Install ggpubr R package for data visualization

You can draw R base graphs as described at this link: R base graphs. Here, we’ll use the ggpubr R package for an easy ggplot2-based data visualization

• Install the latest version from GitHub as follow (recommended):

# Install
if(!require(devtools)) install.packages("devtools")
devtools::install_github("kassambara/ggpubr")

• Or, install from CRAN as follow:

install.packages("ggpubr")

R function to compute unpaired two-samples t-test

To perform two-samples t-test comparing the means of two independent samples (x & y), the R function t.test() can be used as follow:

t.test(x, y, alternative = "two.sided", var.equal = FALSE)

Import your data into R

1. Prepare your data as specified here: Best practices for preparing your data set for R

2. Save your data in an external .txt tab or .csv files

3. Import your data into R as follow:

# If .txt tab file, use this
my_data <- read.delim(file.choose())
# Or, if .csv file, use this
my_data <- read.csv(file.choose())

Here, we’ll use an example data set, which contains the weight of 18 individuals (9 women and 9 men):

# Data in two numeric vectors
women_weight <- c(38.9, 61.2, 73.3, 21.8, 63.4, 64.6, 48.4, 48.8, 48.5)
men_weight <- c(67.8, 60, 63.4, 76, 89.4, 73.3, 67.3, 61.3, 62.4) 
# Create a data frame
my_data <- data.frame( 
                group = rep(c("Woman", "Man"), each = 9),
                weight = c(women_weight,  men_weight)
                )

We want to know, if the average women’s weight differs from the average men’s weight?

Check your data

# Print all data
print(my_data)

   group weight
1  Woman   38.9
2  Woman   61.2
3  Woman   73.3
4  Woman   21.8
5  Woman   63.4
6  Woman   64.6
7  Woman   48.4
8  Woman   48.8
9  Woman   48.5
10   Man   67.8
11   Man   60.0
12   Man   63.4
13   Man   76.0
14   Man   89.4
15   Man   73.3
16   Man   67.3
17   Man   61.3
18   Man   62.4

It’s possible to compute summary statistics (mean and sd) by groups. The dplyr package can be used.

• To install dplyr package, type this:

install.packages("dplyr")

• Compute summary statistics by groups:

library(dplyr)
group_by(my_data, group) %>%
  summarise(
    count = n(),
    mean = mean(weight, na.rm = TRUE),
    sd = sd(weight, na.rm = TRUE)
  )

Source: local data frame [2 x 4]
   group count     mean        sd
  (fctr) (int)    (dbl)     (dbl)
1    Man     9 68.98889  9.375426
2  Woman     9 52.10000 15.596714

Visualize your data using box plots

# Plot weight by group and color by group
library("ggpubr")
ggboxplot(my_data, x = "group", y = "weight", 
          color = "group", palette = c("#00AFBB", "#E7B800"),
        ylab = "Weight", xlab = "Groups")

Unpaired Two-Samples Student’s T-test in R

Preleminary test to check independent t-test assumptions

Assumption 1: Are the two samples independents?

Yes, since the samples from men and women are not related.

Assumtion 2: Are the data from each of the 2 groups follow a normal distribution?

Use Shapiro-Wilk normality test as described at: Normality Test in R. - Null hypothesis: the data are normally distributed - Alternative hypothesis: the data are not normally distributed

We’ll use the functions with() and shapiro.test() to compute Shapiro-Wilk test for each group of samples.

# Shapiro-Wilk normality test for Men's weights
with(my_data, shapiro.test(weight[group == "Man"]))# p = 0.1
# Shapiro-Wilk normality test for Women's weights
with(my_data, shapiro.test(weight[group == "Woman"])) # p = 0.6

From the output, the two p-values are greater than the significance level 0.05 implying that the distribution of the data are not significantly different from the normal distribution. In other words, we can assume the normality.

Note that, if the data are not normally distributed, it’s recommended to use the non parametric two-samples Wilcoxon rank test.

Assumption 3. Do the two populations have the same variances?

We’ll use F-test to test for homogeneity in variances. This can be performed with the function var.test() as follow:

res.ftest <- var.test(weight ~ group, data = my_data)
res.ftest

    F test to compare two variances
data:  weight by group
F = 0.36134, num df = 8, denom df = 8, p-value = 0.1714
alternative hypothesis: true ratio of variances is not equal to 1
95 percent confidence interval:
 0.08150656 1.60191315
sample estimates:
ratio of variances 
         0.3613398 

The p-value of F-test is p = 0.1713596. It’s greater than the significance level alpha = 0.05. In conclusion, there is no significant difference between the variances of the two sets of data. Therefore, we can use the classic t-test witch assume equality of the two variances.

Compute unpaired two-samples t-test

Question : Is there any significant difference between women and men weights?

1) Compute independent t-test - Method 1: The data are saved in two different numeric vectors.

# Compute t-test
res <- t.test(women_weight, men_weight, var.equal = TRUE)
res

    Two Sample t-test
data:  women_weight and men_weight
t = -2.7842, df = 16, p-value = 0.01327
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -29.748019  -4.029759
sample estimates:
mean of x mean of y 
 52.10000  68.98889 

2) Compute independent t-test - Method 2: The data are saved in a data frame.

# Compute t-test
res <- t.test(weight ~ group, data = my_data, var.equal = TRUE)
res

    Two Sample t-test
data:  weight by group
t = 2.7842, df = 16, p-value = 0.01327
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
  4.029759 29.748019
sample estimates:
  mean in group Man mean in group Woman 
           68.98889            52.10000 

As you can see, the two methods give the same results.

t.test(weight ~ group, data = my_data,
        var.equal = TRUE, alternative = "less")

t.test(weight ~ group, data = my_data,
        var.equal = TRUE, alternative = "greater")

Interpretation of the result

The p-value of the test is 0.01327, which is less than the significance level alpha = 0.05. We can conclude that men’s average weight is significantly different from women’s average weight with a p-value = 0.01327.

Access to the values returned by t.test() function

The result of t.test() function is a list containing the following components:

The format of the R code to use for getting these values is as follow:

# printing the p-value
res$p.value

[1] 0.0132656

# printing the mean
res$estimate

  mean in group Man mean in group Woman 
           68.98889            52.10000 

# printing the confidence interval
res$conf.int

[1]  4.029759 29.748019
attr(,"conf.level")
[1] 0.95