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Statistical Significance Calculator

Formula

To calculate the statistical significance:

$Z = \frac{x - u}{\frac{\text{std}}{\sqrt{n}}}$

Where:

$Z$ is the statistical significance
$x$ is the sample mean
$u$ is the population mean
$\text{std}$ is the standard deviation
$n$ is the sample size

Statistical Significance Definition

Statistical significance is a measure of how closely a sample set follows the data of a larger population. It indicates whether the observed effect is likely to be due to chance or if it reflects a true effect in the population.

Example Calculation 1

Let's assume the following values:

Sample Mean ( $x$ ) = 20
Population Mean ( $u$ ) = 15
Standard Deviation ( $\text{std}$ ) = 5
Sample Size ( $n$ ) = 30

Using the formula:

$Z = \frac{20 - 15}{\frac{5}{\sqrt{30}}} \approx 5.48$

The statistical significance (Z) is approximately 5.48.

Example Calculation 2

Let's assume the following values:

Sample Mean ( $x$ ) = 50
Population Mean ( $u$ ) = 45
Standard Deviation ( $\text{std}$ ) = 10
Sample Size ( $n$ ) = 50

Using the formula:

$Z = \frac{50 - 45}{\frac{10}{\sqrt{50}}} \approx 3.54$

The statistical significance (Z) is approximately 3.54.