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.