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*The P-value* is a statistic that helps scientists decide whether their hypothesis is true or false. The P-value is used to determine whether the test results fall within the normal range of observed cases. If the P-value of a data series is lower than a specific pre-specified value (e.g. 0.05), scientists will reject the experiment’s “null hypothesis” – in other words. Otherwise, they will abandon the hypothesis that the experimental variables *have no* real effect on the outcome. Nowadays, p-values are usually found in reference tables by calculating *chi* square values.

**Determine the**Usually, when scientists run an experiment and observe the results, they predict what “normal” or “typical” results will look like. This may be based on experimental results, reliable traceable data series, scientific literature, and/or other sources. For your experiment, determine the expected outcome and express it in numbers.

*expected*outcome of the experiment.- Example: According to previous studies, red cars are more likely to receive speeding tickets than blue cars nationwide. Let’s say the average result is 2:1 in favor of the red car. We wanted to know if the city police also showed this tendency by analyzing the number of speeding tickets issued by them. If we randomly sample 150 speeding tickets for both red and green cars in the city, we estimate
**100**for red cars and**50**for green cars*if the city police are forced to fines according to the trend in the area. country*.

**Determine the observed experimental results.**Now that you have the expected value, run the experiment and find the actual (or “observable”) value. Express the results in numbers. If we act on experimental conditions and the actual results

*are different*from the expected results, two possibilities can happen: either by chance, or by influencing the variables in the experiment

*leading to*the that difference. The purpose of finding the p-value is essentially to determine whether the observed outcome differs from the expected outcome enough to reject the “null hypothesis” – the hypothesis that there is no relationship between the variables. experimental numbers and observed results.

- Example: Suppose, in a city, we randomly select 150 tickets for red and green cars. We discovered
**90**red tickets and**60**green tickets. These numbers differ from the expected results of**100**and**50**respectively. Does our manipulation of the experiment (in this case, changing the data source from the national to the local) lead to a change in the results, or are the city police*more likely to*as the national average shows, and are we observing random variation? The p-value will help us make a decision in this case.

**Determine**Degrees of freedom are a measure of variability in a study, determined by the number of groups you test. The expression of degrees of freedom is written as follows:

*the degrees of freedom*in the experiment.**Degrees of freedom = n-1**, where: “n” is the number of groups or variables analyzed in the experiment.

- Example: The experiment has two groups of results: one for red cars and one for blue cars. So in this experiment, we have 2-1 =
**1 degrees of freedom**. If we compare the red car, the blue car and the green car, we get**2**degrees of freedom, etc..

**Use**The chi-squared value (written as “x

*chi-squared*values to compare expected and actual results.^{2}“) is a numerical value that measures the difference between the

*expected*value and the

*observed*outcome. The chi-square equation is as follows:

**x**, where: “o” is the observed value and “e” is the expected value.

^{2}= Σ((oe)^{2}/e)^{[1] X Research Source}Add the answers to the equation in all possible outcomes (see below).

- Note that this equation includes
*the Σ*(sigma) operator. In other words, you would have to calculate ((|oe|-0.05)^{2}/e) for each of the possibilities – either the red car or the green car gets the ticket. So we will compute ((oe)^{2}/e) twice – one for the red car and the other for the blue car. - Example: Insert the expected and observed values into the equation x
^{2}= Σ((oe)^{2}/e). Remember that because of the sigma operator, we need to compute ((oe)^{2}/e) twice – once for the red car and one for the green car. The calculation is done as follows:- x
^{2}= ((90-100)^{2}/ 100) + (60-50)^{2}/ 50) - x
^{2}= ((-10)^{2}/ 100) + (10)^{2}/ 50) - x
^{2}= (100/100) + (100/50) = 1 + 2 =**3**.

