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Statistics Resources

This guide contains all of the ASC's statistics resources. If you do not see a topic, suggest it through the suggestion box on the Statistics home page.

What is Associated Probability?

When doing hypothesis testing or conducting statistical tests, we may be asked what the "associated probability" is for the test. The associated probability (often referred to as the p-value) is referring to the probability of obtaining the test statistic value if the null hypothesis is true.

The test statistic will depend on the test you're conducting. You can use the test guides to help you determine what the test statistic is for your current analysis. In SPSS, this probability is typically located right next to the test statistic value. It is denoted as "sig." or "significance".


Null HypothesisThere is no relationship between the variables.
Alternative HypothesisThere is a relationship between the variables.
Test statistic: r = .26, p = .154


Applying the definition above, that means there's a 15.4% chance that we would have gotten r = .26, if there was no relationship between the variables. While this value may seem small, in statistics it is only deemed "significant" if the value is below at least 5% (or .05). Therefore, we would conclude here that the evidence supports the null hypothesis: there is no relationship between the variables.

When the associated probability is very small, less than .05, it seems very unlikely that we would have obtained the test statistic unless there was another explanation for the data. That explanation is the alternative hypothesis. Thus, when the p-value is less than .05, we conclude that the data supports the alternative hypothesis: there is a relationship between the variables.