Two Sample Comparison Of Means Calculator

Two Sample Z-Score Formula:

\[ z = \frac{Mean1 - Mean2}{\sqrt{\frac{\sigma1^2}{n1} + \frac{\sigma2^2}{n2}}} \]

Mean 1:

varies

Mean 2:

varies

Standard Deviation 1 (σ1):

varies

Sample Size 1 (n1):

dimensionless

Standard Deviation 2 (σ2):

varies

Sample Size 2 (n2):

dimensionless

Z-Score:

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1. What is the Two Sample Comparison Of Means?

The two-sample z-test compares the means of two independent samples to determine if there is a statistically significant difference between them. It's used when population standard deviations are known and sample sizes are large (typically n > 30).

2. How Does the Calculator Work?

The calculator uses the z-score formula for two sample means:

\[ z = \frac{Mean1 - Mean2}{\sqrt{\frac{\sigma1^2}{n1} + \frac{\sigma2^2}{n2}}} \]

Where:

\( Mean1 \) — Mean of sample 1
\( Mean2 \) — Mean of sample 2
\( \sigma1 \) — Standard deviation of sample 1
\( n1 \) — Size of sample 1
\( \sigma2 \) — Standard deviation of sample 2
\( n2 \) — Size of sample 2

Explanation: The z-score measures how many standard deviations the difference between means is from zero (no difference). A large absolute z-score suggests a significant difference.

3. Importance of Z-Score Calculation

Details: The z-score is fundamental in hypothesis testing. It helps determine whether observed differences between groups are statistically significant or likely due to chance.

4. Using the Calculator

Tips: Enter means, standard deviations, and sample sizes for both groups. All values must be valid (sample sizes > 0, standard deviations ≥ 0).

5. Frequently Asked Questions (FAQ)

Q1: When should I use a z-test vs t-test?
A: Use z-test when population standard deviations are known and sample sizes are large (n > 30). Use t-test for smaller samples or unknown population standard deviations.

Q2: What does a significant z-score mean?
A: Typically, |z| > 1.96 indicates statistical significance at p < 0.05, suggesting the means are likely truly different.

Q3: Can I use this for paired samples?
A: No, this calculator is for independent samples. For paired samples (before/after measurements), use a paired t-test.

Q4: What are assumptions of this test?
A: Assumes independent samples, normally distributed data (or large samples), and known population standard deviations.

Q5: How do I interpret negative z-scores?
A: A negative z-score indicates that mean1 is less than mean2. The sign shows direction, while magnitude shows significance.