1. What is the Difference of Means Test?

The difference of means test (t-test) is a statistical method used to determine whether there is a significant difference between the means of two groups. It calculates a t-value that can be compared to critical values to assess statistical significance.

2. How Does the Calculator Work?

The calculator uses the following formula:

Where:

• \( Mean1 \) — Mean of group 1
• \( Mean2 \) — Mean of group 2
• \( SE1 \) — Standard error of group 1
• \( SE2 \) — Standard error of group 2

Explanation: The formula calculates how many standard errors the difference between means represents. A larger absolute t-value indicates a more significant difference.

3. Interpretation of Results

Details: The calculated t-value needs to be compared with critical values from a t-distribution table. Generally:

• |t| > 1.96 suggests significance at p < 0.05 (for large samples)
• |t| > 2.58 suggests significance at p < 0.01 (for large samples)

4. Using the Calculator

Tips: Enter the means and standard errors for both groups. The units should be consistent between groups. Standard errors must be positive values.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between this and a standard t-test?
A: This calculates the t-value for comparing two independent means when you have the standard errors rather than raw data.

Q2: Can I use this for paired samples?
A: No, this formula is for independent samples. Paired tests require different calculations.

Q3: What if I have standard deviations instead of standard errors?
A: Standard error = standard deviation / √n. You'll need to know the sample sizes to convert.

Q4: How do I determine degrees of freedom for this test?
A: For independent samples, df ≈ n1 + n2 - 2. You'll need the sample sizes.

Q5: What assumptions does this test make?
A: It assumes normally distributed data, equal variances (unless using Welch's correction), and independent samples.