S3.4 - Goodness of fit and contingency tables

The null and alternative hypotheses.; Applications to include the discrete uniform, binomial, n (O − E)2 Normal, Poisson and continuous uniform (rectangular) The use of ∑ i i as an distributions.; Lengthy calculations will not be required.; E i=1 i approximate χ2 statistic.

Use null and alternative hypotheses to connect the rule to the data and decision in the question.

This matters because null and alternative hypotheses determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply null and alternative hypotheses to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: null and alternative hypotheses is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Degrees of freedom.; Students will be expected to determine the degrees of freedom when one or more parameters are estimated from the data.; Cells should be combined when E < 5.; Yates’ i correction is not required.

Use degrees of freedom to connect the rule to the data and decision in the question.

This matters because degrees of freedom determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply degrees of freedom to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Degrees of freedom is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.