Question

Question 1: A researcher is testing 4 different blood coagulation drugs. The drugs are labeled A,B,C and D. He is interested in how the drugs affect the blood coagulation rates of mice. The coagulation rate is the time in seconds that it takes for a cut to stop bleeding. He has 16 mice available for the experiment, so he will use 4 on each drug, randomized.

A                     B                     C                     D

62                    63                    68                    56

60                    67                    66                    62

63                    71                    71                    60

59                    64                                            61

64

a. Perform CRD (completely randomized design) manually as we did in the lectures. You need to write the STEPS clearly.

b. Watch the video on, CRD & CRBD on how to perform EXCEL calculation for CRD

c. Use the attached EXCEL sheet to perform the same calculation.

PART 2:   Three different washing solutions are being compared to study their effectiveness in retarding bacteria growth in 5-gallon milk containers. The analysis is done in a laboratory, and only three trials can be run on any day. Because days could represent a potential source of variability, the experimenter decides to use a randomized block design. Observations are taken for four days, and the data are shown here.

	Days
Solution	1	2	3	4
1	13	22	18	39
2	16	24	17	44
3	5	4	1	22

a. Watch the video on, CRD & CRBD on how to perform EXCEL calculation

b. Use the attached EXCEL sheet to perform the calculation for CRBD

PART 3: Explosive manufacturer conducts an experiment to study the explosive force of 4 different mixtures. It is planned to run five replicates (5 runs with each mixture).. The experiment is conducted outdoors which meant only 4 runs cam be made in a given day. Because conditions on each day and can affect the test results, a randomized block design is used, blocking against each day.

                Data on next sheet

  

Mixture                Day1                  Day2                     Day3                     Day4                         Day5

1                             72                           68                           74                           71                           67

2                              73                           67                           75                           72                           70

3                              75                           68                           78                           73                           68

4                              73                          71                           75                           75                           69

Determine if mixture affects explosive force.

a. Watch the video on, CRD & CRBD on how to perform EXCEL calculation

b. Use the attached EXCEL sheet to perform the calculation for CRBD

Answer 1

Question 1: PART 1:

c.

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
A	5	308	61.6	4.3
B	4	265	66.25	12.91667
C	3	205	68.33333	6.333333
D	4	239	59.75	6.916667
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	174.5708	3	58.19028	7.813689	0.003721	3.490295
Within Groups	89.36667	12	7.447222
Total	263.9375	15

PART 2:

Anova: Two-Factor Without Replication
SUMMARY	Count	Sum	Average	Variance
1	4	92	23	127.3333
2	4	101	25.25	168.9167
3	4	32	8	90
1	3	34	11.33333	32.33333
2	3	50	16.66667	121.3333
3	3	36	12	91
4	3	105	35	133
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Solution	703.5	2	351.75	40.71704	0.000323	5.143253
Days	1106.917	3	368.9722	42.71061	0.000192	4.757063
Error	51.83333	6	8.638889
Total	1862.25	11

Since p-value corresponding Solution<0.05, so effects of three different washing solutions are not all equal.

PART 3:

Anova: Two-Factor Without Replication
SUMMARY	Count	Sum	Average	Variance
1	5	352	70.4	8.3
2	5	357	71.4	9.3
3	5	362	72.4	19.3
4	5	363	72.6	6.8
Day 1	4	293	73.25	1.583333
Day 2	4	274	68.5	3
Day 3	4	302	75.5	3
Day 4	4	291	72.75	2.916667
Day 5	4	274	68.5	1.666667
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Mixture	15.4	3	5.133333	2.919431	0.077554	3.490295
Day	153.7	4	38.425	21.85308	1.94E-05	3.259167
Error	21.1	12	1.758333
Total	190.2	19

Since p-value=0.077554>0.05 so force of 4 different mixtures are insignificantly different at 5% level of significance.