Mathematical Expectation of LS Design lecture 18

 Mathematical Expectation 

of 

LS Design

 lecture 18

The estimated Latin squares model:

SSTotal = SSR + SSC + SST + SSE

Expectation of SSE:

Multiple Choice Questions

1.      1.  The design is used to control two sources of variation is called

i.                    CRD

ii.                  RCBD

iii.                LSD

iv.                GLSD

2.      2. In case of LSD, each row and each column should be a complete

i.                    Column.

ii.                  Block.

iii.                Row.

iv.                Design

3.     3.  For a 6x6 Latin Square design there will be observations

i.                    6

ii.                   12

iii.                 24

iv.                36

4.      4. For a Latin Square design, the SSE can be obtained using the formula:

i.                     SSE=SST+SSTr+SSR+SSC

ii.                  SSE=SST-SSTr-SSR-SSC

iii.                SSE=SST-SSTr+SSR+SSC

iv.                SSE=SST+SSTr-SSR-1.   

5. The error degree of freedom for a P X P   Latin Square design is:

i. P - 1

ii. P (P - 1)

iii. (P -1) (P - 2)

iv. (P - 1) (P - 3)

6. The error degree of freedom for 9 X 9 Latin square is:

i.                    8

ii.                  56

iii.                63

iv.                64

1.      7. A Latin square design is not possible for

i.          Less than 3 X 3

ii.         Less than 5 X 5

iii.        Less than 6 X 6

iv.        Less than  7 X 7

1.      8. A Latin square in which the treatments in the first row and in the first column are arranged in alphabetical order or numerical order.

i.                     Simple Latin square.

ii.                  A standard Latin square.

iii.                Partial Latin square.

iv.                Double Latin square.

1.   9. The F test degree of freedom in a 7 X 7 Latin square design is

                  i. F (7, 6)

ii. F (7, 30)

iii. F (6, 30)

iv. F (6, 24)

• .     Read  GLSD

Q 1   The ANOVA table for LS design is given below:

SV	df	SS	SS	F
Row	4	46.67	11.67	4.98
Column	4	14.02	3.51	1.50
Treatment	4	196.61	49.15	21.00
Error	12	28.04	2.34
Total	24	285.34

          i.                    Find the relative efficiency over CRD

ii.                  Find the relative efficiency over RCBD

iii.                Discuss both the results.

Q 2: An investigator wants to determine which of four movies, to be released soon, should have the greatest audience appeal. These movies are (A) mystery, (B) sci fi, (C) comedy, and (D) drama. Movies are shown to audiences’ of 50 viewers at each showing, four times a day, and over a period of four days. It was thought that time of day and day of the week may influence the results of the study. The response is the number of people out of 50, who recommend the movie to a friend.

Time of day	Day
	Mon	Tue	Wed	Thu
Morning	C 32	D 23	B 36	A 40
Early Afternoon	B 33	A 36	C 31	D 22
Late Afternoon	D 17	C 37	A 34	B 41
Evening	A 35	B 37	D 18	C 31