>     <int>     <dbl> <int> <dbl> <chr>
## 1 age_years  5888    0.0457     1 0.831 Kruskal-Wallis

### Chi-squared test

The chi-square test function accepts a table, so first we create a cross-tabulation. There are many ways to create a cross-tabulation (see Descriptive tables) but here we use tabyl() from janitor and remove the left-most column of value labels before passing to chisq_test().

linelist %>%
tabyl(gender, outcome) %>%
select(-1) %>%
chisq_test()
## # A tibble: 1 x 6
##       n statistic     p    df method          p.signif
## * <dbl>     <dbl> <dbl> <int> <chr>           <chr>
## 1  5888      3.53 0.473     4 Chi-square test ns

Many many more functions and statistical tests can be run with rstatix functions. See the documentation for rstatix online here or by entering ?rstatix.

## 18.4gtsummary package

Use gtsummary if you are looking to add the results of a statistical test to a pretty table that was created with this package (as described in the gtsummary section of the Descriptive tables page).

Performing statistical tests of comparison with tbl_summary is done by adding the add_p function to a table and specifying which test to use. It is possible to get p-values corrected for multiple testing by using the add_q function. Run ?tbl_summary for details.

### Chi-squared test

Compare the proportions of a categorical variable in two groups. The default statistical test for add_p() when applied to a categorical variable is to perform a chi-squared test of independence with continuity correction, but if any expected call count is below 5 then a Fisher’s exact test is used.

linelist %>%
select(gender, outcome) %>%    # keep variables of interest
tbl_summary(by = outcome) %>%  # produce summary table and specify grouping variable
add_p()                        # specify what test to perform
## 1323 observations missing outcome have been removed. To include these observations, use forcats::fct_explicit_na() on outcome column before passing to tbl_summary().
Characteristic Death, N = 2,5821 Recover, N = 1,9831 p-value2
gender >0.9
f 1,227 (50%) 953 (50%)
m 1,228 (50%) 950 (50%)
Unknown 127 80

1 n (%)

2 Pearson's Chi-squared test

### T-tests

Compare the difference in means for a continuous variable in two groups. For example, compare the mean age by patient outcome.

linelist %>%
select(age_years, outcome) %>%             # keep variables of interest
tbl_summary(                               # produce summary table
statistic = age_years ~ "{mean} ({sd})", # specify what statistics to show
by = outcome) %>%                        # specify the grouping variable
add_p(age_years ~ "t.test")                # specify what tests to perform
## 1323 observations missing outcome have been removed. To include these observations, use forcats::fct_explicit_na() on outcome column before passing to tbl_summary().
Characteristic Death, N = 2,5821 Recover, N = 1,9831 p-value2
age_years 16 (12) 16 (13) 0.6
Unknown 32 28

1 Mean (SD)

2 Welch Two Sample t-test

### Wilcoxon rank sum test

Compare the distribution of a continuous variable in two groups. The default is to use the Wilcoxon rank sum test and the median (IQR) when comparing two groups. However for non-normally distributed data or comparing multiple groups, the Kruskal-wallis test is more appropriate.

linelist %>%
select(age_years, outcome) %>%                       # keep variables of interest
tbl_summary(                                         # produce summary table
statistic = age_years ~ "{median} ({p25}, {p75})", # specify what statistic to show (this is default so could remove)
by = outcome) %>%                                  # specify the grouping variable
add_p(age_years ~ "wilcox.test")                     # specify what test to perform (default so could leave brackets empty)
## 1323 observations missing outcome have been removed. To include these observations, use forcats::fct_explicit_na() on outcome column before passing to tbl_summary().
Characteristic Death, N = 2,5821 Recover, N = 1,9831 p-value2
age_years 13 (6, 23) 13 (6, 23) 0.8
Unknown 32 28

1 Median (IQR)

2 Wilcoxon rank sum test

### Kruskal-wallis test

Compare the distribution of a continuous variable in two or more groups, regardless of whether the data is normally distributed.

linelist %>%
select(age_years, outcome) %>%                       # keep variables of interest
tbl_summary(                                         # produce summary table
statistic = age_years ~ "{median} ({p25}, {p75})", # specify what statistic to show (default, so could remove)
by = outcome) %>%                                  # specify the grouping variable
add_p(age_years ~ "kruskal.test")                    # specify what test to perform
## 1323 observations missing outcome have been removed. To include these observations, use forcats::fct_explicit_na() on outcome column before passing to tbl_summary().
Characteristic Death, N = 2,5821 Recover, N = 1,9831 p-value2
age_years 13 (6, 23) 13 (6, 23) 0.8
Unknown 32 28

1 Median (IQR)

2 Kruskal-Wallis rank sum test

## 18.5 Correlations

Correlation between numeric variables can be investigated using the tidyverse
corrr package. It allows you to compute correlations using Pearson, Kendall tau or Spearman rho. The package creates a table and also has a function to automatically plot the values.

correlation_tab <- linelist %>%
select(generation, age, ct_blood, days_onset_hosp, wt_kg, ht_cm) %>%   # keep numeric variables of interest
correlate()      # create correlation table (using default pearson)

correlation_tab    # print
## # A tibble: 6 x 7
##   term            generation       age ct_blood days_onset_hosp    wt_kg    ht_cm
##   <chr>                <dbl>     <dbl>    <dbl>           <dbl>    <dbl>    <dbl>
## 1 generation        NA       -0.0222    0.179         -0.288    -0.0302  -0.00942
## 2 age               -0.0222  NA         0.00849       -0.000635  0.833    0.877
## 3 ct_blood           0.179    0.00849  NA             -0.600    -0.00636  0.0181
## 4 days_onset_hosp   -0.288   -0.000635 -0.600         NA         0.0153  -0.00953
## 5 wt_kg             -0.0302   0.833    -0.00636        0.0153   NA        0.884
## 6 ht_cm             -0.00942  0.877     0.0181        -0.00953   0.884   NA
## remove duplicate entries (the table above is mirrored)
correlation_tab <- correlation_tab %>%
shave()

## view correlation table
correlation_tab
## # A tibble: 6 x 7
##   term            generation       age ct_blood days_onset_hosp  wt_kg ht_cm
##   <chr>                <dbl>     <dbl>    <dbl>           <dbl>  <dbl> <dbl>
## 1 generation        NA       NA        NA              NA       NA        NA
## 2 age               -0.0222  NA        NA              NA       NA        NA
## 3 ct_blood           0.179    0.00849  NA              NA       NA        NA
## 4 days_onset_hosp   -0.288   -0.000635 -0.600          NA       NA        NA
## 5 wt_kg             -0.0302   0.833    -0.00636         0.0153  NA        NA
## 6 ht_cm             -0.00942  0.877     0.0181         -0.00953  0.884    NA
## plot correlations
rplot(correlation_tab)