Mathematics/Statistics/Chi-Square Test

The Chi-Square test, alternatively called Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \chi^2} test, is used to measure two possible things:

• Chi-Square Goodness of Fit test - Determines if a set of sample data matches a larger population.
• Chi-Square Test for Independence - Determines if two variables are at all correlated.

General Notation

In general, Chi-Square is represented by a formula. The notations are as follows:

• O stands for "Observed/Actual".
• E stands for "Expected".
• Spans across some data set of size n.

With this in mind we have the following formulas:

Scientific Notation

Formal:

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \chi^2 = \sum_{i=1}^n \frac{(O_i-E_i)^2}{E_i}}

Less Formal:

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \chi^2 = \sum_{i=1}^n \frac{(Actual_i-Expected_i)^2}{Expected_i}}

Direct Notation

Formal:

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \chi^2 = \frac{(O_1-E_1)^2 + (O_2-E_2)^2 + ... + (O_{n-1}-E_{n-1})^2 + (O_n-E_n)^2}{E_1 + E_2 + ... + E_{n-1} + E_n}}

Less Formal:

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \chi^2 = \frac{(Actual_1-Expected_1)^2 + (Actual_2-Expected_2)^2 + ... + (Actual_{n-1}-Expected_{n-1})^2 + (Actual_n-Expected_n)^2}{Expected_1 + Expected_2 + ... + Expected_{n-1} + Expected_n}}