Human ecology
Mathematics education
Psychology of learning mathematics
Significance of tests

Notes on tests - 14/2/00

Significance of tests.
Minimum of four intervals

Definitions: Size of test? For N people? Random walk error = square root of N

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.


Notes 28/2/00

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

i.e. there is one degree of freedom: n can vary between 0 and 10

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
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Created 20/2/00 from PLM - Notes - 14/2/00
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