STATISTIKA - Uji T Sampel Berpasangan (Paired Samples T Test) Cara Manual + Contoh Soal

Summary

This video explains how to conduct a paired sample t-test manually, using a case study where Jigsaw learning is tested for improving students' mastery of science concepts. The steps include formulating hypotheses, calculating means and variances, determining the correlation coefficient, and computing the t-value. The null hypothesis is tested at a 5% significance level, with the final conclusion showing no significant difference in students' performance before and after using Jigsaw. The tutorial provides a clear, step-by-step guide to understanding the statistical process involved in hypothesis testing.

Takeaways

• 😀 Paired sample t-test is used to compare the means of two related groups to determine if there is a significant difference between them.
• 😀 The hypothesis for the paired sample t-test includes a null hypothesis (H₀) stating no difference and an alternative hypothesis (H₁) stating there is a difference.
• 😀 A two-tailed test is conducted because the test aims to determine if the means are different in either direction, not just one.
• 😀 A significance level (α) of 5% (0.05) is commonly used in hypothesis testing to determine whether the results are statistically significant.
• 😀 In a paired sample t-test, the differences between the paired observations (pre-test and post-test) are calculated to analyze the impact of an intervention.
• 😀 The t-statistic is calculated by comparing the difference in means to the variability of the differences, using sample sizes, variances, and standard deviations.
• 😀 The degrees of freedom (df) for a paired sample t-test is calculated as the number of pairs (n) minus 1.
• 😀 The critical t-value is obtained from the t-distribution table, based on the degrees of freedom and significance level, to compare against the calculated t-value.
• 😀 If the calculated t-value exceeds the critical t-value, the null hypothesis is rejected, indicating a significant difference; otherwise, the null hypothesis is accepted.
• 😀 In this example, the results show no significant difference in students' mastery of IPA concepts before and after the Jigsaw learning method, as the calculated t-value was smaller than the critical t-value.

Q & A

What is the objective of the study described in the script?

The objective of the study is to determine whether Jigsaw learning improves students' understanding of science concepts (IPA) by comparing their pre-test and post-test scores.

What type of statistical test is used in this study?

The study uses a paired sample t-test (uji t sampel berpasangan) to compare the pre-test and post-test scores of the students.

How many students participated in the study?

A total of 10 students participated in the study.

What are the null and alternative hypotheses in this study?

The null hypothesis (H0) states that there is no difference in students' IPA scores before and after using Jigsaw learning, while the alternative hypothesis (H1) suggests there is a significant difference.

What significance level (alpha) is used in the study?

The significance level used in the study is 5%, or 0.05.

How is the t-statistic calculated in this study?

The t-statistic is calculated using the formula: (mean of post-test scores - mean of pre-test scores) divided by the square root of the sum of variances for both sets of data.

What was the calculated t-value and how does it compare to the t-table value?

The calculated t-value was -1.25, and it was compared to the t-table value of 2.26. Since the absolute value of the calculated t-value was less than the t-table value, the null hypothesis was accepted.

What does it mean when the calculated t-value is less than the t-table value?

It means that there is insufficient evidence to reject the null hypothesis, indicating that there is no significant difference in the students' performance before and after the Jigsaw learning method.

What statistical calculations were done before determining the t-value?

Before determining the t-value, the means, variances, and standard deviations for both the pre-test and post-test scores were calculated.

Why is the paired sample t-test appropriate for this study?

The paired sample t-test is appropriate because it compares two related groups, in this case, the same students' scores before and after the Jigsaw learning intervention, to assess whether the intervention caused a significant change.