Employees Discrimination Analysis - Case Study Example

Memorandum XXXX XXXXX Ron Lemond Re: Discrimination in QFC layoffs and rehiring March 6, Former and current employees at QFC are complaining about age discrimination in the company’s hiring and laying off of employees. The parties have approached Foster Pepper for litigation against QFC and data on layoff, which can be inferred to rehiring for the litigation purposes, is available. Below are data analysis results that aim at establishing validity of the claim. The analysis concludes that QFC discriminates its employees on the basis when laying off and this can be inferred to the company’s rehiring that the parties have complained about. Trend in number of weeks of layoff by employees’ age suggests possible discrimination by age as the scatter, appendix 1, suggests a linear relationship. Analysis of the number of weeks of layoff by age groups supports this position. When organized by age groups of from 20 to 29 years old, 30 to 39 years old, 40 to 49 years old, and 60 to 69 years old, mean number of weeks of layoff appear to increase with increase in age. The following table summarizes this. Table 1: Mean number of weeks of layoff by age group Age group Mean number of layoff weeks 20- 29 years 29 30- 39 years 41.68 40- 49 years 63.55 60- 69 years 87 The means shows wide gaps in number of layoff weeks across age group to support the client’s claim of age-based discrimination. It is however important to investigate significance of the observed difference across the age groups. Analysis of variance shows significance of the difference (p-value= 0.00018< 0.005) and this leads to the conclusion that QFC discriminate its employees, based on age, in its layoff. This can then be inferred on the company’s rehiring of employees. Further analysis of the relationship between age and number of layoff weeks supports the result. The following linear model, which is significant (p-value= 0.000< 0.005), explains the relationship. Number of layoff weeks= -12.26+1.64 The model explains about 32 percent of the data (R2= 0.3167) that is significant and it can therefore used to infer on the data set. Based on the model, a unit increases in age increase an employee’s layoff weeks by 1.64 weeks. Analysis of other demographic factors of the employees also supports the discrimination claim, possibly because the organization perceives older people to be less productive. Education, another demographic factor that is important to employee output also identifies discrimination. This is because lower levels of education have higher means of number of layoff weeks and the difference by education level is significant (p-value= 0.000 < 0.05). This means that the organization discriminates employees based on performance indicators, age, and education. There is however no significant difference across measures of tenure, marital status and position in the organization. The analysis results identify age-based discrimination in employees’ layoff in the organization. Identified discrimination, based on level of education, supports this while no discrimination exist along the other factors. The client’s claim is therefore valid. Appendix Based on available data on the number of employees’ layoff weeks and demographic factors, data was analyzed to investigate the relationships between number of layoff weeks and employees’ age. Relationships between number of layoff weeks and other demographic factors were used to support the relationship with age. Hypotheses The following hypotheses were tested. Age Null hypothesis; no significant relationship exist between number of layoff weeks and age Tenure Null hypothesis; no significant difference in mean of layoffs weeks by tenure Education Null hypothesis; no significant difference in mean of layoffs weeks by level of education Marital status Null hypothesis; no significant difference in mean of layoffs weeks by marital status Position Null hypothesis; no significant difference in mean of layoffs weeks by job position Methods Excel data analysis tool was used to analyze the data. Results and Discussion Age The following plot shows the distribution of number of layoff weeks by age. Appendix 1: Distribution of number of weeks by age Excel was used to develop the scatter plot that illustrates possible relationship between number of layoff weeks and employees’ age. The scatter plot describes the data and does not test any hypothesis. Analysis of weeks of layoff by age groups Appendix 2 is a descriptive analysis of the relationship between number of layoff weeks and age, organized into age groups. Excel’s data analysis for descriptive statistics was used to generate the data. Appendix 2: Descriptive statistics of layoff weeks by age group Column1 20- 29 30- 39 40- 49 60- 69 Mean 29 41.68182 63.54545 87 Standard Error 4.452928 4.768396 7.741698 7 Median 25 42.5 65 87 Mode #N/A 30 #N/A #N/A Standard Deviation 17.24612 22.36576 25.67631 9.899495 Minimum 8 6 16 80 Maximum 62 80 98 94 Sum 435 917 699 174 Count 15 22 11 2 The table shows that increase in age, across the age groups, identifies with higher number of layoff weeks. The increase is also consistent and becomes greater as the age groups increase in magnitude. Appendix 3 shows ANOVA results for investigating the possible relationship between number of layoff weeks and age, by age groups. Excel was used for the analysis to test the following set of hypothesis. H0: µ20-29= µ30-39= µ40-49= µ60-69; no significant difference in mean of layoffs weeks by employees’ age H1: Any of the means is different; a significant difference in mean of layoffs weeks by employees’ age exists Appendix 3: ANOVA table for differences by age group ANOVA Source of Variation SS df MS F P-value F crit Between Groups 11381 3 3793.667 8.170073 0.000182 2.806845 