Calculate Your Pooled Standard Deviation
Find the pooled standard deviation for 2–10 groups. Great for comparing classes, A/B tests, or lab sections when variances are assumed equal.
Group Data
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How to Use This Calculator
This **pooled standard deviation calculator** makes it easy to **combine standard deviations** from multiple groups. Follow these simple steps:
- **Enter the number of groups** you are comparing by clicking the 'Add Group' button until you have the required number of rows (minimum of two).
- For each group, enter the **Sample Size ($n_i$)** and the **Sample Standard Deviation ($s_i$)**.
- Select the number of **decimal places** you want for the final result.
- Click the **"Calculate Pooled SD"** button to see the results, including the degrees of freedom and a detailed breakdown table.
Formula Breakdown
$s_{\text{pooled}}=\sqrt{\dfrac{\sum_{i=1}^{k}(n_i-1)s_i^2}{\sum_{i=1}^{k}n_i-k}}$
The formula calculates the pooled standard deviation ($s_{\text{pooled}}$) by finding the weighted average of the variances of each sample. The weights are the degrees of freedom for each sample ($n_i-1$). This calculator uses the k-sample version of the formula, which works for any number of groups (k).
$s_{\text{pooled}}$ works when you can assume that the population variances are equal. This is a common assumption used in independent two-sample t-tests with pooled variance.
Frequently Asked Questions (FAQs)
What is pooled standard deviation?
Pooled standard deviation is a method for estimating a single standard deviation from two or more different data sets or groups. It's an important step when performing statistical tests like the t-test, especially when comparing multiple groups where the population variances are assumed to be equal.
When should I use a pooled standard deviation?
You should use a **k-sample pooled SD** or **two-sample pooled SD** when you believe the underlying population variances for all your samples are the same, even if the sample variances are slightly different. This technique is often used in situations where you want a single, more reliable estimate of the population standard deviation.
What are degrees of freedom ($df$)?
Degrees of freedom, or $df$, represent the number of values in a final calculation that are free to vary. For the pooled standard deviation, the formula is $df = n_1+\dots+n_k-k$. It is a measure of the amount of independent information that goes into the calculation of an estimate.