This statistical significance calculator can help you determine the value of the comparative error, difference & the significance for any given sample size and percentage response. Below the tool you can learn more about the formula used.

## What is statistical significance?

Statistical significance is a concept used in research to test whether a given data set is reliable or not and decide if it can help in a further **decision making or in formulating a relevant conclusion**. The concept itself is based on the comparative error figure that uses the sample size and on the difference between the percentages of response in the data set in question.

The standard formula of the comparative error requires the following variables to be provided:

■ Sample size 1 (s_{1})

■ Percentage response 1 (r_{1})

■ Sample size 2 (s_{2})

■ Percentage response 2 (r_{2})

**Comparative Error = 1.96 * √ (r _{1}(100-r_{1}) ÷ s_{1}) + (r_{2}(100-r_{2}) ÷ s_{2})**

## Example of a statistical significance calculation and its steps

Let’s test the significance occurrence for two sample sizes (s_{1}) of 25 and (s_{2}) of 50 having a percentage of response (r_{1}) of 5%, respectively (r_{2}) of 7%:

### Step 1:

Substitute the figures from the above example in the formula of comparative error:

Comparative Error (c) = 1.96 * √ (r_{1}(100-r_{1}) ÷ s_{1}) + (r_{2}(100-r_{2}) ÷ s_{2}) = 1.96 * √ (5(100-5) ÷ 25) + (7(100-7) ÷ 50) = 1.96 * √ [(475 ÷ 25) + (651 ÷ 50)] = 1.96 * √ (19.00 + 13.02) = 1.96 * √ 32.02 = 1.96 * 5.65862174 = 11.09089861

### Step 2:

Calculate the absolute difference (d) between the two percentages of response r_{1}, r_{2}:

d = r_{1}- r_{2} = |5 – 7| = 2

### Step 3:

Test the significance by checking whether the difference calculated above (d) is greater than the comparative error this way:

■ If the comparative error (c) > difference (d) then **there is no **significance**.**

■ If the comparative error (c) < difference (d) then **there is** significance.

In our example since the comparative error (c) = 11.09089861 is greater than the difference (d) = 2 there is no significance.

This statistical significance calculator uses the algorithm described above and is a quicker alternative than performing this type of calculation by hand, while you only have to input the 4 variables and then press Calculate.

08 Aug, 2015