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Mathematical Requirements for Research Methods

Solving equations for Spearman's rho and chi-square

  • 3 things to know
  • Component 01

Overview

Recall questions on calculating Spearman's rho, interpreting rho values, the chi-square formula, calculating and using degrees of freedom, and why N and units must be substituted correctly into formulae.

What you need to know

Answer each one before you reveal it.

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Numbers

In a Spearman's rho calculation N is 10 and Σd² is 33. Calculate rₛ.

Key term

Why should a calculated value of rₛ never be greater than 1?

Key term

How are the degrees of freedom for a chi-square test calculated?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    In a Spearman's rho calculation N is 10 and Σd² is 33. Calculate rₛ.

    Model answer

    The numerator 6 × 33 is 198 and the denominator 10 × 99 is 990, so rₛ = 1 − 0.2 = 0.8.

  2. 2

    Explain what a Spearman's rho value of 0.8 indicates.

    Model answer

    It indicates a strong positive correlation, since as ranks on one co-variable rise so do ranks on the other.

  3. 3

    Why should a calculated value of rₛ never be greater than 1?

    Model answer

    A correlation coefficient runs only from −1 to +1, so a larger value shows an arithmetic error in the calculation.

  4. 4

    State the formula for the chi-square statistic.

    Model answer

    It is χ² = Σ (O − E)² ÷ E, where O is each observed frequency and E is each expected frequency.

  5. 5

    How are the degrees of freedom for a chi-square test calculated?

    Model answer

    Multiply one less than the number of rows by one less than the number of columns.

  6. 6

    Calculate the degrees of freedom for a chi-square test on a table with two rows and three columns.

    Model answer

    The degrees of freedom are 2, because 1 multiplied by 2 gives 2.

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