Design of Experiments, statistics homework help

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4. A computer chip manufacturer uses a microscope and a CCD camera to measure the size of electronic parts. The microscope's field is divided into 4 rows and 4 columns which we wish to treat as blocking factors. The data file MachineVision.csv has the letter name of the part, the row, the column, the replication number of each measurement, and the length of the part in jm. (a) The experimenter claims that the eight parts were divided into two groups (A, B, C, D and E, F, G, H) and then a Latin-Squares design was used for each group with Row and Column as the blocking factors. Confirm that this design is a Latin Square by drawing the two Latin Squares in the design. (b) Perform an Analysis of Variance testing whether the parts are different lengths controlling for differences in the rows and columns. What do you conclude? (c) Give four appropriate plots of the residuals, and comment on any abnormalities that are seen. (d) Give a 95% confidence interval for the difference in length between parts A and E. (e) The designer of the measurement system wants to know whether or not the position of the chip (within the rows and columns) actually had any effect on the measurement. Perform an appropriate test. What do you conclude?
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Explanation & Answer

Attached.

Surname 1

Student’s Name
Instructor’s Name
Discipline
Date of submission

a) Latin Square Test
1

2

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4

1

D

C

B

A

2

B

A

D

C

3

A

B

C

D

4

C

D

A

B

1

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3

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1

H

G

F

E

2

F

E

H

G

3

E

F

G

F

4

G

H

E

H

This data represents two Latin square with three replications. A latin square should contain
number of rows = number of columns = number ...


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I was struggling with this subject, and this helped me a ton!

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