text: # Salary one-quarter of the oldest employees were
  
  Salary Analysis
  
  Our goal is to analyze
  salaries in a company based on a survey had happened among its employees. 378
  employees took part in our survey. In the survey asked employees about the
  following things:
  
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  ·
  Age (in years)
  
  ·
  Gender
  
  ·
  Job seniority (in years)
  
  ·
  Department (office,
  production, sales)
  
  ·
  Salary
  
  We want to get some
  information about distribution above variables and check which variables have
  the greatest impact on salaries.
  
  Gender
  
  Let’s see gender
  frequency distribution looks like in this company:
  
  Man
  
  240
  
  Woman
  
  138
  
  More than half of the
  company’s employees are men – our company is involved in the production of a
  certain product, so employs many employees which working physically – hence a
  large number of men in company.
  
  Department
  
  As it was mentioned at
  the beginning, our company have three departments – office, production and
  sales. Let’s see how many people work in each of them.
  
  Office
  
  24
  
  Production
  
  274
  
  Sales
  
  80
  
  As we expected – the
  vast majority of employees are production employees – around 70 percent of all
  employees.
  
  Age
  
  The next variable that
  was asked in the survey was the employee’s age. Let’s count the basic
  statistics for this variable:
  
  Statistic
  
  Value
  
  Number
  
  378
  
  Central tendency
  
  Mean
  
  40,1
  
  Median
  
  40
  
  Mode
  
  31
  
  Measures of position
  
  Minimum
  
  23
  
  Maximum
  
  62
  
  First quartile
  
  33
  
  Third quartile
  
  47
  
  Measures of variability
  
  Range
  
  39
  
  Inter-quartile Range
  
  7
  
  Variance
  
  77,97
  
  Standard Deviation
  
  8,83
  
  Coefficient of variation
  
  0,22
  
  Quartile coefficient of dispersion
  
  0,18
  
  Skewness
  
  0,27
  
  Kurtosis
  
  -0,65
  
  The average age of the
  employee was 40.1 years. Half of the employees were 40 years old or less and
  the largest number of employees participating in the study was 31 years old.
  The youngest was 23 years old, the oldest – 63 years old. One-fourth of the youngest
  employees were aged 33 and under, one-quarter of the oldest employees were aged
  40 and over.
  Observed  values of the variable vary
  around 8, 83 years of the average value, about 22%.
  Skewness it is close to zero, so the age distribution can be considered as
  symmetrical.
  Negative kurtosis speaks of a larger dispersion of results compared to the
  standard normal distribution.
  
  Let’s look how it looks
  box-plot of age:
  
  As it was mentioned
  earlier, the distribution of age can be considered symmetrical in relation to
  the average.
  Let’s look how it looks histogram of age:
  
  Histogram shows a slight
  right-sided asymmetry in the age distribution.
  
  Job seniority
  
  Let us now analyze the
  employees’ seniority:
  
  Statistic
  
  Value
  
  Number
  
  378
  
  Central tendency
  
  Mean
  
  11,2
  
  Median
  
  11
  
  Mode
  
  9
  
  Measures of position
  
  Minimum
  
  0
  
  Maximum
  
  36
  
  First
  quartile
  
  6
  
  Third
  quartile
  
  15
  
  Measures of variability
  
  Range
  
  36
  
  Inter-quartile
  Range
  
  5
  
  Variance
  
  50,52
  
  Standard
  Deviation
  
  7,11
  
  Coefficient
  of variation
  
  0,63
  
  Quartile
  coefficient of dispersion
  
  0,43
  
  Skewness
  
  0,73
  
  Kurtosis
  
  0,48
  
  The average job
  seniority of the employee was 11.2 years. Half of the employees work in the
  company for 11 years and more, while the most employees work with them have
  been working in the company for 9 years. Minimum of job seniority is 0, the
  longest working employee has been working in the company for 36 years. Quarter
  of employees work in the company for 6 years and shorter, quarter of employees
  work in the company for 15 years and longer.
  Observed  values of the variable vary
  around 7,11 years of the average value, about 63%, therefore, the variability
  of seniority is high.
  The skewness is positive so the distribution of seniority is positive skew- the
  mass of the distribution is concentrated on the left of the figure.
  Positive kurtosis says that the distribution is leptokurtic – the distribution
  is more concentrated than the standard normal distribution.
  
