Question

An experiment was done to see the effects of diet and a drug on Type II Diabetes in men in the 50’s. Men in the 50’s who were diagnosed with Type II Diabetes that was under moderate control were randomly selected and randomly assigned to one of 4 treatment groups (8 per group). The groups were a Control group, those given a special diet, those given the drug, and those given the diet and the drug. The control group was given the typical information about diet for diabetes. The subjects tested their glucose levels each morning and the average glucose level for a month was the response variable. The data are given below (note: data are simulated).

• Summarize the glucose for each treatment. You may have to rearrange the data in order to get the summary statistics for each group. You can use Excel’s Data Analysis, Descriptive Statistics or you can use the basic Stats Excel file using functions for the mean, median and so forth

. • Using Excel, we are going to run a dummy variable regression on the data. You are going to need to create the dummy variables. Note, there are four groups (Control group, those given a special diet, those given the drug, and those given the diet and the drug). You decide how many dummy variables to create and which group is the reference category. Explain why you chose the reference category.

• For the Dummy Variable Regression, conduct an overall F-test for the treatment stating the following: Null Hypothesis Alternative Hypothesis Assumptions of the Test The Test Statistics F* The Critical value and the p-value for the Tests Statistics The Conclusion of the Test

• Pick one of the individual coefficients and the t-test for that coefficient. Explain the meaning of the test statistic and the conclusion of the test based on the p-value (in other words, what is the test saying and what is your conclusion)?

Treatment | Glucose Level |

Control | 123 |

Control | 149 |

Control | 125 |

Control | 102 |

Control | 132 |

Control | 128 |

Control | 128 |

Control | 84 |

Diet | 94 |

Diet | 72 |

Diet | 71 |

Diet | 87 |

Diet | 85 |

Diet | 110 |

Diet | 102 |

Diet | 98 |

Drug | 77 |

Drug | 64 |

Drug | 103 |

Drug | 94 |

Drug | 102 |

Drug | 93 |

Drug | 94 |

Drug | 120 |

Diet & Drug | 97 |

Diet & Drug | 94 |

Diet & Drug | 113 |

Diet & Drug | 65 |

Diet & Drug | 76 |

Diet & Drug | 121 |

Diet & Drug | 93 |

Diet & Drug | 101 |

Answer #1

Here

H_{0}: There is no significant effect of Druge and Diet
on Glucose level.

H1: There is significant effect of Druge and Diet on Glucose level.

The R-code for given problem is as;(By treating treatments as "Control"=1,"Diet"=2,"Drug"=3,"Diet & Drug"=4)

**y=c(1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4)
x=c(123,149,125,102,132,128,128,84,94,72,71,87,85,110,102,98,77,64,103,94,102,93,94,120,97,94,113,65,76,121,93,101)
d=data.frame(y,x)
summary(aov(y~x,d))**

And the output is as;

**> summary(aov(y~x,d))
Df Sum Sq Mean Sq F value Pr(>F) **

**x 1 6.81 6.811 6.157 0.0189 *
Residuals 30 33.19 1.106
---
Signif. codes:
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1**

Here F value is 6.157 and p-value is 0.0189 which is less than
0.05 . thus we reject H_{0} at 5% l.o.s.

And conclude that There is significant effect of Druge and Diet on Glucose level.

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