An Introduction to Mathematical Statistics Employee Commitment and Tu

Question: Describe about the Examining the relationship between Job Satisfaction, Employee Commitment and Turnover? Answer: Introduction: Data analysis for any industry or business is very important. For any industry or business, an employee plays an important role for the development of the company or industry. Job satisfaction of employee is very important for the healthy growth of the company. Employee commitment is very important factor in any industry to achieve the goals in terms of turnover of the company. For the progress of any company or business, the job satisfaction of employee, commitment of employee is very important part. Here, we want to check the relationship between the job satisfaction of the employee, commitment of the employee and turnover of the company. We have to analyse how the progress of company depends on job satisfaction of the employee, commitment of the employee. We have to check whether the turnover of the company is directly related to these factors or not. For this purpose, the ordinary data is collected from the employee by using the questionnaire. The data collected from employee is used for the further data analysis. This type of data analysis is very important in the scenario of the management team for taking proper action within the company or business. Let us see all this statistical data analysis in detail given as below: Data: Data collection is the first step in any data analysis for any business or company. In this topic, we have to see how the data is collected from the employee of the company. For the study of relationship between the turnover of the company and job satisfaction and commitment of the employee, we select a particular company. From this company, we select 200 employees for the purpose of data collection. The questionnaire given to all these employee and data collected through these questionnaires. Then data collected in a tabular format according to different variables. The information is collected for the different variables such as job satisfaction of the employee, commitment of the employee and the turnover of the employee. The turnover of the company is given in the $ and the information about the job satisfaction and employee commitment is given in the scale system in particular ordinary scale. The codes for these ordinary scales are summarised in the following table: Code Description 0 Very Low 1 Low 2 Moderate 3 Good 4 Better 5 Best Some more information about the data regarding the relationship between the employee commitment, job satisfaction of employee and total turnover of the company is given in the appendix section at the last part of this study. Now, let us see the data analysis for the collected data in detail given in the next topic. Data Analysis: Data analysis is very essential part for the collected data for analysing the facts related to the different variables under study. For this study, we have to study the relationship between the three variables such as the employee commitment, job satisfaction of the employee and turnover of the company. First of all, we have to see the information about the frequency distribution for the variables given in the data set. The frequency distribution for the job satisfaction of the employee is summarised in the following table: Statistics Job_Satisfaction N Valid 200 Missing 0 Job_Satisfaction Frequency Percent Valid Percent Cumulative Percent Valid Very low 28 14.0 14.0 14.0 Low 43 21.5 21.5 35.5 Moderate 26 13.0 13.0 48.5 Good 38 19.0 19.0 67.5 Better 29 14.5 14.5 82.0 Best 36 18.0 18.0 100.0 Total 200 100.0 100.0 The job satisfactions of the employee are arranged from the very low job satisfaction to best satisfaction in the above table. Total of 200 employees filled up the questionnaire and this data from questionnaire is used for the data analysis. For the variable job satisfaction, most of the employee respond as the low job satisfaction as an answer to asked question about job satisfaction. About 43 employees noted low job satisfaction and about 36 employees are noted best job satisfaction in the given questionnaire. 36 employees said that they had best job satisfaction with their job in the company. The diagrammatic representation for this frequency distribution is represented by using the bar diagram which is given as below: The above bar diagram shows the comparison between the different levels of the job satisfaction. The bar for the low job satisfaction is very high and the bar for good job satisfaction is on the second place. The respond as the moderate job satisfaction is noted by minimum respondents or employee of the company. Now, we have to see the frequency distribution for the variable employee commitment. The frequency distribution for this variable is summarised in the following table. The same codes are used for this frequency distribution as used in the above frequency distribution. Statistics Commitment N Valid 200 Missing 0 Commitment Frequency Percent Valid Percent Cumulative Percent Valid Very Low 38 19.0 19.0 19.0 Low 28 14.0 14.0 33.0 Moderate 33 16.5 16.5 49.5 Good 30 15.0 15.0 64.5 Better 34 17.0 17.0 81.5 Best 37 18.5 18.5 100.0 Total 200 100.0 100.0 From the above frequency distribution, it was observed that 38 employees noted the response the very low commitment at their work within the company. About 37 employees are responded as the best commitment during their work within the company. The detail frequency distribution for the different ordinary scale is represent in the above table. The diagrammatic representation of this frequency distribution is given by using the bar diagram which is given as below: The above bar diagram for the variable commitment of the employee is given as above and it gives the comparison between different ordinary levels for the variable commitment. The bar for the very low commitment is very high as compared to other commitment levels. Now, we have to see some other statistical analysis for given variables in the data set. We have to see the descriptive statistics for the third variable as turnover of the company. The study of descriptive statistics consist of the mean, mode, median, minimum, maximum etc. The descriptive statistics for the variable turnover of the company is summarised in the following tables. Descriptive Statistics N Minimum Sum Mean Std. Deviation Variance Turnover 200 1022.00 1110557.00 5552.7850 2636.30951 