Psychology of learning mathematics
Significance of tests
Notes on tests - 14/2/00
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
Size of test? For N people? Random walk error = square root of N
- High/low maths: achieved A level / achieved GCSE?
- High/low DP: 50/50 cut of test results? What is distribution of
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.
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
Using Fisher exact 2x2 test and from the
The hypothesis we want to test is that high DP people are less likely to be
high maths people. The above conditions would produce
i.e. there is one degree of freedom: n can vary between 0 and 10
- 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.
Notes and conclusions
The two goals of the project are:
Conclusions from this hypothetical example
- 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
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Created 20/2/00 from PLM - Notes - 14/2/00