Mathematical Calculators

# P-value-calculator

This incredible tool will allow you to find the p-value. You can use test statistics to determine which p-value is one-sided and which is two-sided.

#### p-value-calculator

What p-value to calculate?

p-value:

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#### Table of contents

## What is the p-value?

The probability that the test statistic will produce values at the least extreme of the value it produced in your sample. It is important to keep in mind that this probability was calculated under the assumption of a true null hypothesis!

The p-value is more intuitive and answers the question: If I assume that the null hypothesis holds, then how likely is it that the test I'm doing for another sample will produce a value at the least as extreme as the one I saw for the sample I have already?

## How do you calculate the p-value using test statistics?

You must understand the distribution of the test statistic, assuming that the null hypothesis holds. The cumulative distribution function (cdf) can be used to express the probability that the test statistics are at least as extreme and as extreme as the x value for the sample.

Left-tailed test: p-value = cdf (x)

Right-tailed test: p-value = 1 - cdf (x)

Two-tailed test: p-value = 2 * min {{cdf (x) , 1 - cdf (x) }}

Hypothesis testing is characterized by the most common probability distributions. This can make it difficult to calculate the p-value manually. It is likely that you will need to use a computer or a statistical table to calculate approximate cdf values.

Now you know how to calculate the p-value. But, why would you want to do this? The p-value approach to hypothesis testing is an alternative to the critical value approach. The significance level (a) is what researchers must set before rejecting the null hypothesis if it is true (so error). To quickly determine whether to reject the null hypotheses at that significance level, you will need to simply compare your p-value with any given value a. We will explain in detail how to interpret p-values.

## How do you interpret the p-value?

We have already mentioned that the p-value answers the following question.

If I assume that the null hypothesis is true, then how likely is it that the test I'm doing for another sample will produce a value at the least as extreme as the one I saw for the one I have already?

What does this mean for you? You have two choices:

A high p-value means your data is compatible with the null hypothesis.

A small value of p is evidence against the null hypothesis. This means that your result would seem very unlikely if the null hypothesis was true.

It may be that the null hypothesis holds, but your sample is very unusual. Imagine that we study the effects of a new drug and get a 0.03 p-value. In 3% of studies similar to ours, this means that even if the drug did not have any effect, random chance could still produce the same value or even higher.

You can answer the question, "What is the p-value?" with the following: A p-value is the lowest level of significance which would lead to the null hypothesis being rejected. Now, you will need to decide about the null hypothesis at some significance level. Simply compare your p-value with.

If the p-value ≤ a, then reject the null hypothesis and accept the alternate hypothesis.

If the p-value ≥ a then doesn't have enough evidence to reject the null hypothesis.

The fate of the null hypothesis is determined by a. If the p-value were 0.03 we would reject the null hypotheses at a significance level of 0.05 but not at 0.01. This is why it's important to specify the significance level in advance and not adjust after the p-value has been determined. A significance level of 0.05 represents the most common value. However, it is not magical.

## How do I use the p-value calculator to calculate p-values from test statistics?

Our p-value calculator makes it easy to calculate the p-value for complex test statistics. These are the steps to follow:

Choose from the alternative hypothesis.

Let us know the distribution for your test statistic in the null hypothesis. Is it N(0.1), t–Student, Snecor's F, chi-squared or t-Student? These sections are for those who are not sure.

If necessary, indicate the freedom distribution of the test statistic.

For your data sample, enter the value for the test statistic computed.

The calculator calculates the test statistic p-value and gives the decision regarding the null hypothesis. The standard significance is 0.05 by default.

If you need to increase the precision to which the calculations are performed or modify the significance, then go to the advanced mode.

## How do I find the p-value of Z-scores?

The following formulae are used to calculate the p-value for the cumulative distribution function (CDF), of the standard normal distribution. It is traditionally denoted by Ph.

Left-tailed z-test:

p-value = Ph (Z==score==)

Right-tailed z-test:

p-value = 1 - (Z==score==)

Two-tailed z-test:

p-value = 2 * Ph (- | Z==score==|)

or

p-value = 2 - 2 * Ph (- | Z==score==|)

If the test statistic approximates the normal distribution N(0.1), we use the. The central limit theorem allows you to count on the approximation when you have large samples (say 50 data points), and treat the distribution as normal.

## How do I find the p-value of t?

The value from the t-score can be calculated using the following formulae. cdf==t, d== represents the cumulative distribution function for the t-Student distribution with degrees freedom.

Left-tailed t-test:

p-value = cdf==t, d==(t==score==)

Right-tailed t-test:

p-value = 1 - cdf==t, d==(t==score==|)

Two-tailed t-test:

p-value = 2 * cdf==t, d==(-|t==score==|)

or

p-value = 2 - 2 * cdf==t, d==(|t==score==|)

If your test statistic is in the student distribution, you can use the t-score option. This distribution is similar in shape to N(0.1) (bell-shaped, symmetrical), but it has more tails. The degrees of freedom parameter determines the exact shape. The t-Student distribution can be distinguished from the normal N(0.1) distribution if the number of degrees is greater than 30.

## Is it possible to have a negative p-value?

The p-value can't be negative. Because probabilities can't be negative, the p-value is the probability that the test statistic will satisfy certain conditions.

## What does a high-value p-value signify?

A high p-value means that there is a high chance that the test statistic for another sample will produce a value that is at least as extreme as the one in your sample. You can't reject the null hypothesis if your p-value is high.

## What does a low-value p-value signify?

Low p-values indicate that there is little chance that the test statistic for another sample will produce a value that is at least as extreme or similar to the one that was observed for the current sample. Low p-values are evidence for the alternative hypothesis. They allow you to reject it.

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Parmis Kazemi

Parmis is a content creator who has a passion for writing and creating new things. She is also highly interested in tech and enjoys learning new things.

###### P-value-calculator English

Published: Thu Jul 28 2022

In category Mathematical calculators

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