6950127.808 Valid N (listwise) 200 Some more descriptive statistics for the variable turnover of the company is given in the following table: Descriptive Statistics N Range Maximum Mean Skewness Kurtosis Statistic Statistic Statistic Std. Error Statistic Std. Error Statistic Std. Error Turnover 200 8860.00 9882.00 186.41523 -.115 .172 -1.241 .342 Valid N (listwise) 200 Now, we have to see the diagrammatic representation for the variable turnover of the company by using the box plot. We have to see the spread of the distribution of the variable turnover of the company by using the box plot which is given as below: Case Processing Summary Cases Valid Missing Total N Percent N Percent N Percent Turnover 200 100.0% 0 0.0% 200 100.0% The above box plot explains the distribution of the turnover of the company. Now, we have to see some other diagrammatic representation for the variable turnover of the company by using the histogram for the variable turnover of the company. Let us see this histogram in detail given as below: The above histogram does not show any pattern or bell shaped curve. This means that the above histogram or the data for the turnover for the company does not follow the approximate normal distribution. The study of inferential statistics plays an important role in the data analysis for the prediction purpose. The inferential statistics includes the study of testing of hypothesis. By using testing of hypothesis, we check the different claims regarding the variables in the data set. Here, we have to check the claim whether there is a same or different turnover for the company with employee having the different ordinary scale of their job satisfaction. For checking this claim, we have to use the one way analysis of variance or ANOVA test in short. Let us see this one way analysis of variance or ANOVA in detail given as below: The null hypothesis for this one way ANOVA test is given as below: Null hypothesis: H0: There is a same turnover for the company with an employee having different scale of job satisfaction. The alternative hypothesis for this one way ANOVA test is given as below: Alternative hypothesis: Ha: There is not a same turnover for the company with an employee having different scale of job satisfaction. Now, we have to see the analysis for this one way ANOVA which is summarised in the following table: The ANOVA table for this test is given as below: ANOVA Turnover Sum of Squares df Mean Square F Sig. Between Groups 66067636.084 5 13213527.217 1.946 .088 Within Groups 1317007797.671 194 6788699.988 Total 1383075433.755 199 For this ANOVA table, we get the p-value as 0.088 and we are given a level of significance as 0.05 or 5%. We know the decision rule is given as below: Decision rule: We reject the null hypothesis if the p-value is less than the given level of significance or alpha value. We do not reject the null hypothesis if the p-value is greater than the given level of significance or alpha value. Here, we are given as level of significance or alpha = 0.05 and we have p-value = 0.088 p-value alpha value So, we do not reject the null hypothesis that there is a same turnover for the company with an employee having different scale of job satisfaction. Now, we have to check another claim regarding the commitment of the employee. Let us see this test in detail given as below: For this hypothesis test we have to use same analysis as we seen in the above test. We have to use the one way analysis of variance or ANOVA test for checking the claim about the commitment of the employee. The null hypothesis for this one way ANOVA test is given as below: Null hypothesis: H0: There is a same turnover for the company with an employee having different scale of employee commitment. The alternative hypothesis for this one way ANOVA test is given as below: Alternative hypothesis: Ha: There is not a same turnover for the company with an employee having different scale of employee commitment. Now, we have to see the analysis for this one way ANOVA test by using the ANOVA table. The ANOVA table for this test is summarised as below: ANOVA Turnover Sum of Squares df Mean Square F Sig. Between Groups 5032708.153 5 1006541.631 .142 .982 Within Groups 1378042725.602 194 7103313.019 Total 1383075433.755 199 For this ANOVA table, we get the p-value as 0.982 and we are given a level of significance as 0.05 or 5%. We know the decision rule is given as below: Decision rule: We reject the null hypothesis if the p-value is less than the given level of significance or alpha value. We do not reject the null hypothesis if the p-value is greater than the given level of significance or alpha value. Here, we are given as level of significance or alpha = 0.05 and we have p-value = 0.982 p-value alpha value So, we do not reject the null hypothesis that there is a same turnover for the company with an employee having different scale of employee commitment. For this study regarding the relationship between the job satisfaction of the employee, commitment of the employee and turnover of the company, we made some conclusions which are summarised in the next topic. Summary: For the variable job satisfaction, most of the employee respond as the low job satisfaction as an answer to asked question about job satisfaction. About 43 employees noted low job satisfaction and about 36 employees are noted best job satisfaction in the given questionnaire. 36 employees said that they had best job satisfaction with their job in the company. It was observed that 38 employees noted the response the very low commitment at their work within the company. About 37 employees are responded as the best commitment during their work within the company. We do not reject the null hypothesis that there is a same turnover for the company with an employee having different scale of job satisfaction. We do not reject the null hypothesis that there is a same turnover for the company with an employee having different scale of employee commitment. References: Robert V. Hogg, Allen T. Craig, Joseph W. McKean, An Introduction to Mathematical Statistics, 6th ed., Prentice Hall, 2004. George Casella, Roger L. Berger, Statistical Inference, 2nd ed., Duxbury Press, 2001. David R. Cox, D. V. Hinkley, Theoretical Statistics, Chapman Hall/CRC, 1979. Peter J. Bickel, Kjell A. Doksum, Mathematical Statistics, Volume 1, Basic Ideas and Selected Topics, 2rd ed. Prentice Hall, 2001. S. 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