What does a P value of 0 Mean?

A P value of 0 simply means that the null hypothesis is false and should be rejected. In order to understand this, we should first understand what a P value is.

A P value is simply a probability value that tells you how likely the null hypothesis is true. The P value always lies between 0 and 1.

How to Interpret a P Value of 0.0000?

1. A smaller P value indicates that the null hypothesis is false.
2. A larger P value indicates that the null hypothesis is true.

When you run a statistical software to obtain a P value, you might find that the P value turns out to be 0.0000. This is because the actual P value might be something like 0.000003 but since the software can display only four decimal digits it can seem that the P value is actually zero.

In such a case, the P value is not zero but a very small number close to zero. As explained above, a P value of 0.0000 means that the null hypothesis is to be rejected. There is a 0% chance that the null hypothesis is true.

Rejection Rule:

Generally speaking, whenever the p value is less than 0.05 we reject the null hypothesis.

If the p value is more than 0.05 then we accept the null hypothesis.

Although 5% is a generally accepted cut off point, it is up to the person to select a suitable level of significance when conducting a statistical test. For example, if you want a 98% degree of confidence in your results, you may stipulate that the cut off point for the p value shall be 2% = 0.02.

Example:

Suppose that a factory manufacturing light bulbs claims that the average lifetime of the bulbs is 18 months. In order to evaluate this claim we formula the null hypothesis and alternative hypothesis as follows:

H₀: µ = 18 vs H₁: µ < 18

We then take a random sample of the light bulbs and calculate the average lifetime of the sample taken. Suppose that on conducting a Z test for equality of means you find that the P value is 0.

In this case, we reject the null hypothesis and conclude that the alternative hypothesis H₁ is true.

This means that the mean lifetime of the bulbs manufactured by the factory is less than 18 hours.