Accusation Against The Industry Of Discriminating

Discuss about the Report for Accusation Against the Industry of Discriminating.|

 

Introduction

A research study was carried out to analyze and determine whether a specific industry in Singapore was discriminating on its female workers with regards to their salary earnings. The sample data was prepared based on an investigation on random 50 employees; noting down their current monthly salaries (S$), highest level of education attained, age, and gender.  Here the monthly salary (in Singapore Dollar (SGD)) is the response or the dependent variable (Y) and the gender (0 female, 1 male), age, and the levels of education are the explanatory or the independent variables (Xs). This report is to present an analysis of the findings based on the research study of 50 employees and make meaningful conclusions and recommendations in a business context.

Analysis and Conclusions  

Descriptive Statistics: The below tables provide the descriptive statistics of the independent and the dependent variables involved in the case study:

Monthly Salary (in S$)
Mean	3546.52
Standard Error	330.2105
Median	2795
Mode	1900
Standard Deviation	2334.9406
Sample Variance	5451947.7241
Kurtosis	-0.0058
Skewness	1.0128
Coefficient of Variation	0.6584
Range	7992
Minimum	1040
Maximum	9032
Sum	177326
Count	50

Consider the variable ‘monthly salary’ of an employee. As observed from the descriptive statistics, the average salary of 50 sampled employees is S$3,546.52 with around 50% of them having a monthly salary of S$2,795. The above distribution is rightly skewed, i.e. not symmetric, and hence not normal. Given the standard deviation of S$2,334.9, it can be said that the absolute variability of the data values around their mean value is considerably high. The respective coefficient of variation value of 0.658 suggests the relative variability.

Descriptive Statistics of the independent variables: Age, Gender and level of education

Age (10 years)
Mean	3.924
Standard Error	0.1728
Median	3.8
Mode	3.8
Standard Deviation	1.2218
Sample Variance	1.4929
Kurtosis	-1.0698
Skewness	0.3802
Range	4
Minimum	2.2
Maximum	6.2
Sum	196.2
Count	50

 

Level of Education	Count
Below Secondary	10
Secondary	5
Post-Secondary	7
Diploma & professional	13
University	15

 

Gender	Count
Females	20
Males	30

The variable ‘monthly salary’ is a quantitative and numerical (discrete) in nature whereas measured on a ratio scale while the variable ‘levels of education’ is a qualitative and categorical variable, measured on an ordinal scale.

Below is the contingency table with respect to the count and percentage of female and male employees having a salary above or below S$3,000.

Contingency Table
	Females	Males	Total
Salary > $3000	4	18	22
Salary < $3000	16	12	28
Total	20	30	50
Contingency Table
	Females	Males	Total % share
Salary > $3000	20%	60%	44%
Salary < $3000	80%	40%	56%
Total % share	40%	60%	100%

From the above table, it is computed that there is a likelihood of 20% that a female worker gets a monthly salary more than S$3,000, in comparison to 60% of male workers who get a salary of more than S$3,000. Hence, it can be said that the distribution of salaries is statistically significant to gender.

The below table represents the average salaries of male and female workers along with their respective standard deviations:

	Monthly Salary (in S$)
	Male	Female
Mean	4279.3	2447.35
Standard Deviation	2421.467	1729.487

Based on the above formulated data, a 90% confidence interval (i.e. using z* multiplier of 1.645) was derived for monthly salary of a male worker as S$(295.987, 8262.613). The spread of the confidence interval is large due to a high standard deviation in monthly salaries of male.

To test the claim that the mean monthly salary of workers in the industry seems to be greater than S$3200, a right-tailed t-test is being carried out at significance level of . The hypotheses are stated as:

Null Hypothesis                      :

Alternative Hypothesis           :

Here, is the hypothesized mean value of the variable “monthly salary’

To test the claim, t-test statistic is used, .

Degree of freedom = n – 1 = 49. Therefore, right-tailed p-value = 0.1497

Since, p-value =0.1497 > 0.05=or , we fail to reject the null hypothesis in favour of alternative hypothesis. Hence, it can be said that there is no statistical evidence to support the claim that the mean monthly salary of workers in the industry seems to be greater than S$3200.

Below is the summary output of simple linear regression for the response variable and the other 3 explanatory variables:

The coefficient estimate for the slope of the variable Gender is 1301.36 and has a p-value of 0.033. Since this p-value is less than the significance level of 5%, i.e. 0.05, it can be said that the result is statistically significant.

Further developing the Hypotheses as:

and

Test Statistic:

Here,

For significance level of , two tailed critical value:

We reject the null hypothesis if

Outcome: Since , we reject

Therefore, we conclude that at a significance level of 5%, there is a statistically significant relationship between the hourly earnings a person makes and the hours of training took.

Following graph shows the distribution and the estimated linear equations of monthly salaries of males and females separately.

The estimated regression equations of monthly salaries of both males and females are computed as  and   respectively. To estimate how much do male workers earn more than female workers, the difference of these two equations is calculated, i.e.

The coefficient estimates for the slope of the variables ‘age’ and ‘level of education’ is 263.36 and 635.06. The signs of the coefficients are positive implying that a greator age (10 years) and a higher educational qualification will result in a greator monthly salary of an employee, which is similar to what was expected.

For the regression model, the adjusted R-square value is equal to 0.2834 implying that 28.34% of the variation in the dependent variable can be explained by the regression model. It is a better measure than R-squared value because an adjusted R-square value, unlike an R-squared value compares the descriptive power of regression models that include diverse numbers of predictors and includes the variation explained by only those explanatory or independent variables (not all!) that in reality affects the dependent variable.

For the obtained regression model, the respective residual and normal probability plots suggest that the data satisfy the assumptions of a linear regression, Linearity, Normality of Errors, and Homoscedasticity of Errors.

Based on the regression model develop above, the predicted monthly salary of a 39-year-old university educated female worker:

The adjusted R-squared value shows that only 28.34% of the variation in monthly salaries of the workers is predicted by aforesaid independent variables, namely, gender, age and level of education, which suggests that it is likely the other factors like the working hours, duration of job, night shifts, number of leaves, etc. may have influenced the monthly salaries of workers.