Good Essay On Applied Quantitative Methods And It Skills For Business

Question #1. What is wage inequality defined in literature? Given the complex data set, explain how you will proceed in order to provide evidence on wage inequality.
As part of the review of the economic theory according to the level of wages from the personal characteristics of the worker always had a pronounced applied nature, as the assessment of the productive characteristics of the worker is a necessary condition for determining the amount of his salary. In connection with this basic tenet that characterizes economic approach to explaining the differences in the level of wages of individual workers, was and is a statement about the inequality of personal qualities and characteristics of workers (both congenital and acquired) which cause differences in individual productivity. Thus, the main cause of inequality of earnings of individual workers from an economic point of view is the inequality of their productive capacity.
Finally, an important condition for the formation of wages of certain categories of workers is becoming common in particular environment (the country or corporation) sociocultural norms. As an example, there is a direct dependence of the size of earnings from the age of the worker at Japanese companies. In the same row is discrimination on the basis of remuneration (explicit or implicit) in many industrialized countries, persons belonging to certain socio-demographic categories, such as women or members of certain ethnic groups. At the same time, discrimination against women has deep historical roots, and as ethnic discrimination, it emerged relatively recently and was the result of a sharp increase in migration flows from developing countries to industrialize. The last example shows that the structure of the social factors that influence the formation of wages, there are constant changes that need to analyze and evaluate.
In this paper we are interested to investigate if there is a wage inequality by gender factor? We will use statistical procedures and methods to compare average wages of males and females to make a conclusion if there is a significant difference between them.
Question #2. Provide the Bureau with the evidence of wage inequality you have found and interpret your results.

We begin with summary descriptive statistics of the workers’ salary by gender:

Descriptive Statistics: WAGE
Variable SEX N N* Mean SE Mean StDev Variance Minimum Q1
WAGE 0 217 0 2,3607 0,0661 0,9744 0,9494 1,2000 1,6000
1 142 0 2,0746 0,0808 0,9625 0,9264 1,2000 1,5000

N for

Variable SEX Median Q3 Maximum Range IQR Mode Mode
WAGE 0 2,1160 2,8740 5,2580 4,0580 1,2740 2 11
1 1,8700 2,3460 8,9000 7,7000 0,8460 1,6 9
We can see that men’s wage is averagely higher than women’s. Let’s test the significance of this difference. To do this we use two-sample Student’s t-test for difference of means.

Null hypothesis: there is no significant difference between wages of men and women.

Alternative hypothesis: there is a significant difference between wages of men and women.
H0: μ1-μ2=0 vs HA: μ1-μ2≠0

Assuming σ1≠σ2

Set level of significance alpha as 0.05
Perform testing:
Two-Sample T-Test and CI: WAGE; SEX
Two-sample T for WAGE
SEX N Mean StDev SE Mean
0 217 2,361 0,974 0,066
1 142 2,075 0,963 0,081
Difference = mu (0) - mu (1)

Estimate for difference: 0,286

95% CI for difference: (0,081; 0,492)
T-Test of difference = 0 (vs not =): T-Value = 2,74 P-Value = 0,006 DF = 304
Since p-value of the test is lesser than level of significance alpha, we reject the null hypothesis. The alternative claim has been approved at 5% level of significance.
The next step of our research is to check if there is a significant difference in wages between those employees who are with Hukou and who are without it. To do this we divide the data on two groups (with Hukou and without Hukou) and do the same procedure like it was done for dividing by sex:
Descriptive Statistics: WAGE

Variable HUKOU N N* Mean SE Mean StDev Variance Minimum Q1

WAGE 0 87 0 2,141 0,100 0,936 0,876 1,200 1,400
1 272 0 2,2817 0,0601 0,9909 0,9819 1,2000 1,6000
N for

Variable HUKOU Median Q3 Maximum Range IQR Mode Mode

WAGE 0 1,900 2,500 5,258 4,058 1,100 1,2; 1,25; 1,5 5
1 2,0000 2,6490 8,9000 7,7000 1,0490 2 14

Now, visualizing these descriptives with graphs. This time we will use box plot:

