Chi Squared Test (x²)

Chi-Squared Test - AQA A Level Biology

Central Idea: Chi-Squared Test

• Statistical test used to determine if there is a significant difference between observed and expected data.

Main Branches:

1. Purpose of Chi-Squared Test

2. Calculation of Chi-Squared Value

3. Degrees of Freedom

4. Critical Value and P-Value

5. Interpretation of Results

1. Purpose of Chi-Squared Test

• Used to analyze categorical data and determine if the observed frequencies differ significantly from the expected frequencies.

• Determines if any observed differences are due to chance or if there is a real relationship between variables.

2. Calculation of Chi-Squared Value

• Calculate the chi-squared value by summing up the squared differences between observed and expected frequencies.

• Formula: χ² = ∑((O - E)² / E)

  • O: Observed frequency

  • E: Expected frequency

3. Degrees of Freedom

• Degrees of freedom (df) represent the number of categories that are free to vary after certain constraints.

• Formula: df = (number of rows - 1) x (number of columns - 1)

4. Critical Value and P-Value

• Critical value: Determines the threshold for rejecting the null hypothesis.

• P-value: Probability of obtaining results as extreme as the observed data, assuming the null hypothesis is true.

• Compare the calculated chi-squared value with the critical value or p-value to determine statistical significance.

5. Interpretation of Results

• If the calculated chi-squared value is greater than the critical value, reject the null hypothesis.

• If the p-value is less than the significance level (e.g., 0.05), reject the null hypothesis.

• If the calculated chi-squared value is less than the critical value or the p-value is greater than the significance level, fail to reject the null hypothesis.

Note: Ensure to refer to the specific AQA A Level Biology syllabus and past papers for detailed examples and further information.