Analysis of Data (Edexcel A-Level Psychology): Revision Notes

Analysis of Data

Chi-squared test

The chi-squared test (χ²) is a statistical test used to analyse nominal data. It examines whether there is an association or difference between two or more independent groups. This test is particularly useful when researchers want to determine if observed patterns differ from what would be expected by chance.

When to use a chi-squared test

A chi-squared test is appropriate in three specific situations:

• Testing for differences or associations: When you have a hypothesis predicting a difference or association between groups. For example, a researcher might predict that boys and girls show differences in their toy choices at nursery.
• Nominal level of measurement: When your data is categorical rather than numerical. For instance, using two categories such as 'stereotypical' and 'non-stereotypical' toys rather than numerical scores.
• Independent measures design: When you have at least two different groups being studied, such as boys and girls, rather than the same participants tested repeatedly.

Understanding the chi-squared test

The chi-squared test compares two or more independent sets of data to determine if they differ or are related. It uses nominal data, where results are grouped into categories. The test gathers frequency data (how many occurrences within each group) rather than scores or measurements.

The data is organised into a contingency table, which displays the observed frequencies for each category. Chi-squared tests can examine differences or commonalities between two or more groups.

Formula for chi-squared

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

Where:

• O = observed frequency (the actual data collected)
• E = expected frequency (what would be expected by chance)
• Σ = sum of all the calculations

Calculating chi-squared: step-by-step procedure

Step 1: Create a contingency table

Organise your observed data into a table with rows and columns. A 2 × 2 contingency table has two rows and two columns, though larger tables (such as 3 × 2) are possible depending on your research design.

Step 2: Calculate expected frequency for each cell

Use the formula:

$E = \frac{\text{row total} \times \text{column total}}{\text{overall total}}$

Calculate this for every cell in the contingency table.

Step 3: Subtract expected value from observed value

For each cell, calculate O - E (observed minus expected).

Step 4: Square the result

Calculate (O - E)² for each cell.

Step 5: Divide by expected frequency

For each cell, calculate:

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

Step 6: Sum all values

Add all the values from Step 5 to obtain the observed chi-squared value (χ²).

Step 7: Calculate degrees of freedom

Use the formula:

$df = (\text{rows} - 1) \times (\text{columns} - 1)$

For a 2 × 2 table: df = (2-1) × (2-1) = 1

Step 8: Find the critical value

Look up the critical value in a chi-squared table using:

• The degrees of freedom
• Your chosen significance level (typically p = 0.05)
• Whether you have a directional (one-tailed) or non-directional (two-tailed) hypothesis

Step 9: Compare values

Compare the observed chi-squared value with the critical value. If the observed value is equal to or greater than the critical value, the result is statistically significant.

Worked example: children and toy choice

Critical values table for chi-squared

Degrees of freedom (df)	0.05 (one-tailed)	0.025 (one-tailed)	0.01 (one-tailed)
	Levels of significance for a two-tailed test
	0.10	0.05	0.02
1	2.71	3.84	5.41
2	4.60	5.99	7.82

Important considerations

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