3. In an experiment designed to measure the effect of sex and fre- quency of tra

Question

3. In an experiment designed to measure the effect of sex and fre- quency of travel on preference for foreign travel a 2 (sex) × 3 (frequency of travel) between-subjects design was adopted. Five respondents were assigned to each cell for a total sample size of 30. Preference for foreign travel was measured on a 9-point scale (1 no preference, 9 strong preference). Sex was coded as male = 1 and female-2. Frequency of travel was coded as light = 1, medium = 2, and heavy = 3, The data obtained are shown here. Number Sex Travel Group Preference 4 4 4 4

Explanation / Answer

MINITAB used.

a).

Two-Sample T-Test and CI: preference, sex

Method

: mean of preference when sex = 1

µ: mean of preference when sex = 2

Difference: - µ

Equal variances are assumed for this analysis.

Descriptive Statistics: preference

sex

N

Mean

StDev

SE Mean

1

15

4.93

2.31

0.60

2

15

5.67

1.35

0.35

Estimation for Difference

Difference

Pooled
StDev

95% CI for
Difference

-0.733

1.892

(-2.149, 0.682)

Test

Null hypothesis

H: - µ = 0

Alternative hypothesis

H: - µ 0

T-Value

DF

P-Value

-1.06

28

0.298

Calculated t=-1.06, P=0.298 which is > 0.05 level. Ho is not rejected.

We conclude that there is no significant mean difference in preference between male and female.

b).

One-way ANOVA: preference versus Tralel Group

Method

Null hypothesis

All means are equal

Alternative hypothesis

Not all means are equal

Significance level

= 0.05

Equal variances were assumed for the analysis.

Factor Information

Factor

Levels

Values

Travel Group

3

1, 2, 3

Analysis of Variance

Source

DF

Adj SS

Adj MS

F-Value

P-Value

Tralel Group

2

55.40

27.700

15.29

0.000

Error

27

48.90

1.811

Total

29

104.30

Model Summary

S

R-sq

R-sq(adj)

R-sq(pred)

1.34578

53.12%

49.64%

42.12%

Means

Travel
Group

N

Mean

StDev

95% CI

1

10

4.600

1.897

(3.727, 5.473)

2

10

4.100

0.876

(3.227, 4.973)

3

10

7.200

1.033

(6.327, 8.073)

Pooled StDev = 1.34578

Tukey Pairwise Comparisons

Grouping Information Using the Tukey Method and 95% Confidence

Tralel
Group

N

Mean

Grouping

3

10

7.200

A

1

10

4.600

B

2

10

4.100

B

Means that do not share a letter are significantly different.

Calculated F=15.29, P=0.000 which is < 0.05 level. Ho is rejected.

We conclude that there is significant mean difference in preference between 3 travel groups.

c).

General Linear Model: preference versus sex, Travel Group

Method

Factor coding

(-1, 0, +1)

Factor Information

Factor

Type

Levels

Values

sex

Fixed

2

1, 2

Travel Group

Fixed

3

1, 2, 3

Analysis of Variance

Source

DF

Adj SS

Adj MS

F-Value

P-Value

sex

1

4.033

4.0333

4.94

0.036

Travel Group

2

55.400

27.7000

33.92

0.000

sex*Travel Group

2

25.267

12.6333

15.47

0.000

Error

24

19.600

0.8167

Total

29

104.300

Model Summary

S

R-sq

R-sq(adj)

R-sq(pred)

0.903696

81.21%

77.29%

70.64%

From the Two way ANOVA, we infer that sex is significant, Travel group is significant and interaction between sex and travel group is significant.

: mean of preference when sex = 1

µ: mean of preference when sex = 2

Difference: - µ

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