Question: This problem requires data from question 1 Assignment 4. Suppose that the researcher had intended to make the following planned comparisons


Comparison 1: A comparison of the two “pleasantness” ratings (meaning and sound) with the two “frequency” ratings (word and syllable)



Comparison 2: The “meaning” treatment versus the other three


Comparison 3: Word frequency versus syllable frequency


a. Construct the coefficients (c i’s) appropriate for the comparisons

b. Form the summary table and evaluate the comparisons to determine whether the differences are significant statistically.

c. If the comparisons named above were unplanned and the Scheffé test were used, what would be the outcome?



PLEASANTNESS OF MEANING



a1







X2

FREQUENCY OF WORD



a2







X2

PLEASANTNESS OF SOUND



a3







X2

FREQUENCY OF SYLLABLES

a4







X2

11

11

12

9

10

13

11

9

10

6

13

7

12

12

9

121

121

144

81

100

169

121

81

100

36

169

49

144

144

81

7

3

10

7

7

4

8

7

5

7

8

11

8

10

9

49

9

100

49

49

16

64

49

25

49

64

121

64

100

81

8

2

8

8

9

4

6

7

7

1

9

3

6

5

11

64

4

64

64

81

16

36

49

49

1

81

9

36

25

121

3

4

3

2

5

2

5

5

2

8

4

8

5

7

7

9

16

9

4

25

4

25

25

4

64

16

64

25

49

49

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Answer: Comparison 1: A comparison of the two “pleasantness” ratings (meaning and sound) with the two “frequency” ratings (word and syllable)



Comparison 2: The “meaning” treatment versus the other three



Comparison 3: Word frequency versus syllable frequency



Construct the coefficients (c i’s) appropriate for the comparisons

Answer: The coefficients (c i’s) is commonly known as contrast. A contrast is a weighted average of the group means in which the weights sum to zero.



µ1

µ2

µ3

µ4

1

-1

1

-1

-3

1

1

1

0

0

1

-1



b. Form the summary table and evaluate the comparisons to determine whether the differences are significant statistically.

Answer:





Contrast Tests





Contrast

Value of Contrast

Std. Error

t

df

Sig. (2-tailed)

Data

Assume equal variances

1

4.563

1.1228

4.064

60

.000

2

-12.438

1.9447

-6.395

60

.000

3

1.688

.7939

2.125

60

.038

Does not assume equal variances

1

4.563

1.1228

4.064

55.231

.000

2

-12.438

1.8005

-6.908

29.532

.000

3

1.688

.8544

1.975

27.544

.058



From the observation we can conclude that the differences are significant statistically



c. If the comparisons named above were unplanned and the Scheffé test were used, what would be the outcome?

Answer:



Data

Scheffea

Group

N

Subset for alpha = 0.05

1

2

3

4.0

16

4.688





3.0

16

6.375

6.375



2.0

16



7.438



1.0

16





10.313

Sig.



.222

.619

1.000

Means for groups in homogeneous subsets are

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