Parametric Inference for two-sample T-test
R
# Example: Performing a two-sample t-test # Assuming you have two sets of data in vectors x and y # Create sample data (replace this with your actual data) x <- c (25, 30, 35, 40, 45) y <- c (22, 27, 33, 38, 41) # Conduct a two-sample t-test result <- t.test (x, y) # Print the results print (result) # Extract specific values like the p-value and confidence intervals p_value <- result$p.value conf_int <- result$conf.int cat ( 'p-value :' ,p_value, '\n' ) cat ( 'Confidence Interval :' ,conf_int) |
Output:
Welch Two Sample t-test
data: x and y
t = 0.56408, df = 7.9983, p-value = 0.5882
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-8.647129 14.247129
sample estimates:
mean of x mean of y
35.0 32.2
p-value : 0.5881658
Confidence Interval : -8.647129 14.24713
- The two-sample t-test findings, including the t-statistic, degrees of freedom, p-value, and confidence intervals, are computed using the t.test function. The assumption that the means of the two samples are equivalent is put to the test.
- The result object prints a summary of the t-test when it is printed. This includes details about the alternative hypothesis, which is often that the means are not equal, the p-value, the confidence interval for the difference in means, and the t-statistic and its related degrees of freedom.
- The p-value obtained from the t-test is stored in the p_value variable. Under the null hypothesis, it estimates the likelihood of discovering the observed difference in means (or a more extreme difference). Stronger evidence that the null hypothesis is incorrect is shown by lower p-values.
- The confidence interval for the mean difference is kept in the conf_int variable. It provides a range, with a defined level of confidence (often 95% by default), within which the genuine difference in means is expected to fall.
Here, let’s dive deeper into the concept of parametric inference in R with examples.
Parametric Inference with R
Parametric inference in R involves the process of drawing statistical conclusions regarding a population using a parametric statistical framework. These parametric models make the assumption that the data adheres to a specific probability distribution, such as the normal, binomial, or Poisson distributions, and they incorporate parameters to characterize these distributions.
It is a technique that involves making assumptions, about the probability distribution underlying your data. Based on these assumptions you can then draw conclusions. Make inferences about population parameters. In the R programming language parametric inference is frequently employed for tasks such, as hypothesis testing and estimating parameters.