How to Use Chi-Square Test in Academic Research

The Chi-Square (χ²) test is a non-parametric statistical test used to determine whether there is a significant association between two categorical variables (e.g., gender, marital status, satisfaction level, income category).
It is one of the most commonly used tools in social sciences, management, education, public health, and business research.

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1. When to Use Chi-Square Test

Use Chi-Square when:

• Your data is categorical (e.g., Yes/No, Male/Female)

• You want to test for relationship/association between variables
  Example: Is there a significant relationship between gender and voting behaviour?

• Sample size is moderate or large (usually ≥ 20)

• Observations must be independent

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2. Types of Chi-Square Tests

There are two main types:

A. Chi-Square Test of Independence

Used when you want to know if two variables are related.
Example: Is there a relationship between educational level and job satisfaction?

B. Chi-Square Goodness-of-Fit Test

Used when you want to know if observed frequencies fit expected frequencies.
Example: Do students equally prefer the 4 faculties in the institution?

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3. Data Requirements

To use Chi-Square:

• Data must be presented in a frequency table (contingency table).

• Categories should be mutually exclusive (no overlap).

• Expected frequency in each cell should be ≥ 5 (for reliability).

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4. Chi-Square Formula

For Chi-Square test of independence:

$$\chi^2 = \sum \frac{(O - E)^2}{E}$$

Where:

• O = Observed frequency (data you collected)

• E = Expected frequency (calculated value)

Expected frequency is calculated as:

$$E = \frac{(Row\ Total \times Column\ Total)}{Grand\ Total}$$

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5. Steps for Using Chi-Square Test (Step-by-Step)

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Step 1: State Your Hypotheses

You always test for independence (no relationship).

Null Hypothesis (H₀):

There is no significant relationship between Variable A and Variable B.

Alternative Hypothesis (H₁):

There is a significant relationship between Variable A and Variable B.

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Step 2: Create a Contingency Table

Example: Relationship between Gender and Product Preference

Gender	Prefer Product A	Prefer Product B	Total
Male	30	20	50
Female	25	45	70
Total	55	65	120

This is your observed (O) data.

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Step 3: Calculate Expected Frequencies (E)

Use the formula:

$$E = \frac{(Row\ Total \times Column\ Total)}{Grand\ Total}$$

Example: For Male + Product A:

$$E = \frac{50 \times 55}{120} = 22.92$$

You calculate E for each of the 4 cells.

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Step 4: Compute the Chi-Square Value (χ²)

Apply:

$$\chi^2 = \sum \frac{(O - E)^2}{E}$$

Do this for each cell and sum the results.

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Step 5: Determine Degrees of Freedom (df)

$$df = (r - 1)(c - 1)$$

Where:

• r = number of rows

• c = number of columns

Example: 2 rows, 2 columns:

$$df = (2 - 1)(2 - 1) = 1$$

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Step 6: Compare with Critical Value or P-Value

If using statistical software (SPSS, R, Excel), you get a p-value automatically.

Decision Rule:

• If p-value < 0.05 → Reject H₀ → Significant relationship exists

• If p-value > 0.05 → Fail to reject H₀ → No significant relationship

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Step 7: Interpret the Results

Write your results in APA-style format:

Example Interpretation

The Chi-square test showed a significant relationship between gender and product preference
(χ² = 12.46, df = 1, p < 0.05).
This indicates that product preference varies significantly by gender.

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6. How to Run Chi-Square Test in SPSS

1. Go to Analyze

2. Select Descriptive Statistics → Crosstabs

3. Move one variable to Rows, the other to Columns

4. Click Statistics, then tick Chi-square

5. Click OK

SPSS outputs:

• Pearson Chi-Square value

• Degrees of freedom

• p-value

You interpret the p-value.

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7. Common Mistakes to Avoid

❌ Using continuous variables (e.g., age) without categorizing them
❌ Small sample sizes with expected frequency < 5
❌ Using Chi-Square for paired or dependent data
❌ Interpreting Chi-Square as measuring the strength of relationship
(Use Cramer's V for strength)

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8. Reporting Chi-Square in Your Research Project

Methodology Chapter

• Mention data type is categorical

• Mention you used Chi-Square to test relationships

• Justify because assumptions are met

Results Chapter

• Present contingency table

• Present χ², df, and p-value

• Provide interpretation

Discussion Chapter

• Compare your findings with previous studies