P-Value Calculator

What is a P-Value?

In statistics, the P-value (Probability Value) is the most important metric for hypothesis testing. It tells you the probability of observing your results (or something more extreme) assuming that the Null Hypothesis is true.

In simple English: It measures how "weird" or "rare" your experimental results are.

• Low P-Value (< 0.05): Your data is very rare under normal conditions. This suggests something interesting is happening. You Reject the Null Hypothesis.
• High P-Value (> 0.05): Your data is common. There is not enough evidence to prove anything changed. You Fail to Reject the Null Hypothesis.

Interpreting Statistical Significance

The "Significance Level" (alpha) is your cutoff line. In most scientific fields (Biology, Psychology, Economics), the standard alpha is 0.05 (5%).

Z-Test vs. T-Test: Which one do I use?

Our calculator allows you to switch between Z and T distributions. Here is how to know which one to select:

Use the Z-Test if:

• Your sample size is large (n > 30).
• You know the population standard deviation (σ).
• The data follows a Normal Distribution.

Use the T-Test if:

• Your sample size is small (n < 30).
• You do not know the population standard deviation.
• This uses "Degrees of Freedom" (n - 1) to account for the uncertainty of smaller data sets.

Left, Right, or Two-Tailed?

The "Tail" refers to the direction of your hypothesis.

• Right-Tailed (>): You are checking if the result is greater than a specific value (e.g., "Is the new medicine BETTER?").
• Left-Tailed (<): You are checking if the result is less than a specific value (e.g., "Did the defect rate DROP?").
• Two-Tailed (≠): You are checking for any difference (e.g., "Did the test scores CHANGE?"). This is the safest and most common test.

The Limits of P-Values

A p-value tells you that a result is significant, but it does not tell you if it is important. With a massive sample size (e.g., 1 million people), even a tiny, meaningless difference can have a p-value of 0.0001. Always look at the "Effect Size" alongside your p-value to understand the real-world impact.