Chi-Squared Test

The Chi-Squared test can be used to confirm if a set of data is significantly different from the expected result. 

The formula is as follows:

(the formula will be provided in the exam, but it is important to understand and memorise what each of the letters represents, as these aren't always provided in the exam).

O = OBSERVED RESULTS

E = EXPECTED RESULTS

Some questions will not provide candidates with the Expected results, in which instance they will have to calculate these themselves from the available data.

CALCULATING THE EXPECTED RESULTS:

If the known expected ratio is 9:3:3:1 (say for a genetic cross investigation), then the ratio is applied to the total population to find the distribution of population over the expected ratio.

e.g:       9       :       3       :       3       :       1          ΣRatio = 16 

O :       58              31             21              2          ΣO = 112

E :  9/16x112   3/16x112   3/16x112   1/16x112

=          63              21             21              7

The Chi-Squared Test demonstrates the liklihood that data sets may be different from the expectation due to chance. 

It is therefore important to be able to describe what the result of the test means.

The null hypothesis normally assumes that there is no difference in the data (meaning that there isn't a reason for any differences, and they are down to chance). 

If the critical value (normally p=0.05 for Biology) is less than the x² then the test has been passed: the differences in data aren't due to chance. There is a reason for them. The null hypothesis can be rejected.

If the critical value is more than the x² then the test has been failed; the differences in data are likely due to chance. There may not be a known reason for them. The null hypothesis can be accepted.