   # P-Value: A Complete Guide

Published by at August 31st, 2021 , Revised On September 21, 2021

## P-Value: A Complete Guide

You might have come across this term many times in hypothesis testing.  Can you tell what p-value is and how to calculate it? For those who are new to this term, sit back and read this guide to find out all the answers. Those already familiar with it, continue reading because you might get a chance to dig deeper about p-value and its significance in statistics.

Before we start with what a p-value is, there are a few other terms you must be clear of. And these are the null hypothesis and alternative hypothesis.

## What Are Null Hypothesis and Alternative Hypothesis?

The alternative hypothesis is your first hypothesis predicting a relationship between different variables. On the contrary, the null hypothesis predicts that there is no relationship between the variables you are playing with.

For instance, if you want to check the impact of two fertilizers on the growth of two sets of plants. Group A of plants is given fertilizer A, while B is given fertilizer B. now by using a two-tailed t test, you can find out the difference between the two fertilizers.

Null Hypothesis: There is no difference in growth between the two sets of plants.

Alternative Hypothesis: There is a difference in growth between the two groups.

What is the p-value?

The p-value in statistics is the probability of getting outcomes at least as extreme as the outcomes of a statistical hypothesis test, assuming the null hypothesis to be correct. To put it in simpler words, it is a calculated number from a statistical test that shows how likely you are to have found a set of observations if the null hypothesis were plausible.

This means that p-values are used as alternatives to rejection points for providing the smallest level of significance at which the null hypothesis can be rejected. If the p-value is small, it implies that the evidence in favor of the alternative hypothesis is bigger. Similarly, if the value is big, the evidence in favor of the alternative hypothesis would be small.

## How is the P-value Calculated?

You can either use the p-value tables or statistical software to calculate the p-value. The calculated numbers are based on the known probability distribution of the statistic being tested.

The online p-value tables depict how frequently you can expect to see test statistics under the null hypothesis. P-value depends on the statistical test one uses to test a hypothesis.

• Different statistical tests can have different predictions, hence develop different test statistics. Researchers can choose a statistical test depending on what best suits their data and the effect they want to test
• The number of independent variables in your test determines how large or small the test statistic must be to produce the same p-value

## When is a p-value Statistically Significant?

Before we talk about when a p-value is statistically significant, let’s first find out what does it mean to be statistically significant.

Any guesses?

To be statistically significant is another way of saying that a p-value is so small that it might reject a null hypothesis.

Now the question is how small?

If a p-value is smaller than 0.05 then it is statistically significant. This means that the evidence against the null hypothesis is strong. The fact that there is less than a 5 percent chance of the null hypothesis being correct and plausible, we can accept the alternative hypothesis and reject the null hypothesis.

Nevertheless, if the p-value is less than the threshold of significance, the null hypothesis can be rejected, but that does not mean there would be a 95 percent probability of the alternative hypothesis being true. Note that the p-value is dependent or conditioned upon the null hypothesis being plausible, but it is not related to the correctness and falsity of the alternative hypothesis.

When the p-value is greater than 0.05, it is not statistically significant. It also indicates that the evidence for the null hypothesis is strong. So, the alternative hypothesis, in this case, is rejected and the null hypothesis is retained. An important thing to keep in mind here is that you still cannot accept the null hypothesis. You can only fail to reject it, or reject it.

Here is a table showing hypothesis interpretations:

P-value Decision
P-value > 0.05 Not statistically significant and do not rejects the null hypothesis.
P-value < 0.05 Statistically significant and rejects the null hypothesis in favour of the alternative hypothesis.
P-value < 0.01 Highly statistically significant and rejects the null hypothesis in favour of the alternative hypothesis.

Is it clear now? We thought so! Let’s move on to the next heading then.

## How to Use p-value in Hypothesis Testing?

Follow these three simple steps to use p-value in hypothesis testing.

Step 1: Find the level of significance. Make sure to choose the level of significance during the initial steps of the design of a hypothesis test. It is usually 0.10, 0.05, and 0.01.

Step 2: Now calculate the p-value. As we discussed earlier, there are two ways of calculating it. A simple way out would be using Microsoft Excel that allows p-value calculation with data Analysis ToolPak.

Step 3: Start comparing the p-value with the level of significance and deduce conclusions accordingly. Following the general rule, if the value is less than the level of significance, there is enough evidence to reject the null hypothesis of an experiment

## FAQs:

It is a statistical theory suggesting that there is no relationship between a set of variables.

The alternative hypothesis is your first hypothesis predicting a relationship between different variables.

The p-value in statistics is the probability of getting outcomes at least as extreme as the outcomes of a statistical hypothesis test, assuming the null hypothesis to be correct. It is a calculated number from a statistical test that shows how likely you are to have found a set of observations if the null hypothesis were plausible.

To be statistically significant is another way of saying that a p-value is so small that it might reject a null hypothesis.
This table shows when the p-value is significant.

P-value Decision
P-value > 0.05 Not statistically significant and do not rejects the null hypothesis.
P-value < 0.05 Statistically significant and rejects the null hypothesis in favour of the alternative hypothesis.
P-value < 0.01 Highly statistically significant and rejects the null hypothesis in favour of the alternative hypothesis. Ingram is a dissertation specialist. He has a master's degree in data sciences. His research work aims to compare the various types of research methods used among academicians and researchers.