Few statistical estimates are as significant as the p-value. The p-value or probability value is a number calculated from astatistical test, which describes the probability of your results if the null hypothesis were true. A P value less than 0.5 is statistically significant, while a value greater than 0.5 indicates that the null hypothesis is true; therefore, it is not statistically significant. What exactly is the P value and why is it so important?

#### Data Analysis Professional Certification Program

In association with Purdue Universitysee course

## What is the P-value?

Nostatistical hypothesis test, The P-value or probability value can be defined as a measure of the probability that a true-value test statistic is at least as extreme as the value actually obtained. The p-value shows the probability that your observations occurred under the null hypothesis. The p values are used in statistical hypothesis tests to determine whether to reject the null hypothesis. The smaller the p-value, the more likely it is to reject the null hypothesis.

P values are expressed as decimals and can be converted to percentages. For example, a p-value of 0.0237 is 2.37%, which means there is a 2.37% chance that the results are random or occur by accident. The lower the P-value, the more significant your results will be.

In a hypothesis test, you can compare the p-value of your test to the selected alpha level as you run the test. Now let's try to understand what is P value versus alpha level.

## P-value vs. Nivel alfa

A P value indicates the probability of having an effect that is no less than what is actually observed in the sample data.

An alpha level gives you the probability of incorrectly rejecting a true null hypothesis. The level is chosen by the researcher and is obtained by subtracting his confidence level from 100%. For example, if you are 95% confident in your survey, the alpha level is 5% (0.05).

If you run the hypothesis test and get:

- If the p-value is small (<=0.05), you should reject the null hypothesis
- If the p-value is large (>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 from your test to determine if your null hypothesis is true.

For example, if you run an F-test to compare two variations in Excel, you'll get a p-value, a critical f-value, and an f-value. Compare the f value with the critical f value. If the f-critical value is less, you should reject the null hypothesis.

#### Master in Data Analyst

In collaboration with IBMexplore course

## How is the P-value calculated?

p-values are usually calculated using p-value tables or spreadsheets, or calculated automatically using statistical software such as R, SPSS, etc.

Based on the test statistic and the degrees of freedom (subtract the number of independent variables from the number of observations) of your test, the tables tell you how often you can expect the test statistic to fall below the null hypothesis.

The way the P-value is calculated depends on the statistical test you use to test your hypothesis.

- Each statistical test uses different assumptions and generates different statistics. Choose the test method that best fits your data and is consistent with the effect or relationship you are testing.
- The number of independent variables included in your test determines how large or small the test statistic must be to generate the same p-value.

Regardless of which test statistic you use, the p-value says the same thing: how often you can expect to get a test statistic as extreme or even more extreme than what your test returns.

## P value in hypothesis tests

The P-value approach to hypothesis testing uses a calculated probability to decide whether there is evidence to reject the null hypothesis, also known as a conjecture. The conjecture is the initial statement about a population of data, while the alternative hypothesis determines whether the observed population parameter differs from the value of the population parameter based on the conjecture.

In fact, the significance level is set in advance to determine how small the p-value must be for the null hypothesis to be rejected. Significance levels vary from one investigator to another; Therefore, it may be difficult for the reader to compare the results of two different tests. So the P value makes things easier.

Readers can interpret statistical significance by referring to the reported P-value of the hypothesis test. This is known as the P-value approach to testing hypotheses. This would allow the reader to decide for himself if the p-value represents a statistically significant difference.

#### FREE Course: Introduction to Data Analysis

Learn about data analysis concepts, tools and skillsstart to learn

## p values and statistical significance

The statistical significance level is usually reported as a p-value between 0 and 1. The smaller the p-value, the more likely it is to reject the null hypothesis.

- A value of p < or = 0.05 is considered statistically significant. Indicates strong evidence against the null hypothesis because the probability that the null is correct is less than 5%. Therefore, we reject the null hypothesis and accept the alternative hypothesis.
- However, if the P value is below the significance threshold, the null hypothesis can be rejected, but this does not mean that the alternative hypothesis has a 95% probability of being true.
- A p value > 0.05 is not statistically significant. Shows strong evidence that the null hypothesis is true. Therefore, we maintain the null hypothesis and reject the alternative hypothesis. We cannot accept a null hypothesis; we can only reject it or not reject it.

A statistically significant result does not prove that a research hypothesis is correct. Rather, it supports or provides evidence for the hypothesis.

## Report P values

- You must provide p-values accurate to two or three decimal places.
- For p values less than 0.001, report as p < 0.001.
- Do not use 0 before the decimal point because it cannot be equal to 1. Write p = 0.001 not p = 0.001
- Make sure that p is always italicized and that there is a space on both sides of the = sign.
- It is impossible to obtain P = 0.000 and must be written as p < 0.001

### example

An investor says that his investment portfolio has performed in accordance with the Standard & Poor's (S&P) 500 Index. To determine this, he performs a two-tailed test.

The null hypothesis here states that portfolio returns are equal to S&P 500 returns, while the alternative hypothesis states that portfolio returns and S&P 500 returns are not equivalent.

The p-value hypothesis test indicates how much evidence there is to reject the null hypothesis. The lower the p-value, the greater the evidence against the null hypothesis.

Therefore, if the investor obtains a P value of 0.001, this indicates strong evidence against the null hypothesis. As such, you confidently conclude that portfolio returns and S&P 500 returns are not equivalent.

#### Free data analysis course.

Start learning today's most in-demand skillsexplore course

## Our students also ask

### 1. What does the P value mean?

The P-value, or probability value, is a number that indicates the probability that your data occurred under the null hypothesis of your test statistic.

### 2. What does p 0.05 mean?

A P value less than 0.05 is considered statistically significant; H. The null hypothesis must be rejected in such a case. A p value greater than 0.05 is not considered statistically significant, which means that the null hypothesis should not be rejected.

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

The p-value, or probability value, is a number calculated from a test statistic that indicates the probability that its results will occur under the null hypothesis of the test.

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

### 4. What is the p-value in the investigation?

The p values are used in the hypothesis test to determine if the null hypothesis should be rejected. It plays an important role when the research results are discussed. Hypothesis testing is a statistical method commonly used in medical and clinical research studies.

### 5. Why is the p-value significant?

Statistical significance is a term researchers use to express how unlikely it is that their observations could have happened if the null hypothesis were true. The statistical significance level is usually reported as a p-value or a probability value between 0 and 1. The smaller the p-value, the more likely it is to reject the null hypothesis.

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

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

The P-value, or probability value, is a number calculated from a test statistic that indicates the probability that its results will occur under the null hypothesis of the test.

get connectedData Analysis Professional Certification Programto learn more than a dozen data analysis tools and skills, and get access to master classes from Purdue faculty and IBM experts, exclusive IBM hackathons, and Ask Me Anything sessions.

## Conclution

The P value is used to determine the significance of the observational data. Whenever researchers note an apparent relationship between two variables, a P-value calculation helps determine whether the observed relationship was accidental. learn more aboutStatistic analysismianalysis of dataand accelerate your career with ourData Analysis Professional Certification Program.