  Box-plot:
  
  Histogram:
  
  As we can see – the
  internship distribution at the company is right-angled, so the majority of
  employees are inexperienced.
  
  Salary
  
  Let us now analyze the
  employees’ salaries:
  
  Statistic
  
  Value
  
  Number
  
  378
  
  Central tendency
  
  Mean
  
  3634,1
  
  Median
  
  3300
  
  Mode
  
  3400
  
  Measures of position
  
  Minimum
  
  1700
  
  Maximum
  
  19500
  
  First
  quartile
  
  2700
  
  Third
  quartile
  
  3950
  
  Measures of variability
  
  Range
  
  17800
  
  Inter-quartile
  Range
  
  625
  
  Variance
  
  3146299,10
  
  Standard
  Deviation
  
  1773,78
  
  Coefficient
  of variation
  
  0,49
  
  Quartile
  coefficient of dispersion
  
  0,19
  
  Skewness
  
  4,07
  
  Kurtosis
  
  25,60
  
  The average salary in
  this company was 3634,1 PLN. Half of employees earn 3300 and less, the most
  people earn 3400. The person who earning the least earns 1700, the most –
  19500. Quarter of employees earn 2700 or less, one fourth of the earners earn
  the most earn 3950 and more.
  Observed  values of the variable vary
  around 1773,78 PLN of the average value, about 49%, therefore, so salaries are
  moderately varied.
  
  The skewness is strong
  positive so the distribution of seniority is positive skew- employees with
  below-average earnings prevail.
  
  Strong positive kurtosis
  says that the distribution is leptokurtic – the distribution is significantly
  more concentrated than the standard normal distribution.
  
  Box-plot:
  
  Histogram:
  
  On the charts you can
  see what we wrote above – strong right-sided asymmetry of the distribution.
  
  Correlation and regression
  
  The only quantitative
  variables in the study were age, seniority and salaries. We want to check
  whether we are able to estimate salaries with the help of age or seniority. For
  this purpose, let’s count the Pearson correlation coefficient between salaries
  and age and seniority:
  
  Pearson correlation coefficient with
  Earnings
  
  Age
  
  Job seniority
  
  0,405
  
  0,413
  
  We see that both age and
  internship can explain the variability of earnings equally. So let’s build a
  linear regression model where the dependent variable will be salaries (Y) and
  an independent seniority (X).
  
  As we can see the relationship
  between salaries and seniority, we can describe the formula:
  
  So, if seniority increases by one year,
  the salary will increase by 103,19 PLN.
  New person at work will get averagely 2473,3 PLN.
  And for example – a person with 10 years of work experience should earn an
  average 3505,2 PLN.
  
  Seniority can explain the variability of
  salaries in 17% – this is a weak dependency.
  
  Estimation
  
  We will try to perform
  point and interval estimation for the salaries of employees.
  
  Average
  
  ·
  Point estimation
  
  ? = 3634,1 ± 91,2
  
  ·
  Interval estimation –
  level of confidence = 0,95
  
  P(3455,3
  < µ < 3812,9) = 0.95   Therefore, at 95% the average salaries in this company are in the range from 4716,6 to 5074,3.   Standard deviation   ·      Point estimation ? = 1773,78 ·      Interval estimation - level of confidence = 0,95 P(1655,71< ? < 1910,13) = 0.95   Therefore, at 95% standard deviation of salaries in this company are in the range from 1655,71 to 1910,13. Hypothesis Let's check whether women and men earn the same amount in this company: ?1  - woman salaries ?2  -man salaries     Woman Salaries Man Salaries Mean 3712,68 3588,96 Standard deviation 1832,00 1741,70 number of observations 138 240 Z 0,644 p-value 0,520   Therefore, at the significance level of 0.05, we can say that there is no reason to argue that men and women earn different amounts.
  
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