Practical 3: Parametric analysis

Practical 3: Parametric analysis

An experiment was carried out at group of student who studied in UCSI university. The subjects chosen were 30 students of applied science college who completed 30 credit hours. The survey was conducted by hours of part-time of the subjects and the grades of subjects were had through one academic year. The subjects who got grade A and B will be categorized as high level, whereas those who got grade C and D will be categorized as low level.

In this experiment, we would like to investigate if the difference in Part-time hours between the subjects with high level and those with low level e is statistically significant. Our research question

is, will level of grade be affected by the part-time’s hours?. The dependent variable is work’s hours of the subjects, while the independent variable is level of grade. To conduct an independent samples t-test, there are two variables in the data set, which are continuous variable and categorical variable. Hours of the subjects is continuous variable, whereas level of grade is categorical variable.

TABLE 1.1 Part-time and level of grade of 30 males who finished 30 credit hours from UCSI University.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Part-time of subjects (hours) 23.00 23.00 20.50 20.50 20.50 18.00 18.00 18.00 18.00 15.50 15.50 15.50 13.00 13.00 12.00

Level of grade low level low level low level low level low level low level low level low level low level low level low level low level low level low level high level

16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Part-time of subjects (hours) 11.00 11.00 10.00 10.00 10.00 9.00 9.00 9.00 9.00 8.00 8.00 8.00 7.00 7.00 6.00

Level of grade high level high level high level high level high level high level high level high level high level high level high level high level high level high level high level

Figure 1.1 Variables on SPSS software.

The continuous variable which is part-time of subjects is described with unit of hour (hour). The measure of hours is scale as it is a continuous variable which can be measured. The measure of level of grade is nominal because it is a categorical variable, in which can have two categories. Before conducting independent samples t-test, we have checked that the data set is normally distributed and there is no outlier. The test of nomality show that the part-time of subjects for both high and low grade of subjects is normally distributed as below.

Results TABLE 2.1 Descriptive table Descriptivesa grade levels hours of parttime per week

high level

Mean 95% Confidence Interval for Mean

low level

Std. Statistic Error 9.0000 .40825 Lower Bound

8.1298

Upper Bound

9.8702

5% Trimmed Mean

9.0000

Median

9.0000

Variance

2.667

Std. Deviation

1.63299

Minimum

6.00

Maximum

12.00

Range

6.00

Interquartile Range

2.00

Skewness

.000

.564

Kurtosis

-.458

1.091

Mean

18.0000 .86919

95% Confidence Interval for Mean

Lower Bound

16.1222

Upper Bound

19.8778

5% Trimmed Mean

18.0000

Median

18.0000

Variance

10.577

Std. Deviation

3.25222

Minimum

13.00

Maximum

23.00

Range

10.00

Interquartile Range

5.00

Skewness

.000

.597

Kurtosis

-.850

1.154

a. There are no valid cases for hours of part-time weekly when grade levels = .000. Statistics cannot be computed for this level.

For low level: 0.0

Skewness = 0.564 =0 Kurtosis =

−0.458 1.091

= -0.420 The values of Skewness and Kurtosis are 0 and -0.420 respectively. Both values are within ±1.96 limits. Thus, the data set is normally distributed. For high level: 0.0

Skewness = 0.597 = 0 Kurtosis =

−0.850 1.154

= -0.737 The values of Skewness and Kurtosis are 0 and -0.737 respectively. Both values are within ±1.96 limits. Thus, the data set is normally distributed. Table 2.2 Kolmogorov-Smirnova and Shapiro-Wilk table Tests of Normalityb grade levels hours of part-time weekly

dimension

Kolmogorov-Smirnova Statistic df Sig. high level .125 16 .200* low level .143

14

.200*

Shapiro-Wilk Statistic df .972 16

Sig. .872

.932

.326

14

a. Lilliefors Significance Correction *. This is a lower bound of the true significance. b. There are no valid cases for hours of part-time weekly when grade levels = .000. Statistics cannot be computed for this level. For high grade level, the p-value of Kolmogorov-Smirnov and Shapiro-Wilk test are 0.200 and 0.872 respectively. Both p-value are more than 0.05, p > 0.05. Hence, the data set is normally distributed. Meanwhile, for low grade level, the p-value of Kolmogorov-Smirnov and Shapiro-Wilk test are 0.200 and 0.326 respectively. Both p-value are more than 0.05, p > 0.05. Hence, the data set is normally distribute

FIGURE 2.1 Histogram of frequency against hours of part time weekly for high level and low level grade

For both high and low grade level, the peak of the bell curve is at the middle of the histogram. Thus, this indicate the data set is normally distributed.

hours of part-time weekly Stem-and-Leaf Plot for Grade= high level Frequency Stem & Leaf 1.00 2.00 3.00 4.00 3.00 2.00 1.00

6. 0 7 . 00 8 . 000 9 . 0000 10 . 000 11 . 00 12 . 0

Stem width: 1.00 Each leaf: 1 case(s) Figure 2.2 Stem-and-leaf plots for high level and low level grade

FIGURE 2.3 Normal Q-Q plot for high level and low level grade

Most of the values fall on the line of expected values in the normal Q-Q plot of hours of parttime weekly for both grade levels, showing that the data is normally distributed.

FIGURE 2.4 Detrended normal Q-Q plot for high level and low level grade

For detrended normal Q-Q plot of hours of part-time weekly for both grade levels, there is no particular pattern and most observed values plotted fall off the line. Thus, the data set is normally distributed.

FIGURE 2.5 Box plots for high level and low level grade

As shown from the box plot above, there is no outlier outside the whiskers. The middle line of boxplot is approximately in the middle of the box and both whiskers also approximately the same length. Thus, the data set is normally distributed. All outputs show that the data set is normally distributed. Thus, the independent sample t-test is conducted.

TABLE 3.1 T-Test Group Statistics level of grade

hours of part-time weekly

dimension

Std.

Std.

N

Mean

Deviation

Mean

low level

16

9.0000

1.63299

.40825

high level

14

18.0000

3.25222

.86919

Error

According to table 3.1, the means for both grade level are very different. For both high level and low level, mean values are 9 and 18 respectively. Hypothesis testing is carried out in order to determine whether the difference between two samples is statistically significant.

TABLE 3.2 Independent Samples Test Independent Samples Test Levene’s Test for Equality of Variances t-test for Equality of Means 95% Confidence Interval of the

hours

Equal

of

variances

part-

assumed

time

Equal

Difference

Sig. (2- Mean

Std. Error

tailed)

Difference

Difference Lower

.000

-9.00000

.92142

-10.88744 -7.11256

-9.372 18.585 .000

-9.00000

.96029

-11.01296 -6.98704

F

Sig. t

df

5.026

.033 -9.768 28

weekly variances not assumed

Independent sample t-test 

Test of homogeneity of variances assumed

Null hypothesis: Equal variances assumed Alternative hypothesis: Equal variances not assumed Test statistics: f-value = .5.026 Significant level, α = 0.05 p-value = .033 (p