Calculator
Example Data Table
| Case | Type | Sample 1 | Sample 2 | Alpha | Alternative |
|---|---|---|---|---|---|
| Mean comparison | Means | Mean 105, SD 12, n 64 | Mean 100, SD 10, n 60 | 0.05 | Two tailed |
| Conversion test | Proportions | 56 successes, n 120 | 42 successes, n 110 | 0.05 | Right tailed |
| Quality result | Means | Mean 48.4, SD 5.2, n 90 | Mean 46.9, SD 4.8, n 85 | 0.01 | Two tailed |
Formula Used
Two Sample Means
Z = [(x̄1 - x̄2) - D0] / √[(σ1² / n1) + (σ2² / n2)]
This formula compares two independent means. It assumes known population standard deviations or strong large sample support.
Two Sample Proportions
Z = [(p̂1 - p̂2) - D0] / SE
When D0 equals zero, the calculator uses the pooled proportion for the test standard error. The confidence interval uses the unpooled standard error.
Confidence Interval
Difference ± z critical × standard error
How to Use This Calculator
- Select whether you want to compare means or proportions.
- Choose the alternative hypothesis for your research question.
- Enter alpha, confidence level, and hypothesized difference.
- Fill the fields related to your selected test type.
- Press Calculate to view the result above the form.
- Use CSV or PDF to download the current report.
Two Sample Z Test Guide
What This Calculator Does
A two sample z test compares two independent groups. It checks whether their means or proportions differ more than random variation can explain. This calculator supports both common versions. You can test two population means with known standard deviations. You can also test two proportions using success counts and sample sizes.
When The Test Fits
Use this test when the two samples are independent. Each observation should belong to only one group. For means, population standard deviations should be known. Large samples can also make the z method practical. For proportions, each group should have enough successes and failures. Small counts may need exact methods instead.
Understanding The Inputs
The hypothesized difference is the value stated by the null hypothesis. It is often zero. Alpha is the risk level for rejecting a true null hypothesis. A common value is 0.05. The alternative hypothesis controls the tail of the test. Use two tailed when either direction matters.
Reading The Output
The z score shows how many standard errors the observed difference sits from the null value. A larger absolute z score gives stronger evidence against the null. The p value measures evidence using the chosen tail. If the p value is less than or equal to alpha, the result is statistically significant.
Confidence Interval Meaning
The confidence interval gives a practical range for the true difference. It is not only a yes or no result. A narrow interval means the estimate is more precise. A wide interval suggests more uncertainty. If a two tailed interval excludes the null difference, it usually agrees with the z test decision.
Why Export Results
Reports help with audits, assignments, lab notes, and business reviews. The CSV file is useful for spreadsheets. The PDF file gives a simple summary. Save both with your source data. Clear records make later checking easier and reduce reporting mistakes.
FAQs
What is a two sample z test?
It is a hypothesis test that compares two independent sample means or two independent sample proportions. It uses the standard normal distribution to estimate the p value and decision.
When should I use the means option?
Use the means option when you compare two independent averages. It is best when population standard deviations are known or when large samples support a normal approximation.
When should I use the proportions option?
Use the proportions option when each group has success counts and total sample sizes. It compares rates, percentages, or conversion levels between two independent groups.
What does the p value mean?
The p value shows how unusual the observed difference is if the null hypothesis is true. Smaller values give stronger evidence against the null hypothesis.
What is alpha?
Alpha is the chosen significance level. It is the cutoff used for the p value. Common alpha values are 0.05, 0.01, and 0.10.
What is a two tailed test?
A two tailed test checks whether the difference is either greater or smaller than the null value. It is useful when any meaningful difference matters.
What is the hypothesized difference?
It is the difference assumed by the null hypothesis. Most tests use zero, meaning no difference between the two populations.
Can I download my results?
Yes. After calculating, use the CSV or PDF buttons in the result section. They download the current inputs and computed statistical results.