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Chi Square Statistic Formula

GoChi Square Statistic given Sample and Population Variances Formula

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Chi Square Statistic is the measure used in chi-square tests to determine if there is a significant association between categorical variables in a contingency table. Check FAQs

χ 2 = \frac{(N - 1) \cdot s^{2}}{σ^{2}}

χ² - Chi Square Statistic?N - Sample Size?s - Sample Standard Deviation?σ - Population Standard Deviation?

Chi Square Statistic Example

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Here is how the Chi Square Statistic equation looks like with Values.

Here is how the Chi Square Statistic equation looks like with Units.

Here is how the Chi Square Statistic equation looks like.

25 = \frac{(10 - 1) \cdot 15^{2}}{9^{2}}

25 = \frac{(10 - 1) \cdot 15^{2}}{9^{2}}

25 = \frac{(10 - 1) \cdot 15^{2}}{9^{2}}

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Chi Square Statistic Solution

Follow our step by step solution on how to calculate Chi Square Statistic?

FIRST Step Consider the formula

χ 2 = \frac{(N - 1) \cdot s^{2}}{σ^{2}}

Next Step Substitute values of Variables

∴

χ 2 = \frac{(10 - 1) \cdot 15^{2}}{9^{2}}

Next Step Prepare to Evaluate

∴

χ 2 = \frac{(10 - 1) \cdot 15^{2}}{9^{2}}

LAST Step Evaluate

∴

χ 2 = 25

Chi Square Statistic Formula Elements

Variables

Chi Square Statistic

Chi Square Statistic is the measure used in chi-square tests to determine if there is a significant association between categorical variables in a contingency table.

Symbol: χ²

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Chi Square Statistic

Sample Size

Sample Size is the total number of individuals or items included in a specific sample.

Symbol: N

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Sample Size

Sample Standard Deviation

Sample Standard Deviation is the measure of how much the values in a specific sample vary.

Symbol: s

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Sample Standard Deviation

Population Standard Deviation

Population Standard Deviation is the measure of how much the values in an entire population vary.

Symbol: σ

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Population Standard Deviation

Other Formulas to find Chi Square Statistic

Go Chi Square Statistic given Sample and Population Variances

χ 2 = \frac{(N - 1) \cdot s 2}{σ 2}

Other formulas in Basic Formulas in Statistics category

Go Number of Classes given Class Width

N Class = \frac{Max - Min}{w Class}

Go Class Width of Data

w Class = \frac{Max - Min}{N Class}

Go Number of Individual Values given Residual Standard Error

n = (\frac{RSS}{{RSE}^{2}}) + 1

Go P Value of Sample

P = \frac{P Sample - P 0(Population)}{\sqrt{\frac{P 0(Population) \cdot (1 - P 0(Population))}{N}}}

How to Evaluate Chi Square Statistic?

Chi Square Statistic evaluator uses Chi Square Statistic = ((Sample Size-1)*Sample Standard Deviation^2)/(Population Standard Deviation^2) to evaluate the Chi Square Statistic, Chi Square Statistic formula is defined as the measure used in chi-square tests to determine if there is a significant association between categorical variables in a contingency table. Chi Square Statistic is denoted by χ² symbol.

How to evaluate Chi Square Statistic using this online evaluator? To use this online evaluator for Chi Square Statistic, enter Sample Size (N), Sample Standard Deviation (s) & Population Standard Deviation (σ) and hit the calculate button.

FAQs on Chi Square Statistic

What is the formula to find Chi Square Statistic?

The formula of Chi Square Statistic is expressed as Chi Square Statistic = ((Sample Size-1)*Sample Standard Deviation^2)/(Population Standard Deviation^2). Here is an example- 1.361111 = ((10-1)*15^2)/(9^2).

How to calculate Chi Square Statistic?

With Sample Size (N), Sample Standard Deviation (s) & Population Standard Deviation (σ) we can find Chi Square Statistic using the formula - Chi Square Statistic = ((Sample Size-1)*Sample Standard Deviation^2)/(Population Standard Deviation^2).

What are the other ways to Calculate Chi Square Statistic?

Here are the different ways to Calculate Chi Square Statistic-

Chi Square Statistic=((Sample Size-1)*Sample Variance)/Population Variance

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Chi Square Statistic Formula

​GoChi Square Statistic given Sample and Population Variances Formula

Chi Square Statistic Example

Chi Square Statistic Solution

Chi Square Statistic Formula Elements

Other Formulas to find Chi Square Statistic

Other formulas in Basic Formulas in Statistics category

How to Evaluate Chi Square Statistic?

FAQs on Chi Square Statistic

Variable Name

GoChi Square Statistic given Sample and Population Variances Formula