Install ggpubr R package for data visualization

You can draw R base graps 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 one-sample t-test

To perform one-sample t-test, the R function t.test() can be used as follow:

t.test(x, mu = 0, alternative = "two.sided")

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 containing the weight of 10 mice.

We want to know, if the average weight of the mice differs from 25g?

set.seed(1234)
my_data <- data.frame(
  name = paste0(rep("M_", 10), 1:10),
  weight = round(rnorm(10, 20, 2), 1)
)

Check your data

# Print the first 10 rows of the data
head(my_data, 10)

   name weight
1   M_1   17.6
2   M_2   20.6
3   M_3   22.2
4   M_4   15.3
5   M_5   20.9
6   M_6   21.0
7   M_7   18.9
8   M_8   18.9
9   M_9   18.9
10 M_10   18.2

# Statistical summaries of weight
summary(my_data$weight)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  15.30   18.38   18.90   19.25   20.82   22.20 

• Min.: the minimum value
• 1st Qu.: The first quartile. 25% of values are lower than this.
• Median: the median value. Half the values are lower; half are higher.
• 3rd Qu.: the third quartile. 75% of values are higher than this.
• Max.: the maximum value

Visualize your data using box plots

library(ggpubr)
ggboxplot(my_data$weight, 
          ylab = "Weight (g)", xlab = FALSE,
          ggtheme = theme_minimal())

One-Sample Student’s T-test in R

Preleminary test to check one-sample t-test assumptions

1. Is this a large sample? - No, because n < 30.
2. Since the sample size is not large enough (less than 30, central limit theorem), we need to check whether the data follow a normal distribution.

How to check the normality?

Read this article: Normality Test in R.

Briefly, it’s possible to use the Shapiro-Wilk normality test and to look at the normality plot.

1. Shapiro-Wilk test:
   • Null hypothesis: the data are normally distributed
   • Alternative hypothesis: the data are not normally distributed

shapiro.test(my_data$weight) # => p-value = 0.6993

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

• Visual inspection of the data normality using Q-Q plots (quantile-quantile plots). Q-Q plot draws the correlation between a given sample and the normal distribution.

library("ggpubr")
ggqqplot(my_data$weight, ylab = "Men's weight",
         ggtheme = theme_minimal())

One-Sample Student’s T-test in R

From the normality plots, we conclude that the data may come from normal distributions.

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

Compute one-sample t-test

We want to know, if the average weight of the mice differs from 25g (two-tailed test)?

# One-sample t-test
res <- t.test(my_data$weight, mu = 25)
# Printing the results
res 

    One Sample t-test
data:  my_data$weight
t = -9.0783, df = 9, p-value = 7.953e-06
alternative hypothesis: true mean is not equal to 25
95 percent confidence interval:
 17.8172 20.6828
sample estimates:
mean of x 
    19.25 

t.test(my_data$weight, mu = 25,
              alternative = "less")

t.test(my_data$weight, mu = 25,
              alternative = "greater")

Interpretation of the result

The p-value of the test is 7.95310^{-6}, which is less than the significance level alpha = 0.05. We can conclude that the mean weight of the mice is significantly different from 25g with a p-value = 7.95310^{-6}.

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] 7.953383e-06

# printing the mean
res$estimate

mean of x 
    19.25 

# printing the confidence interval
res$conf.int

[1] 17.8172 20.6828
attr(,"conf.level")
[1] 0.95