Instruction of online calculator

Paired Sample Test Calculator

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Input Data
Choose Alternative Hypothesis H1
Output

Here’s a clear and structured guide for your Paired Sample T Test Calculator:

Paired Sample T Test Calculator: User Guide

Introduction

The Paired Sample T Test Calculator is a powerful tool for analyzing paired data sets. It helps determine whether the mean difference between two sets of related data is statistically significant. This test is commonly used in scenarios like comparing measurements before and after a treatment or assessing two conditions for the same subjects. The calculator provides results including the t-score and a decision on the alternative hypothesis based on the selected significance level.

How to Use the Calculator

  1. Input Data Requirements:
    • x1 (First Data Set): Enter the numerical values for the first set of paired observations.
    • x2 (Second Data Set): Provide the numerical values for the second set of paired observations, matching each pair with x1.
    • Significance Level (α): Specify the desired level of significance (e.g., 0.05 for a 5% significance level).
    • Delta (δ): Define the hypothesized difference (μ1 – μ0) between the means of the two data sets.
  2. Select the Alternative Hypothesis (H1): Choose the appropriate hypothesis based on your research question:
    • Case 1: μ1 – μ2 ≠ δ (Two-tailed test: checking for any difference).
    • Case 2: μ1 – μ2 < δ (One-tailed test: checking if the mean difference is less than δ).
    • Case 3: μ1 – μ2 > δ (One-tailed test: checking if the mean difference is greater than δ).
  3. Run the Calculation:
    • Submit the input data into the calculator.
    • The tool computes the t-score based on the input and provides the statistical result.
  4. Interpret Results:
    • Review the output, which includes:
      • t-score: The calculated test statistic value.
      • Result: A statement determining whether to accept the alternative hypothesis (H1), with confidence (1 – α).

Example:

  • Input Data:
    • x1: [7, 9, 11, 13]
    • x2: [5, 8, 10, 12]
    • Significance Level (α): 0.05
    • Delta (δ): 0
    • Alternative Hypothesis (H1): μ1 – μ2 > δ
  • Output Example:
    • t-score: 5.0
    • Result: Can accept H1 with the probability of (1 – 0.05).

The example above indicates that at the 5% significance level, there is sufficient evidence to support the claim that μ1 – μ2 > δ.

in the following, you can see the output of online solver for Paired Sample Test Calculator.

I hope this guide aligns with your vision for the calculator! If you need any refinements or additions, feel free to ask!