# Rejection region or p-value

I am writing a research paper where I am using an hypothesis test.

Is it better to give a p-value for this test or use a 5% two-tailed rejection region?

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In cases like these, my advice is to consider your audience and their expectations. Personally if you only present one quantity, I will want to know the p-value, but more generally, I want to know more than that - in two tailed tests, for example, the test statistic conveys something that the p-value does not. – Glen_b Jan 19 '14 at 23:25

In situations like these - it's best to look at things from the reader's perspective. Would the reader care about the actual value of the test statistic? Do you want the reader to know that the $T$-statistic is $2.79$ or $F = 8.91$? In most cases, the reader would not be interested in these values, so just give the p-value along with the test that you used and an estimate of the magnitude of your effect size.

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I suggest you to put a exact p-value for the testing you've done. However if the p-value is very small, e.g. 0.000001, then I would write it as p-value < 0.0001.

Hope this helps.

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Thank you, and why not use the rejection region? – Sjoerd Smaal Jan 19 '14 at 17:48
I guess p-value would be more general. Rejection region would be specific to the 5% confidence interval. – Abhimanyu Arora Jan 19 '14 at 17:59
@AbhimanyuArora 's answer is the reason why p-value is more popular. Let's say that a reader wants to know if $H_0$ is still rejected under the 1%-rule, he will have to calculate another rejection region. With the p-value reported, he'll immediately know this. – Heisenberg Jan 20 '14 at 2:07

I would recommend to report $p$-values and if you have the space go for the test statistics and rejection region. But there is a reason behind that as in the most research journals and software you can see $p$-values. First of all, let me say that the conclusions based on $p$-values and rejection region approach is basically the same i.e. if your $p$-values is less that or equal to $\alpha$ (i.e. your significance level) then the test statistic will fall into the rejection region and vice versa. The rejection region method only provides a decision for a specific value of $\alpha$. However by providing the $p$-values, your reader not only can make his/her decision based on that particular $\alpha$ level but also he/she can see all possible values for $\alpha$ in which the null hypothesis can be rejected. As a result, the $p$-value provides more flexibility than the rejection region method.

You can also have a look at the last paragraph in page 449 of "Statistical Ideas and Methods" by Jessica Utts, Robert Heckard here that addresses this property.

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Just a comment - when doing hypothesis testing you don't set type-I error rates after seeing what the p-value is. For example, suppose you decide a priori that you want to control the type-I error rate at 5 percent and you end up with a p-value of 0.00294. You don't get to then go ahead and set the alpha level at 0.01 since you were going to accept anyway for all p-values less than 0.05. In effect - even though you received a low p-value of 0.00294, the type I error rate is still 0.05. Not sure if this was what you were trying to say, but I thought I'd write about this common fallacy. – Samuel Benidt Jan 20 '14 at 1:57