Master essential R functions for statistical testing. Learn how to perform correlation, covariance, and t-test in R (One-Sample, Independent, Paired) in R. Perfect for data analysts, students, and job test preparation with practical code examples.
Table of Contents
How can one compute correlation and covariances in R?
Computing correlations and covariances is a fundamental task in R, and the language provides several straightforward and powerful ways to do it. One can compute the correlation by using cor() function and cov() function to compute the covariance.
What are the different methods for computing correlation in R?
The cor() function allows you to choose the calculation method. The most common are:
"pearson": Standard correlation coefficient for linear relationships. Assumes data is normally distributed. It is the default method for computing Pearson’s Correlation Coefficient."spearman": Spearman’s rank correlation. A non-parametric method based on ranks, good for monotonic (consistently increasing or decreasing, but not necessarily linear) relationships."kendall": Kendall’s rank correlation. Another non-parametric method, often used for small data sets or when many tied ranks exist.
Explain how t-test is performed in R?
In R, the t.test() function produces a variety of t-tests. The t-test is the most common test in statistics and is used to determine whether the means of two groups are equal to each other.
The primary function for all t-tests in R is t.test(). Its usage changes slightly depending on the type of test you want to perform (one-sample, independent two-sample, or paired).
One-Sample T-Test
To determine if the mean of a single sample is significantly different from a known or hypothesized population mean. The general syntax of the t-test in R is
t.test(x, mu = hypothesized_mean, alternative = "two.sided")
The description of the argument are:
x: A numeric vector of data.mu: The hypothesized true population mean.alternative: The alternative hypothesis. Can be"two.sided","less", or"greater".
Independent Two-Sample T-Test
To compare the means of two independent groups to see if they are significantly different from each other. The general syntax of the two-sample t-test is
t.test(x, y, alternative = "two.sided", var.equal = FALSE)
The description of the important argument is:
x: A numeric vector of data for group 1.y: A numeric vector of data for group 2.var.equal: A crucial argument.var.equal = FALSE: Uses the Welch’s t-test, which does not assume the two groups have equal variances. This is the recommended and safer choice in most real-world situations. It is the default argument value.var.equal = TRUE: Uses the Student’s classic t-test, which does assume equal variances.
The two-sample t-test can be computed by using t.test() function in formula format
t.test(numeric_variable ~ group_variable, data = my_data, ...)
Paired T-Test
To compare the means of the same group at two different times (e.g., before and after a treatment). The data is “paired” because each subject is measured twice. The general syntax for the paired sample t-test is
t.test(x, y, paired = TRUE, alternative = "two.sided")
What are the output objects of t.test() the function, and how can these be extracted?
The t.test() function returns a list object containing all the results. You can store it and extract specific values for reporting.
my_test <- t.test(mtcars$mpg, mu = 15)
One can extract specific values from t.test() function.
- my_test$statistic # t-value
- my_test$parameter # degrees of freedom (df)
- my_test$p.value # p-value
- my_test$estimate # estimated mean (or means)
- my_test$conf.int # confidence interval
One can print a clean summary of objects
cat("t(", my_test$parameter, ") = ", round(my_test$statistic, 2), ", p = ", format.pval(my_test$p.value, digits=2), sep = "")Perform Correlation Analysis
Perform Testing of Hypothesis