# How to Find the Cutoff Point for Rejecting a Null Hypothesis

In statistics, if you want to draw conclusions about a null hypothesis H_{0} (reject or fail to reject) based on a* p-*value, you need to set a predetermined cutoff point where only those *p*-values less than or equal to the cutoff will result in rejecting H_{0}.

While 0.05 is a very popular cutoff value for rejecting H_{0}, cutoff points and resulting decisions can vary — some people use stricter cutoffs, such as 0.01, requiring more evidence before rejecting H_{0}, and others may have less strict cutoffs, such as 0.10, requiring less evidence.

If H_{0} is rejected (that is, the *p*-value is less than or equal to the predetermined significance level), the researcher can say she’s found a statistically significant result. A result is *statistically significant* if it’s too unlikely to have occurred by chance assuming H_{0} is true. If you get a statistically significant result, you have enough evidence to reject the claim, H_{0}, and conclude that something different or new is in effect (that is, H_{a}).

The significance level can be thought of as the highest possible* p-*value that would reject H_{0} and declare the results statistically significant. Following are the general rules for making a decision about H_{0} based on a *p-*value:

If the

*p-*value is less than or equal to your significance level, then it meets your requirements for having enough evidence against H_{0}; you reject H_{0}.If the

*p-*value is greater than your significance level, your data failed to show evidence beyond a reasonable doubt; you fail to reject H_{0}.

However, if you plan to make decisions about H_{0} by comparing the* p-*value to your significance level, you must decide on your significance level ahead of time. It wouldn’t be fair to change your cutoff point after you’ve got a sneak peak at what’s happening in the data.

You may be wondering whether it’s okay to say “Accept H_{0}” instead of “Fail to reject H_{0}.” The answer is a big no. In a hypothesis test, you are *not* trying to show whether or not H_{0} is true (which *accept** *implies) — indeed, if you knew whether H_{0} was true, you wouldn’t be doing the hypothesis test in the first place. You’re trying to show whether you have enough evidence to say H_{0} is false, based on your data. Either you have enough evidence to say it’s false (in which case you reject H_{0}) or you don’t have enough evidence to say it’s false (in which case you fail to reject H_{0}).

These guidelines help you make a decision (reject or fail to reject H_{0}) based on a* p-*value when your significance level is 0.05:

If the

*p-*value is less than 0.01 (very small), the results are considered highly statistically significant — reject H_{0}.If the

*p-*value is between 0.05 and 0.01 (but not super-close to 0.05), the results are considered statistically significant — reject H_{0}.If the

*p-*value is really close to 0.05 (like 0.051 or 0.049), the results should be considered marginally significant — the decision could go either way.If the

*p-*value is greater than (but not super-close to) 0.05, the results are considered non-significant — you fail to reject H_{0}.