Question

ANOVA

A study is designed to examine whether there is a difference in mean daily calcium intake among three groups of adults with normal bone density (Norm), adults with osteopenia (OstPNia) (a low bone density which may lead to osteoporosis) and adults with osteoporosis (OstPSis). A total of twenty-one adults at age 60 was recruited in the study (7 adults in each group). Each participant's daily calcium intake was measured based on reported food intake and supplements in milligrams. We analyze the data using SAS's ANOVA procedure and observe the results shown in Table 2 (see page 6). Based on those findings, answer the following questions.

2) If this null hypothesis is true, then we would expect to see that the average variation between the means (i.e., the “model mean square” in SAS) is equal to the average variation within each group (i.e., the “error mean square” in SAS). We compare the two mean squares as an F ratio, dividing the model mean square by the error mean square.

Locate the two mean squares on the SAS output table and calculate the F ratio. Show your work.

Table 2: Output for Part Two One-Way ANOVA The ANOVA Procedure Dependent Variable: daily_ calcium DF Sum of Squares Mean Square F Value Pr> F 2 777011.111 388505.5569.71 0.0020 Source Model Error Corrected Total 17 1377094.444 15 600083.333 40005.556 R-Square Coeff Var Root MSE daily_ calcium Mean 0.564240 36.40293 200.0139 549.4444 Source DF Anova SS Mean Square F Value Pr>F GROUP 2 777011.1111 388505.55569 9.71 0.0020 One-Way ANOVA The ANOVA Procedure Student Newman Keuls Test for daily calcium Note: This test controls the Type I experimentwise error rate under the complete null hypothesis but not under partial null hypotheses. Alpha Error Degrees of Freedom15 Error Mean Square 0.05 40005.56 Number of Means Critical Range 246.13569 299.95087 daily_calcium SNK Grouping for Means of GROUP (Alpha 0.05) Means covered by the same bar are not significantly different GROUP Estimate Norm 825.00 OstP Nia 500.00 323.33

Answer 1

F = MS model/ MS Error

MS model = 388505.556   {look at first table column mean square}
MS error = 40005.556

F = 388505.556 / 40005.556
=9.71129