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Mathematical Requirements for Research Methods

Calculating chi-square, sign test, Wilcoxon and Mann-Whitney values and reporting results

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  • Component 01

Overview

Recall questions on ranking tied scores, calculating expected frequencies and cell contributions to chi-square, finding N and S for the binomial sign test, and how to report and qualify a significant result.

What you need to know

Answer each one before you reveal it.

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Key term

How should the outcome of a significant test be stated in a report?

Key term

How is the expected frequency for a cell in a chi-square calculation worked out?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    How are tied scores dealt with when ranking data for a non-parametric test?

    Model answer

    They share the mean of the ranks they would have occupied, so two scores tied for third and fourth place are each given the rank 3.5.

  2. 2

    How is the expected frequency for a cell in a chi-square calculation worked out?

    Model answer

    Multiply the row total by the column total and divide by the overall total, so a row total of 40 and a column total of 30 in a study of 100 gives an expected frequency of 12.

  3. 3

    One cell has an observed frequency of 18 against an expected frequency of 12. What does this cell contribute to chi-square?

    Model answer

    The difference of 6 is squared to give 36 and divided by 12, so the cell contributes 3.

  4. 4

    What does the value of chi-square get larger with?

    Model answer

    The size of the differences between the observed and expected frequencies.

  5. 5

    What is the value of S in a binomial sign test?

    Model answer

    The number of participants showing the less frequent direction of change.

  6. 6

    Fourteen participants take part; 11 improve and 3 get worse. State N and S for a binomial sign test.

    Model answer

    N is 14 and S is 3, because 3 is the smaller number of signs.

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