A t-test is a statistical test used to compare the means of two groups and determine if they are significantly different from each other. In R, you can perform one-sample t-tests and paired t-tests using the t.test() function. Here’s how to conduct these t-tests with examples:
- One-Sample T-Test:
The one-sample t-test is used to determine whether the mean of a sample is significantly different from a hypothesized population mean.
Example: One-sample t-test
Hypothesized population mean: 50
Sample data: Exam scores
scores ← c(56, 62, 58, 53, 60, 57, 59, 61, 55, 54)
Perform one-sample t-test
t_test_result ← t.test(scores, mu = 50)
Print the t-test result
print(t_test_result)
A t-test is a statistical test used to compare the means of two groups and determine if they are significantly different from each other. In R, you can perform one-sample t-tests and paired t-tests using the t.test() function. Here’s how to conduct these t-tests with examples:
- One-Sample T-Test:
The one-sample t-test is used to determine whether the mean of a sample is significantly different from a hypothesized population mean.
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Example: One-sample t-test
Hypothesized population mean: 50
Sample data: Exam scores
scores ← c(56, 62, 58, 53, 60, 57, 59, 61, 55, 54)
Perform one-sample t-test
t_test_result ← t.test(scores, mu = 50)
Print the t-test result
print(t_test_result)
- Paired T-Test:
The paired t-test is used when you have two related samples (e.g., before and after measurements) and want to determine if there is a significant difference in means.
Example: Paired t-test
Sample data: Before and after weights of individuals
before ← c(150, 155, 160, 145, 170)
after ← c(148, 157, 159, 143, 167)
Perform paired t-test
paired_t_test_result ← t.test(before, after, paired = TRUE)
Print the paired t-test result
print(paired_t_test_result)
In both examples, the t.test() function calculates the t-test and provides various output, including the t-statistic, degrees of freedom, p-value, and confidence interval. The mu parameter in the one-sample t-test specifies the hypothesized population mean.
Remember that when interpreting the results, you’ll typically focus on the p-value. If the p-value is less than a chosen significance level (e.g., 0.05), you may conclude that there is a significant difference between the sample means.
These examples demonstrate how to perform one-sample and paired t-tests in R using the t.test() function. The t-test is a common tool for hypothesis testing and determining whether observed differences are statistically significant.