Within Groups 21359.5 46 464.337 Total 32740.5 49         The result is significant and means that the null hypothesis is rejected. This is because of the low p-value (0.00018< 0.05, F= 8.17> 2.8). The results means that the observed differences in means across the age groups is significant and therefore suggest that the organization uses age as a factor in determining number of layoff weeks. The following excel extract shows summary statistics for regression analysis of the relationship between age and number of layoff weeks. The analysis tested the following hypothesis using excel. H0: β=0; no significant relationship exist between number of layoff weeks and employees’ age H1: β≠0; a significant relationship exist between number of layoff weeks and employees’ age Appendix 4: Summary output for regression analysis Regression Statistics Multiple R 0.574975 R Square 0.330596 Adjusted R Square 0.31665 Standard Error 21.36812 Observations 50 The R2 value (31.665) shows that the developed model explains 31.665 of the data. This percentage is large enough for use in interpreting the data and indicates reliability derived conclusions from the analysis. Appendix 5: ANOVA table for regression analysis The following is the ANOVA, generated from Excel. ANOVA   df SS MS F Significance F Regression 1 10823.87 10823.87 23.70555 1.26E-05 Residual 48 21916.63 456.5965 Total 49 32740.5       The null hypothesis is rejected because of the low p-value (1.26*10-5, F= 23.7056). This means that a significant relationship exists between age and number of layoff days and age is therefore a significant factor in the organization’s layoff decision. The following appendix is the table of coefficients for the relationship. Appendix 6: Table of coefficients for regression analysis   Coefficients Standard Error t Stat P-value Intercept -12.2605 12.04322 -1.01804 0.313762 Age 1.640477 0.336934 4.868834 1.26E-05 The low p-value for variable (p-value=1.26*10-5, t= 4.867) means that age is a significant factor and yields the following equation. Number of layoff weeks= -12.26+1.64 Tenure Appendix 7: Summary statistics Descriptive statistics, derived from Anova: Single Factor SUMMARY Groups Count Sum Average Variance 1 4 159 39.75 42.25 2 5 163 32.6 910.3 3 1 35 35 #DIV/0! 4 1 55 55 #DIV/0! 5 1 30 30 #DIV/0! 6 9 469 52.11111 391.3611 7 2 29 14.5 0.5 8 9 307 34.11111 741.3611 9 1 25 25 #DIV/0! 10 2 71 35.5 760.5 11 4 114 28.5 537.6667 12 2 99 49.5 1860.5 13 2 121 60.5 4.5 16 2 170 85 50 17 1 98 98 #DIV/0! 22 2 136 68 32 30 1 82 82 #DIV/0! The table identifies random distribution in means by tenure and suggests that tenure does not determine number of layoff weeks. Appendix 8: Anova table for layoff weeks by tenure The following is the ANOVA results based on the following hypothesis set. H0: µi are equal, no significant difference in mean of layoffs weeks by tenure H1: Any of the means is different; a significant difference exists in mean of layoffs weeks by tenure ANOVA Source of Variation SS df MS F P-value F crit Between Groups 15277.27 16 954.8295 1.78153 0.080452 1.971683 Within Groups 17150.73 32 535.9602 Total 32428 48         The high p-value (0.08, F= 1.78) means that the null hypothesis is rejected to the conclusion that observed differences in mean of number of layoff weeks are not significant. Education Appendix 9: Anova table for difference by level of education The following set of hypothesis was tested and yielded the following table. H0: µi are equal, no significant difference in mean of layoffs weeks by education H1: Any of the means is different; a significant difference exists in mean of layoffs weeks by education ANOVA Source of Variation SS df MS F P-value F crit Between Groups 24506.67 13 1885.128 8.242167 2.49E-07 2.003208 Within Groups 8233.832 36 228.7175 Total 32740.5 49         The low p-value (2.49*10-07, F= 8.24) means that the null hypothesis is rejected to the conclusion that level of education determines, significantly, number of layoff days. Marital status Appendix 10 shows analysis results for the following set of hypothesis. H0: µi are equal, no significant difference in mean of layoffs weeks by marital status H1: Any of the means is different; a significant difference exists in mean of layoffs weeks by marital status Appendix 10: Anova table for difference by level of education Anova table ANOVA Source of Variation SS df MS F P-value F crit Between Groups 40.02381 1 40.02381 0.05875 0.809516 4.042652 Within Groups 32700.48 48 681.2599 Total 32740.5 49         The high p-value (0.809, F= 0.0588) means that the null hypothesis is not rejected to the conclusion that marital status does not determine number of layoff weeks. Position The following hypothesis set was tested and yielded the following results H0: µi are equal, no significant difference in mean of layoffs weeks by position H1: Any of the means is different; a significant difference exists in mean of layoffs weeks by position Appendix 11: Anova table for difference by position ANOVA Source of Variation SS df MS F P-value F crit Between Groups 2303.661 2 1151.831 1.778635 0.180046 3.195056 Within Groups 30436.84 47 647.5923 Total 32740.5 49         The high p-value (0.18, F= 1.77) means that the null hypothesis is not rejected to the conclusion that position does not influence number of layoff weeks. Conclusion The analysis results identify age-based discrimination in employees’ layoff in the organization. Identified discrimination, based on level of education, supports this. Tenure, marital status and employees’ position are not significant to number of layoff weeks and their lower impacts on productivity supports the notion that the organization discriminated on age and education, for productivity objectives, on employees’ layoffs. The client’s claim is therefore valid. Read More