Distribution of Current Salaries - Assignment Example

Running Head: DATA ANALYSIS Data Analysis [Name of the Writer] [Name of the Institution] Executive Summary The act of transforming the data to get information that is useful and help in conclusion is known as data analysis. Data analysis may include application of statistical procedure that helps to give the appropriate results. This report is based on the analysis of the data gathered by the government of USA relating to the salaries. By using statistical software MINITAB, here is the analysis of the data and its graphical presentation as well. Table of Content Data Analysis 4 Methodology 4 Data Analysis Introduction In this paper we have two task to done, in Task 1 there is a data obtained by the U.S. government regarding the salaries of the employee, with respect to gender, education and ethnicity, here we have to analyse this data to know the impact of ethnicity, and gender on the salaries of the employee. In task 2, we have to gather the data regarding the salaries at the different positions in U.K. and U.S. and we have to analyse this data as well. Methodology The given data sets are analysed using a statistical package called Minitab (version 14), which is designed to ‘make data analysis easier’. Cross tabulation, descriptive statistics, are the tools provided in MINITAB that helps to make the data easy and understandable. Correlation and regression are the important features in Minitab that helps to identify the variables that give impact on the variables, along with it the graphs are the pictorial presentation of the data. Statistical Analysis In this paper we have two tasks, first we are doing analysis on the data that is related to the salaries of employee in the U.S., in our second task we will compare the salaries given in the U.S. and the U.K. for different job titles. Task 1 Table 1: Breakdown by Gender Gender Count Male 258 Female 216 Total 474 Plot 1 Here the table and Pie chart give us the breakdown of the data by gender and it helps to know that from the 474 selected participants there were 46% female employees and 54% were males. Table2: Breakdown by Job Category Job Category Frequency Clerical 363 Supervisory 27 Managerial 84 Total 474 Plot 2 Here the bar chart represent the breakdown of respondents by their job category, we find that most of the respondents were at the clerical position, then at the managerial position and there were afew participant who were supervisor from the selected participants. Table 3: Breakdown by gender and Job Category Job Category   Clerical Supervisory Managerial Total Male 157 27 74 258 Female 206 0 10 216 Total 363 27 84 474 Plot 3 Table 3 is the cross tabulation of gender and job categories, it help us to know that from 474 participants there were 258 male and 216 female participants. The Plot 2 shows that most of the participants have clerical job, there were no female from the participants who is on the post of supervisor and there were 74 male participants who had managerial position and only 10 females from the participants were on that position. Table 4: Distribution of Current Salaries Descriptive Statistics Variable N Mean Median StDev SE Mean Min Max Q1 Q3 Current Salaries 474 34420 28875 17076 784 15750 135000 24000 37163 Plot 4 The descriptive statistics show that the minimum current salary of an employee from the selected sample is $15750 and the maximum is $135000 in a year and the average salary of the selected sample is $34420. Histogram separates the data into intervals on the x-axis, and draws a bar for each interval whose height, by default, is the number of observations (or frequency) in the interval. Minitab places observations that fall on interval boundaries into the interval to the right (except those in the interval farthest to the right, which are placed in the left interval). Here the histogram shows that most of the respondents had salaries from $20000 to $40000 in a year. Plot 5: Distribution of Current Salary by Ethnicity Box plot is also called as box-and-whisker plot. The whiskers are the lines that extend from the top and bottom of the box to the adjacent values, the lowest and highest observations still inside the region defined by the lower limit Q1 - 1.5 (Q3 - Q1) and the upper limit Q3 + 1.5 (Q3 - Q1). Outliers are points outside the lower and upper limits, plotted with asterisks (*). Here is a simple box plot that shows the current salary obtained by the minority and majority groups. Plot shows that the participants who didn’t belong to minority group were getting more as compare to those who were from the minority group. Plot 6: Relationship of Current Salary to Starting Salary Here the box plots use to get the relation among the starting and current salaries of the respondents. The plots show that there is positive association among the current and the starting salaries of employee. Regression Analysis Regression investigates the dependence of one variable conventionally called the dependent variable on one or more variables called independent variable and provide an equation to be used for estimating or predicting the average value of the dependent variable from the known values of independent variable. The regression procedure fits the model: Y = a + (b x X) + e Where, Y is the predictor, X is the predictor, “a” is the value of Y when X equals zero and is called Y-intercept, and “b” indicates the changes in Y for a unit change in X and is called the slope of the line and “e” is an error term having a normal distribution with mean of zero and standard deviation σ (Fisher, 1922, 560). Here we are obtaining the regression equation by considering starting salary as an independent variable and current salary as a dependent variable. The regression equation is Starting salary ($) = 3053 + 0.406 Current Salary ($) S = 3741 R-Sq = 77.5% R-Sq(adj) = 77.4% Correlation association tell us about the association among the variables. By applying correlation analysis we find the Pearson correlation between Starting Salary and Current Salary = 0.88 Correlation value shows the strong positive association among the staring and current salaries. R-Square is the sstatistical measure of how well a regression line approximates real data points; R-square is a descriptive measure between zero and one, indicating how good one term is at predicting another. An R-squared of 1.0(100%) indicates a perfect fit. Here we have R-square value = 77.5% it shows that the fir is perfect. In order to know the impact of previous experience on the salary of the employee we apply the correlation on the variables, previous experience and current salaries and we get the Pearson correlation = -0.097, that is approximately equals to zero; it shows that there is no association among the previous experience and the current salary getting by the employee. Plot 7: Relationship of Current Salary and Starting Salary Here the regression plot shows that the current salaries and the starting salaries have positive relationship. In the graph we can see that most of the participants had salaries from $10,000 to $40,000. Task 2 In this paper our second task is to compare the salaries in U.K and U.S., for this purpose we gathered the data from the data source: Tower Perrin. Table Average Annual Salaries in U.K. and U.S. Job Category Salaries in U.S. (£) Salaries in U.K. (£) Director Human Resources 274773 190540 Accountant 42032 72018 Computer Programmer 41154 36439 Manufacturing Workers 28638 26325 Call Centre Workers 15115 15288 Off Shore Workers 35000 27005 Plot Here the line graph shows that in most of the position the salaries in United States are more as compare to in United Kingdom, we find that from the job position that we have in table there was only the position of Accountant who were getting more in U.K. as compare to U.S. Conclusion Task 1 The paper helps to know the salary difference among the minority and majority groups in U.S., we also analysed the association among the starting and current salaries of employee, effect of gender, it was noticed that from the participants there were a few respondents who were at the post of Manager from minority group and the current salaries of them were less than the majority group. Correlation analysis shows that starting salaries and current salaries are highly positive associated with each other but it was found that there is no association among the previous experience of the respondents and their current salaries. Task 2 In task 2 we analyse the difference among the salaries in U.K. and U.S. at the same positions. We find that at most of the positions salaries in U.S. are more than the salaries in United Kingdom. References R.A. Fisher. (1922). The goodness of fit regression formulae, and the distribution of regression coefficients, Journal Royal Statistics, 597-612. Read More