- x

**Select**Now that we have degrees of freedom and chi-squared values for the experiment, the last thing to do before finding the p-value is to determine the level of statistical significance. Essentially, the level of statistical significance is a measure of the certainty of an outcome – low statistical significance corresponds to a low probability that an experimental outcome is random, and vice versa. The level of statistical significance is written as a decimal (such as 0.01), corresponding to the proportion of experimental results obtained at random (in this case, 1%).

*the level of statistical significance*.- As a rule, scientists take the level of statistical significance for an experiment to be 0.05, or 5 percent.
^{[2] X Research Source}This means that an experimental result that meets the statistical significance level has at most a 5% chance of being a completely random result. In other words, there is a 95% chance that the results are due to the scientist’s influence on the variables in the experiment rather than by chance. For most experiments, 95% certainty about the association between two variables is considered “success”. - Example: In the red and green car experiment, let’s follow the scientific practice and take the statistical significance level to be
**0.05**.

**Use the chi-square distribution table to calculate the p-value.**Scientists and mathematicians use tables with multiple chi-squared values to calculate p-values for their experiments. These data tables are usually created with the vertical axis on the left corresponding to degrees of freedom and the horizontal axis above corresponding to the p-value. Use these tables by finding the degrees of freedom first, then reading the lines from left to right until you find the first value

*greater than*the chi squared value. Look at the corresponding p-value at the top of the column – the p-value is between that value and the next largest value (the one on the adjacent left side).

- There are many references to chi-square distribution tables – you can easily find them online or in science and statistics textbooks. If not available, use the table in the photo above or for free online, like the one on the website: medcalc.org here.
- Example: The chi-squared value is 3. So use the chi-squared distribution table in the image above to find the approximate p-value. We already know the experiment has degrees of freedom of
**1**, let’s start from the first row. Going from left to right of that row we find a value higher than**3**– the value of chi squared. The first value we encounter is 3.84. Looking at the top of the column, we see that the corresponding p value is 0.05. That means the p-value will**be between 0.05 and 0.1**(the next largest p-value in the table).

**Decide whether to keep or reject the null hypothesis.**Now that you have found an approximate p-value for your experiment, you can now decide to reject or accept the null hypothesis of the experiment (remember, this is the hypothesis that the variables in the experiment do not exist). you influence

*does not*affect the observed results). If the p-value is below statistical significance, congratulations – you have demonstrated a high probability of a relationship between the variables you affect and the observed outcomes. If the p-value is above the statistical significance level, you cannot be sure whether the actual results were due to pure randomness or your manipulation during the experiment.

- Example: The p-value is between 0.05 and 0.1. This means that the value is absolutely
*not*less than 0.05, so unfortunately we**cannot reject the null hypothesis**. That means we don’t reach the minimum 95% certainty threshold to be able to say that the city police issue tickets for red and green cars at rates that are significantly different from the national average. - In other words, there is a 5-10% chance that the observed results are not due to a change in location (analysis of city data rather than national data), but simply by chance. Since we are looking for a less than 5% probability, we cannot say with certainty that we
**are certain that**the city police will pay less attention to red cars – although it is less, there is still a statistically significant chance that they do not. do like that.

## Advice

- Pocket calculators can calculate much faster. You can use the online calculator.
- You can calculate the p-value using computer programs, such as regular spreadsheet software or more specialized statistical software.

wikiHow is a “wiki” site, which means that many of the articles here are written by multiple authors. To create this article, 20 people, some of whom are anonymous, have edited and improved the article over time.

There are 8 references cited in this article that you can see at the bottom of the page.

This article has been viewed 44,446 times.

*The P-value* is a statistic that helps scientists decide whether their hypothesis is true or false. The P-value is used to determine whether the test results fall within the normal range of observed cases. If the P-value of a data series is lower than a specific pre-specified value (e.g. 0.05), scientists will reject the experiment’s “null hypothesis” – in other words. Otherwise, they will abandon the hypothesis that the experimental variables *have no* real effect on the outcome. Nowadays, p-values are usually found in reference tables by calculating *chi* square values.

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