Question

Quade (1992) reports data obtained by Cartwrigtht, Lindahl and Bawden (1968) in their two-year study designed to evaluate the effectiveness of two treatments in reducing the incidence of dental caries, as compared with a placebo. The two treatments were stannous fluoride (SF) and acid-phosphate fluoride (APF), and the placebo was distilled water (W). A total of 69 female children completed the study. For each child, the number of decayed, missing or filled teeth (DMFT) was recorded before (B) and after (A) the study; the response to be analyzed is the difference (or change) in the number of DMFT, calculated as Y = A – B. Covariates that could be taken into account are (1) the initial DMFT count (before), (2) the age (in years) at the beginning of the study, and (3) the institution where the child resided (there were 3 different institutions). Note that the change in the number of DMFT, the initial DMFT count and age can be considered continuous here, whereas the institution and treatment group are categorical. Using a 0.05 significance level and the given computer output, you need to test the claim that the children residing in the 3 institutions using any of the 3 treatments have the same mean change in the number of DMFT by answering the questions that follow.

What type of analysis should you perform to test the given hypothesis?

Select one:

a. ANCOVA

b. Linear regression

c. Logistic Regression

d. One-way ANOVA

e. Two-way ANOVA

Answer 1

Solution

ANCOVA Option (a) Answer

Rationale

‘you need to test the claim that the children residing in the 3 institutions using any of the 3 treatments have the same mean change in the number of DMFT’ => this is two factor experiment => the tool must be Two-way ANOVA.

Further, ‘Covariates that could be taken into account are (1) the initial DMFT count (before), (2) the age (in years) at the beginning of the study, and (3) the institution where the child resided (there were 3 different institutions).’ => effect of the first two of these covariates are to be eliminated to get the true effect of the two main factors under study. So, ANOVA is inadequate and ANCOVA is the most appropriate tool of analysis.

DONE