Pooled variance calculator

Welcome to our user-friendly Pooled Variance Calculator. This tool rapidly and accurately calculates the pooled variance (s²p) from your data. Whether you're a student, researcher, or statistician, our calculator offers a complete solution with a single click.

What is Pooled Variance?

Pooled variance is a statistical method that estimates the variance of many populations whose means are anticipated to be equal. It is often used in t-tests and ANOVA to compare the means of two or more groups.

How to Calculate Pooled Variance

To calculate pooled variance, we need the sample sizes and standard deviations of our data sets. The formula for pooled variance is:

\( \mathrm{s_{p}^{2} =\frac{(n_{1}-1)\times s_{1}^{2}+(n_{2}-1)\times s_{2}^{2}}{n_{1}+n_{2}-2}} \)

where:

• \(\mathrm{n_{1}}\) and \(\mathrm{n_{2}}\) ​ are the sample sizes.
• \(\mathrm{s_{1}}\) and \(\mathrm{s_{2}}\) ​ are the sample standard deviation.

Using Our Pooled Variance Calculator

Our calculator allows you to input your data directly or provide a data set. Here's how it works:

1. Select Data Type: Choose whether you want to enter data directly or provide a data set.
2. Enter Values: Depending on your selection, input the necessary values:
   • Direct Input: Enter the sample sizes and standard deviations.
   • Data Provided: Enter the individual data points for each sample.
3. Calculate: Click the "Calculate" button to get your results.

Features of Our Calculator

Easy to navigate and input your data.

Provides a step-by-step breakdown of the calculations.

Round results to your desired number of decimal places.

Example Calculation

Let's say you have two samples:

Sample \(1\) : \(\mathrm{n_{1}} = 10\), \(\mathrm{s_{1} =3.2 }\)

Sample \(2\) : \(\mathrm{n_{2}} = 15\), \(\mathrm{s_{2} =6.2 }\)

Using our calculator, you would enter these values, and it will compute the pooled variance for you.

Why Use our Pooled Variance Calculator ?

Pooled variance is critical when performing hypothesis tests on two or more samples. It delivers a more accurate variance estimate by merging data from all samples, particularly when sample sizes are different.