The x2 test
The unit from the Continuing Mathematics Project focuses on the x2 test as it is one of the most widely used statistical techniques. It is employed to compare theory with practice in biology, geography and the social sciences.
This unit is concerned with the practicalities of using the x2 test; stating a suitable hypothesis; calculating the x2 value; using significance levels; and drawing an appropriate conclusion from the x2 value in terms of the experiment or testing situation.
The emphasis is upon using the x2 test as a tool. Little attempt is made to explain the formula for x2 or even the notion of 'degrees of freedom'.
The objectives for this unit are that, given a set of data, students will be able to:
(i) state a suitable hypothesis for testing (including a null hypothesis where appropriate);
(ii) calculate the 'expected' values, E, on the basis of the hypothesis
(iii) find the number of degrees of freedom;
(iv) calculate the value of x2;
(v) use the tables to judge whether the x2 value is significantly high or not;
(vi) understand the notion of significance in terms of the 'degree of confidence' with which the hypothesis under test is rejected, and the probability that the hypothesis under test has been wrongly rejected (for example 5% or 1%).
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