How To Calculate A P-Value When Testing A Null Hypothesis

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Hypothesis tests are used to test the validity of a claim that is made about a population. This claim that’s on trial, in essence, is called the null hypothesis (H0). The alternative hypothesis (Ha) is the one you would believe if the null hypothesis is concluded to be untrue. Learning how to find the p-value in statistics is a fundamental skill in testing, helping you weigh the evidence against the null hypothesis.

The evidence in the trial is your data and the statistics that go along with it. All hypothesis tests ultimately use a p-value to weigh the strength of the evidence (what the data are telling you about the population). The p-value is a number between 0 and 1 and is interpreted in the following way:

  • A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so you reject it.
  • A large p-value (> 0.05) indicates weak evidence against the null hypothesis, so you fail to reject it.
  • P-values very close to the cutoff (0.05) are considered to be marginal (could go either way). Always report the p-value so your readers can draw their own conclusions.
This guide will offer valuable content on how to find a p-value from a test statistic, a crucial step when determining whether the observed data's standard deviation differs significantly from the null hypothesis.

How to find a p-value from a test statistic

When you test a hypothesis about a population, you find a p-value and use your test statistic to decide whether to reject the null hypothesis. Mastering the process of how to find a p-value from a test statistic is vital for identifying a statistical error in our hypothesis testing.

A p-value chart can be extremely useful in visually interpreting the strength of evidence against the null hypothesis in your study. To find a p-value from a test statistic, you must reference a Z-table, find your test statistic on it, and determine its corresponding probability.

The following figure shows the locations of a test statistic and their corresponding conclusions.

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