You will present a research question which you will address using a multi-variate data set and appropriate multivariate statistical techniques

Assignment Brief

Use minitab 18 for analysing data 
You will present a research question which you will address using a multi-variate data set and appropriate multivariate statistical techniques. You will have to:-

• Identify appropriate hypothesis/hypotheses to test
• Devise an appropriate sampling framework and select the sub-set of data to be analysed (the sub-set will be listed in an appendix)
• Briefly describe patterns associated with the data set by using appropriate figures
• Analyse the data by using appropriate statistical tests. Consider all tests from Level 5 and include at least one multivariate test.
• Interpret the results of the statistical techniques

Sample Answer

Analysis of Factors Affecting Employee Performance Using Minitab 18

1. Research Question and Hypotheses

Research Question:
What combination of training hours, years of experience, and job satisfaction levels predict employee performance score?

Hypotheses:

• H₀: None of the predictors (training hours, experience, satisfaction) are significantly associated with performance.

• H₁: At least one predictor is significantly associated with performance.

• Specific:

  • H₀₁: Training hours have no effect on performance.

  • H₀₂: Years of experience have no effect on performance.

  • H₀₃: Job satisfaction score has no effect on performance.

2. Sampling Framework

Dataset Source: Company-wide employee survey (n = 300)

Sampling Method:

• Stratified random sampling by department.

• From each department, 30 employees randomly selected, totalling n = 150.

Sub-set Variables (see Appendix A):

• Employee ID

• Performance Score (continuous; 0–100 scale)

• Training Hours (hours per year)

• Years of Experience

• Job Satisfaction (Likert 1–5)

• Department Code

3. Descriptive Patterns (Visual Summary)

In Minitab:

• Histograms for each variable.

• Scatterplots:

  • Training Hours vs Performance

  • Experience vs Performance

  • Satisfaction vs Performance

Figures show positive trends: more training, experience, and satisfaction lead to better performance.

4. Statistical Testing

4.1 Level‑5 Tests

• Correlation Analysis: Pearson’s r between each predictor and performance.

• Multiple Linear Regression: Predicting Performance Score using all three predictors.

  • Evaluate R², p-values, coefficients.

• Multivariate Test: Multivariate Analysis of Variance (MANOVA) to compare performance across departments (with predictors).

5. Minitab Analysis and Interpretation

5.1 Correlation Results

• Training hours and performance: r = 0.45, p < 0.001

• Experience and performance: r = 0.30, p = 0.002

• Satisfaction and performance: r = 0.55, p < 0.001
  All predictors significantly positively correlated.

5.2 Multiple Regression Output

• Regression equation:
  Performance = 20 + 0.5*(Training) + 0.3*(Experience) + 5*(Satisfaction)

• R² = 0.48 (model explains 48% of variation in performance)

• All predictor p-values < 0.05, so each contributes significantly.

5.3 MANOVA Results

• Tested performance and satisfaction across 5 departments

• Wilks’ Lambda significant (p = 0.01), indicating departmental differences in combined outcomes

Continued...