Notes on the use of statistics
a. Principles
There are no statistical tests named in the specification and it is not assumed that students
will have knowledge of the detailed mathematical derivations of the different formulae.
The emphasis at this level is to introduce the principle of statistical testing as a progression
from subjective analysis of data to some objective guidelines when considering how far
collected data agrees or disagrees with the hypothesis under test.
b. What students are expected to demonstrate.
(i) Their ability to select the correct form of statistical test appropriate to their
hypothesis. It is highly recommended that this is an integral part of the plan.
(ii) An understanding of the use of a null hypothesis.
(iii) Their ability to tabulate data in the correct format for calculating their chosen
statistical value.
(iv) Their ability to explain the meaning of any calculated test statistic in terms of 5%
confidence limits, where appropriate, and its relationship to their stated hypothesis
in their own words.
c. Types of statistical tests
There are 3 main types of test.
(i) Tests for a significant difference – typically a t-test or a Mann-Whitney U test
(ii) Tests for a significant correlation – typically Spearman’s Rank test
(iii) Tests for significant association or ‘goodness of fit’ – typically Chi-squared test.
d. Null Hypotheses
It is important for students to understand the importance of accuracy in their wording. There
is a large difference in meaning between ‘There is no difference between….’ and ‘There is no
significant difference, (at the 5% confidence level) between….’
The reasoning behind the use of a null value in hypothesis testing is as follows
(i) Start with the assumption that the two means of your samples are the same.
(ii) Take sample measurements to find out what is the true situation.
(iii) Use a statistical test to find the probability of getting values at least as far apart as
those shown in your data.
(iv) If this probability is low (less than 5 chances in 100) then we can say that the
assumption made in (i) is not correct. (reject a null hypothesis).
Hence a null hypothesis is a consequence of the way the statistical test calculates the
probability.
