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Mathematical Requirements for Research Methods

Critical values and deciding whether a result is significant

  • 4 things to know
  • Component 01

Overview

Recall questions on what a critical value is, the information needed to find one, one-tailed and two-tailed values, which tests need calculated values below or above the critical value, and deciding significance for Wilcoxon, chi-square and Mann-Whitney results.

What you need to know

Answer each one before you reveal it.

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Key term

Why is it harder to obtain a significant result with a two-tailed test?

Study

A chi-square test gives a calculated value of 4.10 against a critical value of 5.99 at p ≤ 0.05. What is concluded?

Key term

A Mann-Whitney U test yields U = 23 with a critical value of 27. State the outcome.

Key term

Which three pieces of information are needed to find a critical value in a table?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    What is a critical value?

    Model answer

    The value taken from a table of critical values against which the calculated value of a test is compared in order to decide significance.

  2. 2

    Which three pieces of information are needed to find a critical value in a table?

    Model answer

    The number of participants or the degrees of freedom, the chosen level of significance, and whether the hypothesis is one-tailed or two-tailed.

  3. 3

    When is a one-tailed critical value used?

    Model answer

    When the hypothesis is directional, that is when it predicts which way the difference or relationship will go.

  4. 4

    Why is it harder to obtain a significant result with a two-tailed test?

    Model answer

    The chance of error is shared between both directions, so the critical value is more demanding than for a one-tailed test at the same level.

  5. 5

    For which tests must the calculated value be equal to or lower than the critical value to be significant?

    Model answer

    The Mann-Whitney U test, the Wilcoxon signed ranks test and the binomial sign test.

  6. 6

    For which tests must the calculated value be equal to or greater than the critical value to be significant?

    Model answer

    The chi-square test and Spearman's rho.

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