1. What is a P Value?

The p-value is the probability of obtaining test results at least as extreme as the observed results, assuming the null hypothesis is true. It helps determine statistical significance in hypothesis testing.

2. How Does the Calculator Work?

The calculator uses the t-test formula:

Where:

• \( t \) — t-statistic calculated from means, standard deviations, and sample sizes
• \( df \) — degrees of freedom (\( n1 + n2 - 2 \))
• \( t\_cdf \) — cumulative distribution function for the t-distribution

Explanation: The calculator first computes the pooled standard deviation, then the t-statistic, and finally the two-tailed p-value from the t-distribution.

3. Importance of P Value

Details: P values help researchers determine whether to reject the null hypothesis. A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis.

4. Using the Calculator

Tips: Enter the means, standard deviations, and sample sizes for both groups. The calculator assumes independent samples and normally distributed data with equal variances.

5. Frequently Asked Questions (FAQ)

Q1: What does p < 0.05 mean?
A: There's less than a 5% probability the observed difference occurred by chance if the null hypothesis were true.

Q2: When should I use a one-tailed vs two-tailed test?
A: Use one-tailed when you're only interested in one direction of effect. This calculator provides two-tailed p-values.

Q3: What if my sample sizes are unequal?
A: The calculator handles unequal sample sizes correctly using the pooled standard deviation method.

Q4: What if my data violates the assumptions?
A: Consider non-parametric tests like Mann-Whitney U if data isn't normally distributed or variances are unequal.

Q5: How precise is this calculator?
A: It provides p-values with 4 decimal places, suitable for most research purposes.