Higher Skills in Mathematics – Normal Distribution and Testing

Overview

Framework:
Access to HE 2024
Level:
Level 3
Unit No:
Not available
Credits:
6
Guided learning hours:
Not available

Qualification Grading Type

Graded

Unit Learning Outcomes

1.

Understand normal distribution.

Using the Z-Score formula to calculate the Z-score. Using the Z-score and published tables to obtain percentages under a normal distribution.

Assessment Criteria

  • 1.1

    Obtain percentages of a normal distribution using standard deviations.

  • 1.2

    Explain what is meant by a skewed distribution.

  • 1.3

    Calculate the z score.

  • 1.4

    Use published tables for the normal distribution to calculate probabilities.

  • 1.5

    Use published tables to calculate the probability for a distribution of the sample mean.

2.

Understand the nature of hypotheses.

Classify tests as one-tailed or two-tailed. E.g. directional or non-directional

Formulating the experimental/alternative hypothesis. Students then need to formulate a corresponding null hypothesis.

Explain which hypothesis is being tested. Students need to explain why it is the null hypothesis that is being tested. Students discuss Popper’s ideas around falsification and deductive reasoning.

Distinguish between type 1 and type 2 errors when it comes to hypothesis testing. 

Assessment Criteria

  • 2.1

    Classify tests as one-tailed or two-tailed.

  • 2.2

    Formulate the experimental/alternative hypothesis and the corresponding null hypothesis.

  • 2.3

    Explain which hypothesis is being tested.

  • 2.4

    Distinguish between type 1 and type 2 error.

3.

Be able to use non-parametric tests.

Non-parametric tests include but are not restricted to Wilcoxon and Mann Whitney U.

Assessment Criteria

  • 3.1

    Use non-parametric tests correctly by:

    (a) calculating the statistic

    (b) locating the statistic in the tables

    and

    (c) drawing the correct conclusion.

4.

Understand the use of parametric tests.

T-tests could include tests for related/unrelated designs.

Assessment Criteria

  • 4.1

    Explain the conditions for using a parametric test.

  • 4.2

    Use t-tests correctly for related or unrelated samples by:

    (a) calculating the statistic

    (b) locating the statistic in the tables

    (c) drawing the correct conclusions.

5.

Be able to conduct correlational tests.

Students could complete a simple 2X2 contingency table showing observed frequencies. Using this table, students can calculate expected frequencies, X2 and degrees of freedom. 

Assessment Criteria

  • 5.1

    Correctly carry out X2 tests by:

    (a) drawing up a contingency table

    (b) calculating degrees of freedom

    (c) calculating X2

    (d) using the tables correctly

    (e) drawing the correct conclusion.

  • 5.2

    Correctly carry out a correlational test for two continuous variables (e.g. Pearson Correlation coefficient, Spearman correlation coefficient).