The visualization via box plot shows that there is no significant difference in wages between the groups with and without Hukou. It seems, that the wage level doesn’t depend on Hukou. However, to prove our hypothesized conclusion, we have to perform testing operation.
Null hypothesis: there is no significant difference between wages of those who are with Hukou and those who are without Hukou.
Alternative hypothesis: there is a significant difference between wages of those who are with Hukou and those who are without Hukou.
H0: μ1-μ2=0 vs HA: μ1-μ2≠0
Assuming σ1≠σ2
Set level of significance alpha as 0.05
Perform testing:

Two-Sample T-Test and CI: WAGE; HUKOU

Two-sample T for WAGE

HUKOU N Mean StDev SE Mean

0 87 2,141 0,936 0,10
1 272 2,282 0,991 0,060
Difference = mu (0) - mu (1)

Estimate for difference: -0,141

95% CI for difference: (-0,372; 0,090)
T-Test of difference = 0 (vs not =): T-Value = -1,20 P-Value = 0,230 DF = 152
Since p-value of the test is 0.23 and it is higher than significance level alpha (0.05), we failed to reject the null hypothesis. There is no evidence to say that there is a significant difference between wages of those who are with Hukou and those who are without Hukou (at 5% level of significance).
The third step of our research is to investigate the influence of party membership on a wage level. Divide the data by party membership and display descriptive statistics:
Descriptive Statistics: WAGE

PARTY

Variable MEMBER N N* Mean SE Mean StDev Variance Minimum Q1
WAGE 0 274 0 2,2261 0,0614 1,0160 1,0324 1,2000 1,5000
1 85 0 2,3168 0,0919 0,8477 0,7185 1,2000 1,7830

PARTY N for

Variable MEMBER Median Q3 Maximum Range IQR Mode Mode
WAGE 0 1,9160 2,6050 8,9000 7,7000 1,1050 1,5 12
1 2,1500 2,6710 5,2000 4,0000 0,8880 2 7
Visualization with box plot is very comfortable to see the significant difference between means. We may use it again for our purposes:
It seems that there is no significant difference between the group. However, the first group has many outliers with very big wage level. Let’s check the difference with two-sample t-test:

Null hypothesis: there is no significant difference between wages of party members and not party members.

Alternative hypothesis: there is a significant difference between wages of party members and not party members.
H0: μ1-μ2=0 vs HA: μ1-μ2≠0
Assuming σ1≠σ2
Set level of significance alpha as 0.05
Perform testing:

Two-Sample T-Test and CI: WAGE; PARTY MEMBER

Two-sample T for WAGE

PARTY

MEMBER N Mean StDev SE Mean
0 274 2,23 1,02 0,061
1 85 2,317 0,848 0,092
Difference = mu (0) - mu (1)

Estimate for difference: -0,091

95% CI for difference: (-0,309; 0,128)
T-Test of difference = 0 (vs not =): T-Value = -0,82 P-Value = 0,413 DF = 165
Since p-value of the test is 0.413 and it is bigger than 0.05 (significance level), we failed to reject the null hypothesis. There is no evidence to say that here is a significant difference between wages of party members and not party members (at 5% level of significance).
The last step of the research is to divide the subsamples of manufacturing, construction and other sectors into male and female workers. We begin from the “other” sector group:
Descriptive Statistics: WAGE
Variable SEX N N* Mean SE Mean StDev Variance Minimum Q1

WAGE 0 148 0 2,3851 0,0846 1,0292 1,0593 1,2000 1,5435

1 120 0 2,0710 0,0905 0,9911 0,9823 1,2000 1,5000
N for
Variable SEX Median Q3 Maximum Range IQR Mode Mode

WAGE 0 2,1120 2,9270 5,2580 4,0580 1,3835 1,5 7

1 1,8220 2,3895 8,9000 7,7000 0,8895 1,6 8

Let’s check the difference with two-sample t-test:

