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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.

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Process

Infiltration is measured at ten points under woodland and ten under pasture, giving means of 46 and 28 mm per hour and variances of 216 and 144. Using t = (x̄₁ − x̄₂) ÷ √(s₁²/n₁ + s₂²/n₂), calculate t.

Process

State the formula for chi-squared.

Process

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. 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. 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. 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. 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. 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. 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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