OCR A-Level Geography H481
Coastal Landscapes
Glaciated Landscapes
Dryland Landscapes
Earth’s Life Support Systems
Changing Spaces; Making Places
Trade in the Contemporary World
Global Migration
Human Rights
Power and Borders
Climate Change
Disease Dilemmas
Exploring Oceans
Future of Food
Hazardous Earth
Geographical Skills
Geographical Skills
Significance tests: chi-squared, Mann-Whitney U and the t-test
- 3 things to know
- Components 01, 02 and 03
Overview
Recall questions on the chi-squared test, its formula and conditions, a worked corrie aspect calculation, degrees of freedom and critical values, the non-parametric Mann-Whitney U test with worked pebble data, the t-test with worked infiltration data, choosing between Spearman's rank, chi-squared, Mann-Whitney U and the t-test, and non-significant results.
What you need to know
Answer each one before you reveal it.
State the formula for chi-squared.
How are the degrees of freedom calculated for a one-way chi-squared test?
Questions from this subtopic
Each one with the model answer underneath.
- 1
What does the chi-squared test compare?
Model answer
It compares observed frequencies in categories with the frequencies expected if there were no pattern, and tests whether the difference between them is significant.
- 2
State the formula for chi-squared.
Model answer
χ² = Σ((O − E)² ÷ E), where O is each observed frequency and E is the corresponding expected frequency.
- 3
Give three conditions for using the chi-squared test.
Model answer
The data must be raw counts rather than percentages, the categories must not overlap, and every expected frequency should be at least 5.
- 4
Forty corries are counted by aspect: 18 face north, 11 east, 3 south and 8 west. Assuming an equal expected frequency in each class, calculate chi-squared.
Model answer
Each expected frequency is 40 ÷ 4 = 10, so χ² = (64 + 1 + 49 + 4) ÷ 10 = 118 ÷ 10 = 11.8.
- 5
How are the degrees of freedom calculated for a one-way chi-squared test?
Model answer
The degrees of freedom equal the number of categories minus one, so four aspect classes give 3 degrees of freedom.
- 6
A chi-squared value of 11.8 is obtained for corrie aspect with 3 degrees of freedom, where the critical values are 7.81 at the 0.05 level and 11.34 at the 0.01 level. What should be concluded?
Model answer
The value exceeds both critical values, so the null hypothesis is rejected at the 0.01 level and the corries are significantly concentrated on particular aspects.
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