Few statistical estimates are as significant as the p-value. The p-value or probability value is a number, calculated from a statistical test, that describes how likely your results would have occurred if the null hypothesis were true. A P-value less than 0.5 is statistically significant, while a value higher than 0.5 indicates the null hypothesis is true; hence it is not statistically significant. So, what is P-Value exactly, and why is it so important?

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What Is P-Value? 

In statistical hypothesis testing, P-Value or probability value can be defined as the measure of the probability that a real-valued test statistic is at least as extreme as the value actually obtained. P-value shows how likely it is that your set of observations could have occurred under the null hypothesis. P-Values are used in statistical hypothesis testing to determine whether to reject the null hypothesis. The smaller the p-value, the stronger the likelihood that you should reject the null hypothesis. 

P-values are expressed as decimals and can be converted into percentage. For example, a p-value of 0.0237 is 2.37%, which means there's a 2.37% chance of your results being random or having happened by chance. The smaller the P-value, the more significant your results are. 

In a hypothesis test, you can compare the p value from your test with the alpha level selected while running the test. Now, let’s try to understand what is P-Value vs Alpha level.    

P Value vs Alpha Level

A P-value indicates the probability of getting an effect no less than that actually observed in the sample data.

An alpha level will tell you the probability of wrongly rejecting a true null hypothesis. The level is selected by the researcher and obtained by subtracting your confidence level from 100%. For instance, if you are 95% confident in your research, the alpha level will be 5% (0.05).

When you run the hypothesis test, if you get:

  • A small p value (<=0.05), you should reject the null hypothesis
  • A large p value (>0.05), you should not reject the null hypothesis

P Values and Critical Values

In addition to the P-value, you can use other values given by your test to determine if your null hypothesis is true. 

For example, if you run an F-test to compare two variances in Excel, you will obtain a p-value, an f-critical value, and a f-value. Compare the f-value with f-critical value. If f-critical value is lower, you should reject the null hypothesis. 

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How Is P-Value Calculated?

P-Values are usually calculated using p-value tables or spreadsheets, or calculated automatically using statistical software like R, SPSS, etc. 

Depending on the test statistic and degrees of freedom (subtracting no. of independent variables from no. of observations) of your test, you can find out from the tables how frequently you can expect the test statistic to be under the null hypothesis. 

How to calculate P-value depends on which statistical test you’re using to test your hypothesis.  

  • Every statistical test uses different assumptions and generates different statistics. Select the test method that best suits your data and matches the effect or relationship being tested.
  • The number of independent variables included in your test determines how big or small the test statistic should be in order to generate the same p-value. 

Regardless of what statistical test you are using, the p-value will always denote the same thing – how frequently you can expect to get a test statistic as extreme or even more extreme than the one given by your test. 

P-Value in Hypothesis Testing

In the P-Value approach to hypothesis testing, a calculated probability is used to decide if there’s evidence to reject the null hypothesis, also known as the conjecture. The conjecture is the initial claim about a data population, while the alternative hypothesis ascertains if the observed population parameter differs from the population parameter value according to the conjecture. 

Effectively, the significance level is declared in advance to determine how small the P-value needs to be such that the null hypothesis is rejected.  The levels of significance vary from one researcher to another; so it can get difficult for readers to compare results from two different tests. That is when P-value makes things easier. 

Readers could interpret the statistical significance by referring to the reported P-value of the hypothesis test. This is known as the P-value approach to hypothesis testing. Using this, readers could decide for themselves whether the p value represents a statistically significant difference.  

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P-Values and Statistical Significance

The level of statistical significance is usually represented as a P-value between 0 and 1. The smaller the p-value, the more likely it is that you would reject the null hypothesis. 

  • A P-Value < or = 0.05 is considered statistically significant. It denotes strong evidence against the null hypothesis, since there is below 5% probability of the null being correct. So, we reject the null hypothesis and accept the alternative hypothesis.
  • But if P-Value is lower than your threshold of significance, though the null hypothesis can be rejected, it does not mean that there is 95% probability of the alternative hypothesis being true. 
  • A P-Value >0.05 is not statistically significant. It denotes strong evidence for the null hypothesis being true. Thus, we retain the null hypothesis and reject the alternative hypothesis. We cannot accept null hypothesis; we can only reject or not reject it. 

A statistically significant result does not prove a research hypothesis to be correct. Instead, it provides support for or provides evidence for the hypothesis. 

Reporting P-Values

  • You should report exact P-Values upto two or three decimal places. 
  • For P-values less than .001, report as p < .001. 
  • Do not use 0 before the decimal point as it cannot equal1. Write p = .001, and not p = 0.001
  • Make sure p is always italicized and there is space on either side of the = sign. 
  • It is impossible to get P = .000, and should be written as p < .001

Example

An investor says that the performance of their investment portfolio is equivalent to that of the Standard & Poor’s (S&P) 500 Index. He performs a two-tailed test to determine this. 

The null hypothesis here says that the portfolio’s returns are equivalent to the returns of S&P 500, while the alternative hypothesis says that the returns of the portfolio and the returns of the S&P 500 are not equivalent.  

The p-value hypothesis test gives a measure of how much evidence is present to reject the null hypothesis. The smaller the p value, the higher the evidence against null hypothesis. 

Therefore, if the investor gets a P value of .001, it indicates strong evidence against null hypothesis. So he confidently deduces that the portfolio’s returns and the S&P 500’s returns are not equivalent.

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Our Learners Also Ask

1. What does P-value mean?

P-Value or probability value is a number that denotes the likelihood of your data having occurred under the null hypothesis of your statistical test. 

2. What does p 0.05 mean?

A P-value less than 0.05 is deemed to be statistically significant, meaning the null hypothesis should be rejected in such a case. A P-Value greater than 0.05 is not considered to be statistically significant, meaning the null hypothesis should not be rejected. 

3. What is P-value and how is it calculated?

The p-value or probability value is a number, calculated from a statistical test, that tells how likely it is that your results would have occurred under the null hypothesis of the test.  

P-values are usually automatically calculated using statistical software. They can also be calculated using p-value tables for the relevant statistical test. P values are calculated based on the null distribution of the test statistic. In case the test statistic is far from the mean of the null distribution, the p-value obtained is small. It indicates that the test statistic is unlikely to have occurred under the null hypothesis. 

4. What is p-value in research?

P values are used in hypothesis testing to help determine whether the null hypothesis should be rejected. It plays a major role when results of research are discussed. Hypothesis testing is a statistical methodology frequently used in medical and clinical research studies. 

5. Why is the p-value significant?

Statistical significance is a term that researchers use to say that it is not likely that their observations could have occurred if the null hypothesis were true. The level of statistical significance is usually represented as a P-value or probability value between 0 and 1. The smaller the p-value, the more likely it is that you would reject the null hypothesis. 

6. What is null hypothesis and what is p-value?

A null hypothesis is a kind of statistical hypothesis that suggests that there is no statistical significance in a set of given observations. It says there is no relationship between your variables.   

P-value or probability value is a number, calculated from a statistical test, that tells how likely it is that your results would have occurred under the null hypothesis of the test.   

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