A pharmaceutical science researcher tried to evaluate patient’s effectiveness (outcomes) in three different settings with three...
A pharmaceutical science researcher tried to evaluate patient’s effectiveness (outcomes) in three different settings with three different formulations. Effectiveness scores as continuous data were collected during the study period. If the researcher conducted a two-way ANOVA, we have a summary table below (see Table 2). Please answer following questions: (Please show your work!)
Table 2. Summary Table of Two-Way ANOVA
|
Source |
Degree of freedom |
Sum of Squares |
Mean Squares |
F |
|
Between |
||||
|
Rows (setting) |
2 |
51.04 |
? |
? |
|
Column (formulation) |
2 |
612.71 |
? |
? |
|
Interaction (setting x formulation) |
? |
? |
246.94 |
? |
|
Within (error) |
26 |
340.67 |
||
|
Total |
? |
? |
a) What is the degree of freedom for interaction (setting x formulation)?
b) What is total degree of freedom?
c) What is the sum of squares for interaction (setting x formulation)?
d) What is the total sum of squares?
e) What is the mean square for setting (row)?
f) What is the mean square for formulation (column)?
g) What are F ratios for setting, formulation and interaction?
Homework Answers
A)What is the degree of freedom for interaction (setting x formulation)?
=(k-1)*(l-1)
=2*2
=4
b) What is total degree of freedom?
=2+2+4+26
=34
C)What is the sum of squares for interaction
SS interaction =Mse*DF
=246.94*4
= 987.76
d) What is the total sum of squares?
=51.04+612.71+987.76+340.67
=1992.18
e)What is the mean square for setting (row)?
=51.04/2
=25.52
f)What is the mean square for formulations (colomn)?
=612.71/2
=306.355
What are F ratios for setting, formulation and interaction?
F ratios for setting: 25.52/340.67
=0.07429
F ratios for formulation= 306.35/340.67
=0.8992
What are F ratios for interaction
=246.94/340.67
=0.7072
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