Analysis of Employee Survey Data - Assignment Example

Memorandum Date: To: Charlie McArthy, Head of Human Resources From: Candice Bergen, Manager of Research and Analysis Subject: RE: Analysis of employee survey data Dear Charlie, In response to the request you made for a statistical analysis on a sample of 48 employees who were surveyed, here is the memo response. For the first question, we select the inter-quartile range and the median. This is because the inter-quartile range is more useful in measuring dispersion compared with the standard deviation if there is skewness in the distribution. As well, the median is more useful in measuring central tendency in comparison to the mean. The data relating to the 48 employees’ salaries for weekly normal time indicates that the employees earn an average of approximately $742.50. Nonetheless, most of the employees earn $500 weekly. Therefore, there is a huge difference, suggesting that the shape is slightly positively skewed. In addition, there are no outliers. Gender-based tables and box plots show that men’s average earnings ($810.00) are higher than women’s average earnings ($680.00) weekly. The middle of 50 percent of male employees’ salaries ranges from $525.00 to $986.25 while that of females ranges from $512.50 to $1,293.75. Therefore, the variance in females’ salaries is higher than that for males. Shapes of weekly normal time salaries earned by both women and men are positively skewed at 0.537 and 0.693 for women and men respectively. However, the skewness for females is weaker. As well, there are no outliers in the set of data. Moreover, gender seems to have an impact on the level of salary that is earned, hence the variables are related in such a way that salary is dependent on gender. Based on the box plots and tables that show weekly ordinary normal salary relating to one’s position, on average, managers earn much higher salaries than non-managers, at $810.00 and $535.00 per week respectively. But there was more in variation salaries earned by non-managers and those earned by managers. The middle 50 percent of workers in management positions ranges from $675.00 to $1212.25 compared with $492.50 to $1,227.50 for the same category relating to non-managers. The there is positive skewness in weekly normal time salary received by managers and non-managers at 0.672 and 0.727 respectively. As well, there is strong positive skewness in the distribution of salaries relating to non-managers. No outliers are seen since the data ranges between the lower and upper category. There seems to be an effect of position on the salary earned, hence the relationship between the variables is that salary is dependent on position. Graphs relating to job security show that the median of secure level is the highest at about $867.50. This is followed by the median of very secure level, at $860.00. Both values are greater than insecure level which is at $680.00. The middle 50 percent individuals who feel insecure begins at $459.50 and ends at $1485.00. The middle 50 percent of individuals who feel very secure ranges from 457.50 to 1,303.50. The middle 50 percent of individuals who feel secure ranges from $532.50 to $1,200.50. Salaries earned by individuals who feel insecure had the highest dispersion. As well, the dispersion for very secure employees is higher compared to that of secure employees. Additionally, there is a strong positive skewness for people with low security level (0.950) compared with those who feel secure or very secure (0.467 & 0.380 respectively). No outliers are seen in this dataset. There seems to be an effect of security level on the salary earned, hence the variables are related in such a way that weekly normal time salary is dependent on level of security of the job. The following memo response relates to the second question. For the second question, we select inter-quartile range and median. This due to the point that the inter-quartile range is more appropriate in measuring dispersion compared with the standard deviation if there is skewness in the distribution. Additionally, the median is more appropriate in measuring central tendency in comparison to the mean. A bar graph is selected to represent the data instead of a histogram since the job satisfaction variable (Jobsat) is categorical. Data relating to job satisfaction for the 48 employees indicates that the median employees’ feeling level based on a scale ranging from 0 to 20 is 14.00. Therefore, there is some gap, suggesting that the shape is slightly negatively skewed. Additionally, no outliers are present. Graphs relating to job satisfaction based on gender show that females (13.00) are likely to be more unsatisfied than men (15.00). The middle 50 percent of male employees ranges from 12.75 to 17.00 compared with 11.00–1 4.00 for the middle 50 percent of female workers. The level of men’s job satisfaction is more variable compared to that of women. That for men is strongly skewed in the negative, at -0.833, while that of women is slightly positively skewed, at 0. 