City of Seattle Wages Comparison

Wages for male and females are mostly believed to differ in various places of unemployment. The purpose of this paper is to compare wages by gender in the city of Seattle. The data used to make the comparison was obtained from https://www.data.gov/ . In order to determine if there is a significant difference between male and female wages in the region, an appropriate statistical test is conducted. In this case, the appropriate statistical test is the independent sample t-test since the samples of the data are the male and female groups which are not dependent on one another. 

From the problem definition, the research question is: 

Is there a significant difference between the wages of male and female employees? 

Assumptions of the Test 

The level of measurement for the collected data is the ratio scale 

The data is normally distributed 

The data should be from a simple random sample 

The data should be from a relatively large sample 

Descriptive Statistics of the Data 

Descriptive statistics provide a summary and overview of the data through statistical measures. Table 1 shows the descriptive statistics of the wages of male and female employees in Seattle city. 

Table 1 

Descriptive Statistics of hourly wages 

Female Avg Hrly Rate		Male Avg Hrly Rate
Mean	37.1526097	Mean	37.2355
Standard Error	0.526179288	Standard Error		0.536464
Median	36.3	Median		36.3
Mode	36.3	Mode		36.3
Standard Deviation	10.94908173	Standard Deviation		11.16309
Sample Variance	119.8823906	Sample Variance		124.6145
Kurtosis	1.169275198	Kurtosis		1.593303
Skewness	0.554986528	Skewness		0.648105
Range	81.23	Range		82.67
Minimum	5.11	Minimum		5.11
Maximum	86.34	Maximum		87.78
Sum	16087.08	Sum		16122.97
Count	433	Count		433

The descriptive statistics show that the typical hourly wage of female employees is 37.15 and that of male employees is 37.24. From these measures, it can be seen that the average hourly wages of female and male employees are slightly different from one another. Also, the median and the mode values are equal for both the male and female and male employees; mode=median=36.3. Notably, 36.3 is also slightly different from the mean value of the average hourly wage. Since the mean, median, and mode are approximately equal, the wage data for male and female employees are approximately normally distributed. Therefore, the data meet the normality assumption of the independent sample t-test. 

Moreover, the standard deviations for male and female wages are 11.15 and 10.94, respectively. Therefore, both groups seem to have approximately equal variation in hourly wages. With the approximately equal standard deviations, the male and female hourly wages would possibly exhibit insignificant difference. 

Visual Representation 

Visualization of data help in comparing groups of participants in a study. In this case, the male and female wages can be compared using graphs such as the bar graphs and histograms. Figure 1 shows the histogram for the male hourly wages. 

Figure 1. Histogram of male hourly wages 

Figure 1 shows that the histogram of male hourly wages is approximately a bell-shaped graph. Therefore, the wages of the male follow a normal distribution. Hence the normality assumption of the data is met, and an independent sample t-test can be performed on the data against another normally distribution data. Figure 2 shows the histogram for the female hourly wages. 

Figure 2. Histogram of female hourly wages 

Figure 2 also shows that the histogram of female hourly wages is approximately a bell-shaped graph. Therefore, the wages of female follow a normal distribution. Hence the normality assumption of the data is met, and an independent sample t-test can be performed on the data against another normally distribution data. 

The boxplots for the groups of participants’ wages can also be used to assess the normality of the data on top of being the visualization of the five-number summary of the data. Figure 3 shows the boxplot for the male hourly wages. 

Figure 3. Boxplot of male hourly wages 

Figure 3 shows that the median hourly wage of males is exactly in the middle between the first and the third quartile; this shows that the data is normally distributed since there is an almost equal number of values below and above the median value. Again, this boxplot shows that the normality assumption of the male hourly wages is met. 

Figure 4 shows the boxplot for the female hourly wages. 

Figure 4. Boxplot of female hourly wages 

Figure 4 shows that the median hourly wage of females is exactly in the middle between the first and the third quartile; this shows that the data is normally distributed since there is an almost equal number of values below and above the median value. Again, this boxplot shows that the normality assumption of the female hourly wages is met. 

Assessing the Assumptions of Independent Sample T-Test 

Some of the assumptions of the t-test have been assessed from the descriptive statistics and visualization of the data. Notably, the descriptive statistics have shown that the mean, mode, and the median of the hourly wages for both male and females are approximately equal, implying a normal distribution of data. The histograms and boxplots have also shown that the wages follow a normal distribution. 

The assumption that the level of measurements of data is ratio is seen from the fact that the values of wages contain the absolute zero. In other words, quantitative analyses can be performed on this data. Besides, the assumption that the data should be obtained from a simple random sample is met since this data was obtained from the city of Seattle, a randomly selected region, and the randomly selected male and female employees from various job classifications. 

Independent Sample T-Test 

Since all the assumptions are met, the independent sample t-test is conducted to compare the means of wages by gender. The hypothesis statement for this test is as follows: 

H 0 : There is no significant difference between the wages of male and female employees 

H 1 : There is a significant difference between the wages of male and female employees 

Table 2 shows the excel output for the independent sample t-test, assuming unequal variance of the wages between the groups. 

Table 2 

t-Test: Two-Sample Assuming Unequal Variances
	Female Avg Hrly Rate	Male Avg Hrly Rate
Mean	37.1526097	37.23549654
Variance	119.8823906	124.6144702
Observations	433	433
Hypothesized Mean Difference	0
df	864
t Stat	-0.110304408
P(T<=t) one-tail	0.456096789
t Critical one-tail	1.646619153
P(T<=t) two-tail	0.912193578
t Critical two-tail	1.962713454

The table shows that the average hourly wage for female employees is slightly less than that of male employees. However, the p-value of the two-tailed tests is 0.9122>0.05, implying that the null hypothesis is not rejected. Therefore, there is no significant evidence to show that there is a significant difference between the wages of male and female employees. 

Conclusion 

In conclusion, the analysis has shown that the wages between male and female employees do not significantly differ. Through the use of the descriptive statistics, data visualization, and the independent samples t-test, it could be seen that the difference between the wages of the two groups is not significant. Therefore, it can be said that employees of all gender get equal chances of jobs, which provide them will wage at the same levels in all cities in America. 

References 

City of Seattle Wages: Comparison by Gender - All Job Classifications. (2019, May 21). Retrieved from https://catalog.data.gov/dataset/city-of-seattle-wages-comparison-by-gender-all-job-classifications-e471a 

Naghettini, M. (2016). Statistical Hypothesis Testing. Fundamentals of Statistical Hydrology , 251-309. doi:10.1007/978-3-319-43561-9_7 

Two-Sample t-Test: Independent Samples Design. (2016). Statistical Methods , 129-138. doi:10.4324/9781315265803-10