Hypothesis Testing Calculator Two Samples

Two-Sample t-test Formula:

\[ t = \frac{x_1 - x_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}} \]

Sample 1 Mean (x₁):

Sample 2 Mean (x₂):

Sample 1 Std Dev (s₁):

Sample 2 Std Dev (s₂):

Sample 1 Size (n₁):

Sample 2 Size (n₂):

Calculated t-statistic:

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1. What is Two-Sample Hypothesis Testing?

The two-sample t-test compares the means of two independent groups to determine if there is statistical evidence that their population means are different. It's commonly used in research to compare experimental and control groups.

2. How Does the Calculator Work?

The calculator uses the two-sample t-test formula:

\[ t = \frac{x_1 - x_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}} \]

Where:

\( x_1 \) — Mean of sample 1
\( x_2 \) — Mean of sample 2
\( s_1 \) — Standard deviation of sample 1
\( s_2 \) — Standard deviation of sample 2
\( n_1 \) — Size of sample 1
\( n_2 \) — Size of sample 2

Explanation: The formula calculates how many standard errors the difference between means lies from zero. A larger absolute t-value suggests stronger evidence against the null hypothesis.

3. Interpretation of Results

Details: Compare the calculated t-value to critical values from the t-distribution table. The degrees of freedom can be approximated using the Welch-Satterthwaite equation for unequal variances.

4. Using the Calculator

Tips: Enter the sample means, standard deviations, and sizes for both groups. The calculator assumes independent samples and approximately normal distributions.

5. Frequently Asked Questions (FAQ)

Q1: When should I use a two-sample t-test?
A: Use when comparing means of two independent groups with continuous data that is approximately normally distributed.

Q2: What's the difference between paired and two-sample t-tests?
A: Paired tests compare the same subjects under two conditions, while two-sample tests compare different groups.

Q3: How do I interpret the t-value?
A: Higher absolute t-values indicate stronger evidence against the null hypothesis of equal means.

Q4: What if my sample sizes are very different?
A: Consider using the Welch's t-test which doesn't assume equal variances.

Q5: What are the assumptions of this test?
A: Independence of observations, approximately normal distributions, and equal variances (unless using Welch's version).