Medical Statistics at a Glance
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Chapter 25, Question 1.
3x3 Chi-squared test


An investigator obtained a Chi-squared test statistic of 26.2 (P < 0.001) when analysing the data from a sample of 650 children to investigate the association between the oral hygiene of children (graded as Good, Average or Poor) and the 'social grades' of the schools they attended (classified as Above Average, Average or Below Average). Under the null hypothesis of no association between a child's oral hygiene and his/her school's social grade, the expected frequencies of 8 out of the 9 cells of the 3x3 contingency table were greater than 5. Select all of the following statements which you believe to be true.

In order to satisfy the assumptions underlying the Chi-squared test, at least two rows or two columns of the table have to be combined so that all the cells of the table have expected frequencies greater than 5.
The degrees of freedom of the test statistic are 4.
The degrees of freedom of the test statistic are 5.
There is evidence of an association between oral hygiene and the social grade of school attended by the children.
The observed frequencies and those expected under the null hypothesis are in close agreement.