Question

For questions 47-53, refer to the following study and the accompanying SAS output: 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) 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 S was (before), (2) the age (in years) at the beginning of the (1) the initial DMFT count account are 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 These data were analyzed using two different models. Results from the analysis are provided below labeled SAS Output 1 and SAS Output 2. To answer you need to fill in some critical pieces of information that have been deleted. some of the questions that follow SAS Output 1 Sum of F Value Source DF Squares Mean Square Pr F Model 9.9567222 0.0003 Error 1,5928317 Corrected Total 68 141.7681159 Coeff Var DMFTdiff Mean Root MSE R-Square 0.280930 55.46696 1,262074 2.275362 F Value Type III s Mean Square Source DF Pr F 4.78907605 1.50 INSTITUTION 2.39453803 0.2301 TREATMENT 2 30.85357822 15.42678911 9.69 e.ee02 Standard Pr t Parameter Estimate t Value Error Intercept 3.264017447 B 0.35233162 9.26 <.0001 INSTITUTION 1 e.347238040 B 0.40888805 e.85 0.3989 -1.15 INSTITUTION 2 -0.411650654 B 0.35898961. e.2558 INSTITUTION 3 0.000000000 B TREATMENT APE -1.681287310 B 0.38344242 -4,38 <.0001 TREATMENT SF -0.881197881 B 0.40899969 -2.15 e.0350 TREATMENT W 0.000000000 B

1. Which model is more appropriate for these data: the model in SAS Output 1 or the model in SAS Output 2? Which test statistic and p-value should you use to make this decision?
2. 1. Output 1 because the interaction is not significant (F = 0.92, p-value = 0.4594).
   2. Output 1 because the interaction is not significant (F = 6.25, p-value = 0.0003).
   3. Output 1 because the interaction is significant (F = 6.25, p-value = 0.0003).
   4. Output 2 because the interaction is significant (F = 3.57, p-value 0.0019).
   5. Output 2 because the interaction is not significant (F = 0.92, p-value = 0.4594).
3. In SAS Output 1, what is the value of the test statistic for the omnibus null hypothesis H₀? a. 1.26

b.   1.50

c. 6.25

d.   9.69

e. 9.96

Answer 1

1)

Ans : C).Output 1 because the interaction is significant (F= 6.25, p-value = 0.0003).

Because pvalue is less for output 1 as compared to output 2.

2)

Ans: d 9.69