STATISTICAL ANALYSIS

Statistical Analysis



Question number 01

Solution

Hypothesis

Ho: there a significant effect of gender upon enjoyment of opera

H1: there no significant effect of gender upon enjoyment of opera

Analysis

To check the effect of gender on the enjoyment of opera, we applied general linear model on the study variables - gender (male and female) and enjoyment rating [1 (not at all enjoyable) to 10 (extremely enjoyable)]. We took enjoyment rating (scale variable) as a dependent variable where as gender as categorical (independent variable). In the situation where the dependent variable is a scale variable and the predictor is a categorical variable, general linear model is recommended to study the impact of categorical variable (Fox, 2008, Pp. 14-22). After applying GML, we got following tables, which we interpret to know whether to accept the null hypothesis or not.

Between-Subjects Factors

Value Label

N

Gender

0

Female

12

1

Male

12

The above table shows the number of observation, which are being included in the analysis. For the purpose of this study, we have collected the data from 12 male and 12 females.

Descriptive Statistics

Dependent Variable: Enjoyment

Gender

Mean

Std. Deviation

N

Female

7.0833

1.44338

12

Male

3.4167

1.83196

12

Total

5.2500

2.47158

24

Furthermore, descriptive statistics shows that mean of enjoyment rate of female participants is seven (7.083) with standard deviation of 1. 44. On the other hand, mean of enjoyment rate of male participants is less than what female participants mean score is. The mean score for the male participants is 3.4 with standard deviation of 1.83. There is a great difference between the enjoyment level of opera between two groups- male and female. However, we will analyze other tables to prove whether this deviation is by chance or not. Mean score of both groups (combined) is 5.2 with standard deviation of 2.47. (Rencher & Schaafe, 2008, Pp. 99-105)

Tests of Between-Subjects Effects

Dependent Variable: Enjoyment

Source

Type III Sum of Squares

df

Mean Square

F

Sig.

Partial Eta Squared

Corrected Model

80.667a

1

80.667

29.660

.000

.574

Intercept

661.500

1

661.500

243.226

.000

.917

Gender

80.667

1

80.667

29.660

.000

.574

Error

59.833

22

2.720

Total

802.000

24

Corrected Total

140.500

23

a. R Squared = .574 (Adjusted R Squared = .555)

Each term in the model, plus the model as a whole, is tested for its ability to account for variation in the dependent variable (Searle, 1971, Pp. 456-459). The significant value for gender less than 0.05, which means the gender, is statistically significant. Practical significant of the gender is shown by partial Eta, which is based on the ration of variation contributed by gender to the variation left to error (Graybill, 1976, Pp. 236-241). Here the larger the value of partial Eta mean higher variation accounted for the term. The partial Eta value of gender is 0.574, which means the variation is enjoyment rate is accounted for the gender. Therefore, we can say that the there a significant effect of gender upon enjoyment of opera. Moreover, value of R square shows that gender is contributing about 57% variation in enjoyment rate of opera.

Parameter Estimates

Dependent Variable: Enjoyment

Parameter

B

Std. Error

t

Sig.

95% Confidence Interval

Partial Eta Squared

Lower Bound

Upper Bound

Intercept

3.417

.476

7.177

.000

2.429

4.404

.701

[Gender=.00]

3.667

.673

5.446

.000

2.270

5.063

.574

[Gender=1.00]

0a

.

.

.

.

.

.

a. This parameter is set to zero because it is redundant.

Similarly, parameter estimates helps us to develop a regression equation, which can predict the enjoyment rate of gender. We can develop equation as follows:

Enjoyment rate = 3.417 + 3.667*Female

However, above analysis shows that the gender has significant impact on the ...