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Chi-Square

 

Chi-Square is a statistical test that can be used to analyze results from categorical variables. Categorical variables are variables that contain clearly different groups. The chi-square statistic is used with frequency data. 


The chi-square value is reported with a probability (p) value indicating significance. 


For example, we can use chi-square to test for an association between frequency of attendance at organizational meetings and age groups (category variable). 


Common measures of effect size associated with chi-square analyses are Cramer’s V or the phi coefficient.


Read more details about Chi Square below the book information.




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The Chi-Square test is a statistical method used to determine whether there is a significant association between categorical variables. It compares the observed data with the expected data under the assumption that the variables are independent. Here's the formula for the Chi-Square statistic:

χ² = Σ [(Oáµ¢ - Eáµ¢)² / Eáµ¢]

Where:

  • χ² is the Chi-Square statistic.

  • Oáµ¢ represents the observed frequency for each category.

  • Eáµ¢ represents the expected frequency for each category.

  • The summation (Σ) indicates that you sum this calculation across all categories.

Now, let me break this down with an example tailored for psychology students:

Example: Are preferences for studying environments dependent on gender?

Imagine a psychology professor surveys 100 students to understand their study environment preferences. The two categorical variables are Gender (Male/Female) and Study Environment Preference (Quiet/Background Noise). The observed frequencies (O) are as follows:

GenderQuietBackground NoiseTotal
Male252045
Female352055
Total6040100

Step 1: Calculate the Expected Frequencies (E) The expected frequency is determined by this formula:  Eáµ¢ = (Row Total × Column Total) / Grand Total

For "Male, Quiet":  E = (45 × 60) / 100 = 27 For "Male, Background Noise":  E = (45 × 40) / 100 = 18 For "Female, Quiet":  E = (55 × 60) / 100 = 33 For "Female, Background Noise":  E = (55 × 40) / 100 = 22

The expected frequency table is:

GenderQuietBackground Noise
Male2718
Female3322

Step 2: Apply the Formula Now, calculate χ² for each category using (Oáµ¢ - Eáµ¢)² / Eáµ¢:

For "Male, Quiet":  (25 - 27)² / 27 = 0.148 For "Male, Background Noise":  (20 - 18)² / 18 = 0.222 For "Female, Quiet": (35 - 33)² / 33 = 0.121 For "Female, Background Noise":  (20 - 22)² / 22 = 0.182

Step 3: Sum Up All Values  χ² = 0.148 + 0.222 + 0.121 + 0.182 = 0.673

Step 4: Interpret the Result

The χ² value (0.673) is compared to a critical value from the Chi-Square distribution table for the appropriate degrees of freedom (df). Here, df = (rows - 1) × (columns - 1) = 1 × 1 = 1. If our χ² value exceeds the critical value (e.g., at α = 0.05), we reject the null hypothesis and conclude that study preferences and gender are associated. Otherwise, we fail to reject the null hypothesis.



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Resource Links: 

All Measures A – Z Test Index

Spirituality Measures A - Z

Statistical Concepts A - Z

See Cramer's V


NOTICE:

The information about scales and measures is provided for clinicians and researchers based on professional publications. The links to authors, materials, and references can change. You may be able to locate details by contacting the main author of the original article or another author on the article list.


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Geoffrey W. Sutton PhD is Emeritus Professor of Psychology who publishes book and articles about clinical and social psychology including the psychology of religion. Website:     www.suttong.com

   

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