Chi Square Test – Types, Table, Formula and Example

# Chi Square Test – Types, Table, Formula and Example

## What is Chi Square Test?

The chi square test is a statistical test used to determine whether there is a statistically significant difference between the observed frequencies and the expected frequencies in a given sample. The chi square test is used to determine whether there is a statistically significant difference between the observed frequencies and the expected frequencies in a given sample.

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## What is the Chi Square Test?

The chi-square (χ2) test is a statistical tool used to determine whether there is a significant difference between the observed and expected frequencies of an event. The chi-square test is used to test the null hypothesis that there is no difference between the observed and expected frequencies.

## Chi Square Method

The chi square statistic is a measure of how well a given set of data fits a particular model. The chi square statistic is calculated by taking the difference between the observed values and the expected values, squaring them, and dividing by the expected value.

The chi square statistic is used to determine whether a set of data fits a particular model. The chi square statistic is calculated by taking the difference between the observed values and the expected values, squaring them, and dividing by the expected value.

The chi square statistic can be used to determine whether a set of data fits a particular distribution. The chi square statistic is calculated by taking the difference between the observed values and the expected values, squaring them, and dividing by the expected value.

## Chi Square Distribution Formula

The chi square distribution formula is:

\chi^{2}(x) = \frac{1}{\Gamma(\frac{n+1}{2})} \sum_{i=1}^{n} {(o_i – e_i)^2}

Where:

\chi^{2}(x) = the chi square distribution

\Gamma(\frac{n+1}{2}) = the gamma function

n = the number of degrees of freedom

o_i = the observed frequencies

e_i = the expected frequencies

## Chi Square Test Example

In the example below, there are six treatments and five response categories. The chi square statistic is calculated to determine if the observed frequencies are significantly different from the expected frequencies.

Treatment A Treatment B Treatment C Treatment D Treatment E Treatment F

Response Category 1 4 5 2 1 3

Response Category 2 2 3 1 5 4

Response Category 3 1 1 4 3 2

Response Category 4 3 2 5 4 1

Response Category 5 2 5 1 3 4

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