Null hypothesis: there is no significant difference in “other” sectors between wages of males and females.
Alternative hypothesis: there is a significant difference in “other” sectors between wages of males and females.
H0: μ1-μ2=0 vs HA: μ1-μ2≠0
Assuming σ1≠σ2
Set level of significance alpha as 0.05
Perform testing:
Two-Sample T-Test and CI: WAGE; SEX
Two-sample T for WAGE
SEX N Mean StDev SE Mean
0 148 2,39 1,03 0,085
1 120 2,071 0,991 0,090
Difference = mu (0) - mu (1)

Estimate for difference: 0,314

95% CI for difference: (0,070; 0,558)
T-Test of difference = 0 (vs not =): T-Value = 2,54 P-Value = 0,012 DF = 258
Since p-value is lesser than alpha, we reject the null hypothesis. In other sectors, there is a significant difference in “other” sectors between wages of males and females (at 5% level of significance).

Now check manufacturing sector. Divide the data of manufacturing employees by SEX and store descriptive statistics:

Descriptive Statistics: WAGE

Variable SEX N N* Mean SE Mean StDev Variance Minimum Q1 Median

WAGE 0 51 0 2,390 0,130 0,928 0,861 1,200 1,700 2,200
1 21 0 2,083 0,180 0,826 0,683 1,200 1,430 2,100
N for

Variable SEX Q3 Maximum Range IQR Mode Mode

WAGE 0 3,000 4,996 3,796 1,300 2,2; 2,4; 3 3
1 2,303 4,566 3,366 0,873 2,124 2

Null hypothesis: there is no significant difference in manufacturing sector between wages of males and females.

Alternative hypothesis: there is a significant difference in manufacturing sector between wages of males and females.
H0: μ1-μ2=0 vs HA: μ1-μ2≠0
Assuming σ1≠σ2
Set level of significance alpha as 0.05
Perform testing:
Two-Sample T-Test and CI: WAGE; SEX
Two-sample T for WAGE

SEX N Mean StDev SE Mean

0 51 2,390 0,928 0,13
1 21 2,083 0,826 0,18
Difference = mu (0) - mu (1)

Estimate for difference: 0,307

95% CI for difference: (-0,142; 0,756)
T-Test of difference = 0 (vs not =): T-Value = 1,38 P-Value = 0,174 DF = 41
Since p-value of the test is higher than alpha level, we failed to reject the null hypothesis. There is no evidence to say that there is a significant difference in manufacturing sector between wages of males and females (at 5% level of significance).

Now consider construction sector.

Variable SEX N N* Mean SE Mean StDev Variance Minimum Q1 Median
WAGE 0 18 0 2,078 0,124 0,527 0,278 1,200 1,716 2,000
1 1 0 2,3340 * * * 2,3340 * 2,3340
N for

Variable SEX Q3 Maximum Range IQR Mode Mode

WAGE 0 2,458 3,000 1,800 0,743 2 3
1 * 2,3340 0,000000 * * 0
There is only one female in this sector. This is not enough to perform an analysis of mean difference if we have one of two samples with only 1 observation. That’s why we can’t do any statistical conclusions regarding wage inequality between males and females in construction sector. To go further, we have to find more data of females working in construction.
Question #3. Draw sensible conclusions based on your findings and provide suggestions to the Bureau.
According to our statistical investigation we have obtained that on average, women’s wage are lower than men’s. This is an evidence of discrimination on the work place by gender. The local government should pay attention to this issue and use some tools to take an influence on employers. The employers should not use gender as a motivation to make the salary lower or higher, this is not fair.

Works Cited

Finley, Moses I. (1973). The ancient economy. Berkeley: University of California Press. p. 65. ISBN 9780520024366.
Thompson, E. P. (1967). "Time, Work-Discipline, and Industrial Capitalism". Past and Present (38): 56–97. JSTOR 649749.