In: Math
Data Table: Decreases in body temperature (degrees Fahrenheit) for each patient
| Mean | |||||||
| Group 1 (aspirin) | 0.95 | 1.48 | 1.33 | 1.28 | 1.26 | ||
| Group 2 (ibuprofen) | 0.39 | 0.44 | 1.31 | 2.48 | 1.39 | 1.20 | |
| Group 3 (acetaminophen) | 0.19 | 1.02 | 0.07 | 0.01 | 0.62 | -0.39 | 0.25 | 
The ANOVA table that corresponds to this data is below.
ANOVA Table:
| Fev_red | Sum of Squares | df | Mean Square | F | Sig. | 
| Between groups | 3.426 | 2 | 1.713 | 4.777 | 0.030 | 
| Within groups | 4.303 | 12 | 0.359 | ||
| Total | 7.729 | 14 | 
a. Effect of three treatments (aspirin, ibuprofen and acetaminophen) are equal or not.
b. ANOVA table:
One-way ANOVA: body temperature versus Group
Source DF     SS    
MS     F      P
Group    2 3.426 1.713 4.78 0.030
Error   12 4.303 0.359
Total   14 7.729
Since p-value<0.05 so there is enough evidence to conclude that three treatments are not equally effective.
c. Since Mean temperature decreased for aspirin is maximum so we recommend aspirin to reduce a fever for this population. d. We perform multiple comparison methods to compare each treatment group to the other (2 at a time) without inflating the type I error (α). There are several multiple comparison methods. For this problem we generally use Tukey's post hoc test.
Minitab output:
Grouping Information Using Tukey Method
Group N    Mean Grouping
1      4 1.2600 A
2      5 1.2020 A
3      6 0.2533 A
Means that do not share a letter are significantly different.
Tukey 95% Simultaneous Confidence Intervals
All Pairwise Comparisons among Levels of Group
Individual confidence level = 97.94%
Group = 1 subtracted from:
Group    Lower   Center  
Upper    
+---------+---------+---------+---------
2      -1.1288 -0.0580
1.0128             
(---------*----------)
3      -2.0371 -1.0067
0.0238     (---------*---------)
                                   
+---------+---------+---------+---------
                                
-2.0     
-1.0      
0.0       1.0
Group = 2 subtracted from:
Group    Lower   Center  
Upper    
+---------+---------+---------+---------
3      -1.9153 -0.9487
0.0180      (---------*--------)
                                   
+---------+---------+---------+---------
-2.0 -1.0 0.0 1.0
From the above confidence intervals we see that all three treatments are equally effective.
e. When we perform a large number of statistical tests, P-values of some of them is less than our critical value or level of significance and we reject corresponding null hypotheses. But These decisions may be wrong; the corresponding null hypotheses might be true, and the significant results might be due to chance. This is occurred because overall Type I error is increased. So we need to control the overall type I error and this is done by using some post hoc tests.