Assume you are hoping to submit a grant proposal to investigate dose-response a

Question

Assume you are hoping to submit a grant proposal to investigate dose-response a relationships in a psychopharmacological study of depression, planning to pursue your work in New Mexico, where psychologists were recently granted prescription privileges. From the range of acceptable dosages of your favorite antidepressant, you select three dosages at random for investigation. Four psychologists are available for the study, and you regard them as representative of the pool of psychologists who might eventually be granted prescription privileges. Each psychologist in your pilot study prescribes each of the three dosage levels to an equal number of patients. When scores on a depression scale are gathered at the end of the study and analyzed, the following mean squares are obtained, with the associated degrees of freedom shown in the following table (the DOF error has been pre-filled for you). (i) How many patients did each psychologist use in the study? (ii) Complete the ANOVA and suggest whether the factors and interaction are significant

Explanation / Answer

Since three dosages are selected the dof for drug is given by 3-1=2

Since 4 Psychologists are participated the dof for Psychologist is 4-1=3

Hence the d0f for interaction of drug dosage and psychologists is 2*3=6

Given Error dof = 48

Therfore the total dof =59

Hence total number of patients = 59+1=60

therfore the number of patients each Psychologist used = (60/4)=15

The Anova table is as follows

i) Since F statistic value is greater than the critical value for drug dosage i.e., 72 > 3.19, reject H0 and conclude that the drug dosage is significant

ii) Since F statistic value is greater than the critical value for the Psychologists i.e., 32 > 2.80, reject H0 and conclude that the Psychologists are significant

iii) Since F statistic value is greater than the critical value for the interaction i.e., 8 > 2.29, reject H0 and conclude that the interaction significant

Source dof Sum of square Mean Square F F-critical Drug 2 3 1.5 72 3.19 Psychologist 3 2 0.67 32 2.80 drug * psychologist 6 1 0.17 8 2.29 Error 48 1 0.02 Total 59 7

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