122. No outliers are present in the dataset. As well, there seems to no effect of gender on the level of job satisfaction. Therefore, the variables are related as follows: job satisfaction is dependent on gender. Box plots and tables relating to position suggest that on average, the feeling of both managers and non-managers is the same, at 14.00. Nevertheless, the level of job satisfaction of non-managers varies more compared to that of managers. The middle 50 percent of managers ranges from 12.00 to 15.75 whereas that of non-managers is in the range of 11.25 to 15.75. Shapes of data relating to job satisfaction for both managers and non-managers are slightly negatively skewed, at -0.247 and -0.361 respectively. No outliers are present in the dataset. Position appears to affect job satisfaction; hence, the variables are related in such a way that job satisfaction is dependent on position. Data pertaining to tables and box plots of three levels of levels of job security are as follows. The median for employees who feel that they are very secure leads, at 15.00. Employees who feel very secure also have higher median than that for those who feel insecure, at 14.50 and 12.00 respectively. The middle 50 percent of people whose feel insecure is in the range of 11.00 to 13.00. The middle 50 percent of people who feel secure ranges from 13.00 to 16.75. The middle 50 percent of people who feel very secure ranges from 13.75 to 17. The level of job satisfaction for people who feel secure is associated with the highest dispersion. As well, the level for ‘very secure’ employees varies more than that for ‘secure’ employees. Moreover, the shapes relating to data for people who feel secure and very secure are both negatively skewed. But the shape relating to data for people who are secure is very strongly skewed in the negative, at -0.886, while the shape relating to individuals who are every secure is slightly negatively skewed, at -0.184. In contrast, the shape of data relating to employees who feel insecure is strongly positively skewed, at 0.714. No outliers are present in the dataset. There seems to be an effect of the level of job security on job satisfaction; hence, the variables are related in such a way that job satisfaction is dependent on the level of job security. The following response is for the third question. Scatter diagrams suggest that there is no correlation between the different numerical variables: productivity performance and number of years employed; weekly ordinary time salary and years of education; productivity performance and weekly ordinary time salary; days absent and age of respondents; and unpaid overtime and age of respondents. A non-linear correlation is seen between productivity performance and days absent. For weekly ordinary time salary and years of education, there is a strong positive linear correlation. There is also a 74.9% variation in regard to weekly normal time salary, which is illustrated by the difference in number of years of employment at Conrobar. The rest of the variation (25.1%) is explained by factors that were not included in the present study. There is also a very strong positive linear correlation between weekly normal time salary and the respondents’ age. A variation in ordinary time salary not including paid overtime in the range of 86.2% is explained by the difference in terms of the age of respondents. The rest of the variation (13.8%) is explained by factors outside the present study. The next section is a response to the fourth question. We begin by explaining the difference between median and mean EducYrs of females and males. Both have means that are bigger than the median. As well, we proceed by explaining the differences in median and mean EducYrs between men and women. The mean EducYrs of men is lower than that of women – that is 13.00 and 14.55 respectively. In addition, the median EducYrs of mean is less than that of women, at 12.00 and 14.00 respectively. The next point is to provide a summary of statistics that would answer the question as to whether women in the sample reported higher absenteeism than men. Both datasets are skewed, so we look at the median in a specialised way. Since the table shows that males have a higher median (3.500) compared to women (1.250), it can be noted that men reported higher absenteeism than women. For the sixth question, the interpretation is as follows. There is 95 percent confidence level, meaning that the mean productivity of the company’s employees is in the range of 97.583 to 100.138. For female employees, the 95 percent confidence level means that all of the company’s female employees are in the range of 95.499 to 99.579. The average productivity of men is much higher than that of women at a 95 percent confidence level, which ranges from 98.376 to 101.585. Thus, it is concluded that men are doing better than women on average. The minimum size of the sample that is necessary, which would be needed to approximate the mean productivity of the population with 10 as the margin of error with 95 percent confidence is one. Next, the answer for the seventh question is provided. The 95 percent confidence interval for the average age of the company’s employees is as follows: all employees, on average, could not be achieving 40 percent. All men could be able to achieve 40.00 percent on average. But women could not he able to attain this level of 40.00 percent on average. At 95 percent confidence, it is concluded that men are older than women. We are also 95 percent confident that the mean age of all employees is in the range of 33.14 to 39.78 years old. The age of men ranges from 34.29 to 42.55 years while that of women ranges from 29.10 to 39.90. Finally, we turn to the eighth question that regards Hypothesis Test. Based on the One-Sample Test Table, the p-value, which is indicated as sig. two tailed in this question, is zero. Assuming that α = 5%, since p-value < α, the null hypothesis is rejected in favour of the alternative hypothesis. To sum up, the available evidence denotes that mean H for all Conrobar employees is not 45 years of age. Read More