Instruction of online calculator

Two-Sample T Test Calculator

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Input Data
Choose Alternative Hypothesis H1
Output

Two-Sample T-Test Calculator: Instruction Guide

Introduction

The Two-Sample T-Test Calculator is an interactive tool designed to help users test the difference between the means of two independent samples. It is commonly used for hypothesis testing in research, statistics, and data analysis, and accommodates both equal and unequal variance cases. With this calculator, users can determine whether there is sufficient evidence to support an alternative hypothesis.

How to Use

  1. Input Data:
    • x₁: Provide the list of values for the first data set.
    • x₂: Provide the list of values for the second data set.
    • Significance Level (α): Set the significance level, such as 0.05.
    • δ (Delta): Enter the hypothesized difference between means (μ₁ – μ₂).
    • Variance Assumption: Choose between:
      • Equal Variance (assumes variances of the two data sets are the same).
      • Unequal Variance (variances are considered different).
    • Alternative Hypothesis (H₁): Select one of the following forms:
      • μ₁ – μ₂ ≠ δ (two-tailed test)
      • μ₁ – μ₂ < δ (left-tailed test)
      • μ₁ – μ₂ > δ (right-tailed test)
  2. Calculation Process:
    • Click the “Calculate” button after entering the required input values. The calculator will compute the test statistic based on the chosen parameters.
  3. Output:
    • t-Score: Displays the calculated t-statistic value.
    • Result: Indicates whether to accept the alternative hypothesis (H₁), depending on the significance level (1 – α).

Example

  • Input:
    • x₁ = [18, 20, 22, 19, 21]
    • x₂ = [25, 28, 24, 27, 26]
    • Significance Level (α): 0.05
    • δ: 2
    • Variance Case: Unequal Variance
    • Alternative Hypothesis (H₁): μ₁ – μ₂ < δ (left-tailed test)
  • Output:
    • t-Score: -25.29
    • Result: Can accept H₁ with the probability of 1 – α.

In the following, you can see the output of the online solver.

This guide should enable you to effectively utilize the Two-Sample T-Test Calculator for your data analysis needs. If you have any questions, feel free to reach out!