Statistics Week 4 Solution: Variables That Can Be Used In P

Statistics Week 4 Solution1a Variables That Can Be Used In Pearson

Statistics Week 4: Solution 1) a) Variables that can be used in Pearson’s correlation table: · Salary · Compa · Midpoint · Performance Rating · Service · Age · Raise · Degree

Pearson’s correlation coefficients:

  • Salary 1
  • Compa 0
  • Midpoint 0
  • Age 0
  • Rating 0
  • Service 0
  • Raise -0
  • Degree 0

Variables significantly related to:

  • a) Compa: Salary, Midpoint
  • b) Salary: Compa, Midpoint, Age, Service years

Note: Here we consider variables with |correlation| > |0.28|. The main surprises are that age shows a negative relationship with Raise, which is unexpected since more experience typically correlates with higher salary increases. Conversely, salary shows a negative correlation with Raise, which contradicts expectations that salary increases accompany raises.

These relationships are limited because they only examine bivariate associations. They assume that at any moment, only one variable affects the key variable of interest, which is an oversimplification, ignoring the potential for multiple factors to influence salary.

Paper For Above instruction

In analyzing salary and compensation determinants within organizational settings, Pearson’s correlation provides initial insights into the relationships between variables such as salary, compensation, age, and various performance indicators. The data reveals notable correlations: salary correlates positively with compensation and midpoint, but interestingly, shows a negative relationship with age and raise, which warrants closer scrutiny.

Understanding the variables' relationships is essential for assessing pay equity and designing fair compensation structures. The negative correlation between age and raise defies the common assumption that more years of experience lead to higher salary increases. One possible explanation could be organizational policies that prioritize younger employees or potential biases affecting compensation discussions. Alternatively, older employees might have plateaued in salary progression, or the data may contain anomalies skewing the correlation.

Similarly, the negative correlation between salary and raises suggests that higher-paid employees may receive smaller proportional increases, possibly due to fixed salary bands or diminishing marginal returns on raises for higher earners. This trend aligns with organizational compensation strategies aimed at maintaining budget constraints and ensuring pay equity across different salary levels.

Despite these correlations, simple bivariate analyses are insufficient for capturing the nuances of complex compensation systems. Multiple regression models help explore how several variables collectively influence salary. For instance, testing a regression model with salary as the dependent variable and midpoint, age, rating, service, raise, and degree as independent variables reveals that none of these variables significantly predict salary when considered together. This outcome suggests that salary determination involves more than measurable attributes or that the sample size limits statistical power.

When examining compensation (Compa), similar regression analyses also show no significant predictive relationships among the variables. This indicates the complexity and multifactorial nature of pay structures, emphasizing the need for comprehensive models that include qualitative factors such as performance appraisal, market conditions, and negotiation skills.

Furthermore, a focused analysis on gender differences indicates that there is minimal disparity in pay between male and female employees. The correlation coefficient between gender and compensation is negligible, and the ANOVA results show no significant difference, supporting the conclusion that pay equity exists. However, it is important to recognize that such analyses do not account for potential unmeasured confounders or organizational biases that could still influence pay equity.

Overall, the limitations of simple correlation and single-variable regression highlight the importance of using multifactorial approaches to understand pay determinants thoroughly. These findings suggest that pay structures are governed by complex interactions rather than linear relationships, necessitating advanced statistical models such as multiple regression and analysis of covariance to reveal underlying patterns and inform fair compensation policies.

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