In: Statistics and Probability
Blood tests were performed on three groups of patients that had cornoavirus and suffered mild, severe or critical symptoms.
The immune system makes antibodies to protect the body from viruses and the levels of the IgG antibody was measured in each patient. IgG is the most common antibody in blood and the researchers wanted to examine if there were different levels within the three groups of patients and particularly in the critical group that eventually succumbed to the disease and died.
IgG can take time to form after an infection and values were recorded in the three groups on the 14th day after getting symptoms
The results are recorded in the following table.
IgG (AU/ml) 
Mild 
Severe 
Critical 

180 241 195 199 207 201 222 189 201 
150 175 180 201 168 175 192 195 
175 148 153 135 166 

Means 
203.8889 
179.5 
155.4 
StDev 
18.1207 
16.4838 
15.5981 
Ho: Average levels of IgG antibody are the same in the groups.
H1: Average levels of IgG antibody are different in the groups.
(a) Complete the ANOVA table. Use α=0.05 significance level.
(Round the SS and Variance values to 2 decimal places and Fteststatistic to 1 decimal place. )
Source of Variation 
Sums of Squares (SS) (2dp) 
DF 
Variance (2dp) 
F (1 dp) 

Between Groups  7811.9111  
Within Groups  
Total  21 
(b) 
Look up the critical value from
tables to answer the question below. 

There are (significant/insignificant) differences in the levels of IgG antibody across the groups. 
SolutionA:
Install analysis tool pak in excel
Go to Data>Data analysis>ANOVA single factor we get
ANSWER(A)
ANSWER(B)
Critical F value is
F crit
3.52
Test statistic is greater than critical F value
Reject Ho
There are (significant) differences in the levels of IgG antibody across the groups.