Question

In: Statistics and Probability

Blood tests were performed on three groups of patients that had cornoavirus and suffered mild, severe...

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

St-Dev

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 F-test-statistic to 1 decimal place. Leave no cells blank)

Source of Variation   

Sums of Squares

(SS)  (2dp)

DF

Variance

(2dp)

F

(1 dp)

Between Groups 7811.9111 Answer Answer Answer
Within Groups Answer Answer Answer
Total Answer 21

(b)
   Look up the critical value from tables to answer the question below.
There are Answer significant differences/not significant differences in the levels of IgG antibody across the groups.

(1 Mark)

Solutions

Expert Solution

(a)

The ANOVA Table is completed as follows:

Source of Variation Sum of Squares DF Variance F
Between groups 7811.9111 2 7811.9111/2=3905.96 3905.96/289.58=13.5
Within groups 5502.0889 19 5502.0889/19=289.58
Total 13314

The entries in the Table are got as follows:

From the given data the following Table is calculated:

Mild Severe Critical
n 9 8 5
Sum 1835 1436 777
Mean 203.889 179.5 155.4
376763 259664 121719
Std. Dev. 18.121 16.484 15.598
SS 2626.889 1902 973.2

(b)

Calculated value of F = 3905.9556/289.5836=13.5

Degrees of Freedom fornumerator = 2

Degrees of Freedom for denominator = 19

= 0.05

From Table, critical value of F =3.52

Since Calculated value of F =13.5 is greater than critical value of F = 3.52, the difference is significant. Reject null hypothesis.

Conclusion:

There are significant difference in the levels of IgG antibody across the groups.

Related Solutions

Blood tests were performed on three groups of patients that had cornoavirus and suffered mild, severe...
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.  ...
The following tests were performed as a group from one blood sample: lipid panel – total...
The following tests were performed as a group from one blood sample: lipid panel – total serum cholesterol, HDL and triglycerides; electrolyte panel – carbon dioxide, chloride, potassium, and sodium. Code the labs What is the CPT code(s)? Modifiers if appropriate?
Depressed patients were randomly assigned to one of three groups: a placebo group, a group that...
Depressed patients were randomly assigned to one of three groups: a placebo group, a group that received a moderate dose of the drug, and a group that received a high dose of the drug. After four weeks of treatment, the patients completed the Beck Depression Inventory. The higher the score, the more depressed the patient. We are now also interested if a patient's weight has an effect on the drug's effectiveness. Patients were categorized as either underweight, overweight, or 'medium...
Depressed patients were randomly assigned to one of three groups: a placebo group, a group that...
Depressed patients were randomly assigned to one of three groups: a placebo group, a group that received a moderate dose of the drug, and a group that received a high dose of the drug. After four weeks of treatment, the patients completed the Beck Depression Inventory. The higher the score, the more depressed the patient. We are now also interested if a patient's weight has an effect on the drug's effectiveness. Patients were categorized as either underweight, overweight, or 'medium...
The number of blood tests performed and the related costs over the last nine months in...
The number of blood tests performed and the related costs over the last nine months in Brentline Hospital are given below:   Month Blood Tests Performed Blood Test Costs   January 5,120     $ 67,900   February 5,400     $ 70,530   March 4,695     $ 61,932   April 4,290     $ 56,782   May 4,425     $ 59,041   June 3,600     $ 48,570   July 4,020     $ 53,212   August 5,315     $ 69,419   September 5,245     $ 69,025 Required: 1. Using the high–low method, estimate...
what are the five (5) core tests performed in a blood unit? According to World Health...
what are the five (5) core tests performed in a blood unit? According to World Health Organization
Direct shear tests were performed on a dry, sandy soil. The size of the specimen was...
Direct shear tests were performed on a dry, sandy soil. The size of the specimen was 50 mm x 50 mm x 20 mm (LxWxH). Test results are given in the following table. Find the shear stress parameters. Estimate the major and minor principal stresses, and the orientation of the principal stresses at failure for Test 2 Test No. Normal Force (N) Shear force at failure (N) 1 90 55 2 135 80 3 315 190
At four UK hospitals, patients with severe asthma were screened for fungal sensitization by skin prick...
At four UK hospitals, patients with severe asthma were screened for fungal sensitization by skin prick testing. those 3,610 who were positive by skin prick were randomized to one of two treatment regimens: 1,805 were assigned to take an antifungal agent in tablet form while 1,805 were assigned to take a similar looking placebo tablet. The primary end point was the development of a particular type of lung infection by 32 weeks. By the end of the study, 1,492 of...
Patients with high blood pressure were randomly allocated to receive one of two treatments. All patients...
Patients with high blood pressure were randomly allocated to receive one of two treatments. All patients had been treated with cognitive behaviour therapy (CBT) and were then assigned (at random) to recieve no further treatment (NFT) or beta-blockers (BB). Six weeks later it was noted whether or not each of the patients showed a decrease in their blood pressure. For the NFT group 15 out of 50 patients showed a decrease after 6 weeks, whereas this happened for 26 out...
Patients with high blood pressure were randomly allocated to receive one of two treatments. All patients...
Patients with high blood pressure were randomly allocated to receive one of two treatments. All patients had been treated with cognitive behaviour therapy (CBT) and were then assigned (at random) to recieve no further treatment (NFT) or beta-blockers (BB). Six weeks later it was noted whether or not each of the patients showed a decrease in their blood pressure. For the NFT group 15 out of 50 patients showed a decrease after 6 weeks, whereas this happened for 26 out...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT