P-value calculator :

What is a P-Value?

The defination of the p-value is the probability of obtaining test results at least as extreme as the observed results, assuming that the null hypothesis is true.

The most important point about the p-value is that it is always between 0 and 1 inclusive. The small p-value represents that the observed data is less likely to occur under the null hypothesis so there is more chance that the alternative hypothesis is correct.

How to Use the P-Value Calculator

Using our p-value calculator is straightforward:

1. Select the Test Type: Choose from Z test, T test, Chi-Square test, or F test.
2. Choose the Tail Type: Specify whether you need a left-tailed, right-tailed, or two-tailed p-value.
3. Enter the Test Statistic: Input your test statistic (Z-score, T-score, Chi-Square score, or F-score).
4. Degrees of Freedom: For T, Chi-Square, and F tests, enter the degrees of freedom as required.
5. Sample Size: For F tests, provide the numerator and denominator degrees of freedom.
6. Round Results: Specify how many decimal places you want your result rounded to.
7. Calculate: Click the 'Calculate' button to get your p-value instantly.

Related Calculators :

Below are more calculators which use the critical value to perform statistical analysis.

Finding P-value Using Tables

To find a p-value from tables, here's a step-by-step guide:

Using a Z-table

• Calculate the Z-score from your sample data.
• Use the Z-table to find the probability (p-value) for that Z-score.
• For a two-tailed test, double the p-value if you're looking for the probability of extreme values on both ends.

Using a t-table

• Determine the degrees of freedom (df).
• Calculate the t-statistic.
• Find the closest value in the t-table.
• Identify the corresponding p-value range. For two-tailed tests, double it.

Using a Chi-square table

• Calculate the chi-square statistic.
• Determine the degrees of freedom (df).
• Find the closest value in the chi-square table.
• The table provides the right-tail probability (p-value).

Example

Z-Test :

Find p-value of a z-score for left tailed test when z = 1.96 ?

Solution :

The z score is z = 1.96

The hypothesis test is a right tailed test

Let z be the standard normal random variable with mean, \(\mu = 0\) and \( \sigma= 1 \).

Standard Normal Distribution Tables :

The tables below represent the area to the left of the given Z-score.

Step to find the p-value from a z-table

1. Locate the row that corresponds to the first digit of your z-score.
2. Locate the column that corresponds to the second digit of your z-score.
3. The intersection of the row and column will give you the p-value for that z-score.

The p-value is highlighted in the table for better understanding

P-value with test statistic, \( \mathrm{z = 1.96}\) is

\( \mathrm{ P(Z < 1.96 )=0.975 }\)

Why use Our Calculator?

Our calculator is designed to be user-friendly and efficient, allowing you to quickly compute p-values for various statistical tests. Here’s what you can do with our calculator:

• Z-Test: Calculate p-values for Z test statistics, which are used when the sample size is large, and the population variance is known.
• T-Test: Find p-values for T test statistics, ideal for smaller sample sizes or when the population variance is unknown.
• Chi-Square Test (χ²): Determine p-values for Chi-Square test statistics, commonly used for categorical data analysis.
• F-Test: Compute p-values for F test statistics, typically used to compare variances between groups.

Advantages of Using Our calculator

• Accuracy: Our calculator ensures precise computation of p-values, critical for making informed decisions in statistical analysis.
• Convenience: Perform multiple statistical tests from a single platform without the need for complex software.
• User-Friendly Interface: Navigate easily with our intuitive design and straightforward input fields.

Practical Applications of P-Values

Understanding p-values is crucial for various fields, including:

• Academic Research: Validate hypotheses and ensure the reliability of your research findings.
• Medical Studies: Determine the effectiveness of new treatments or drugs by comparing observed outcomes.
• Business Analytics: Make data-driven decisions by analyzing customer behavior and market trends.
• Engineering: Improve product quality and processes through rigorous statistical testing.