Significance of tests.
Minimum of four intervals

• High maths, high divergent production (DP)
• Low maths, high DP
• High maths, low DP
• Low maths, low DP

• High/low maths: achieved A level / achieved GCSE?
• High/low DP: 50/50 cut of test results? What is distribution of test results?

Divide people into groups of high maths and low maths

Null hypothesis: in each maths group there should be equal numbers of high DP and low DP people.

Hypothetical example

If the test involved 30 people, 10 of which were in the high maths group, what distributions would show 5% and 1% significant deviation from the null hypothesis?

Using Fisher exact 2x2 test and from the above possibilities:

The hypothesis we want to test is that high DP people are less likely to be high maths people. The above conditions would produce

• High maths
  • Number of high DP = n
  • Number of low DP = (10 - n)
• Low maths
  • Number of high DP = (15 - n)
  • Number of low DP = 15 - (10 - n) = n + 5

The most extreme case of our hypothesis would be that n=0.

From the Fisher test, the probability of this case occuring by chance is:

p(n=0) = .0099%

The next probabilities are:

p(n=1) = .25%

p(n=2) = 2.2%

p(n=3) = 9.7%

The cumulative probabilities are:

p(n<1) = .0099%

p(n<2) = .25%

p(n<3) = 2.5%

p(n<4) = 12%

From these figures we can see that our 5% and 1% significance cases occur when n=2 and n=1 respectively.

The two goals of the project are:

• 1. A pilot study to see whether Hudson's results are still generally applicable as a measure of the difference between the subjects of biology and mathematics.
• 2. Identification of individual students that may have problems with certain aspects of mathematics.

• If I can get 60 pupils, Goal 1. might be achievable.
• For less than 30 pupils, it might be better to concentrate on goal 2. Changes to the tests might involve longer tests to about ten people.

• Kolmogorov - Smirnov test