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Calculating the value of p is an essential concept in mathematics and statistics. Represented by the Greek letter π, the value of p is a mathematical constant that represents the ratio of a circle’s circumference to its diameter. While its exact value cannot be expressed as a finite decimal or fraction, it is commonly approximated as 3.14. However, it is important to note that the value of p is an irrational number, meaning it goes on infinitely without repeating. In this guide, we will explore various methods and formulas to accurately calculate the value of p to a desired level of precision, enabling us to solve a wide range of mathematical problems and understand the relationship between a circle’s dimensions and its circumference or diameter.
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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.
- 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 .
- 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.
- 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..
- 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 .
- 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 .
- 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).
- 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.
In conclusion, the value of p can be calculated using various mathematical methods, depending on the problem or equation at hand. One of the most commonly used methods is the approximation of p as 3.14159, which is accurate to five decimal places. This value is widely used in many mathematical and scientific calculations. However, more precise values of p can be obtained through various techniques, such as the Monte Carlo method or using infinite series such as the Gregory-Leibniz series. It is important to note that no exact numerical value for p exists due to its irrational and transcendental nature. Nevertheless, the value of p is an incredibly important and fundamental constant in mathematics and is used extensively in numerous fields such as physics, engineering, and statistics.
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