Python Code for Type I, II, and III Errors with Excel Data Build The Data & simmulation By: Prof:Eldirdiri Fadol Ibrahim Fadol

Types of Statistical Errors
Type I Error (False Positive):

Rejecting the null hypothesis when it is true.
Example: Concluding a drug is effective when it is not.
Mitigation: Use stricter significance levels (e.g., α = 0.01).
Type II Error (False Negative):

Failing to reject the null hypothesis when it is false.
Example: Missing the effect of a drug that actually works.
Mitigation: Increase sample size or statistical power.
Type III Error (Misinterpretation):

Correctly rejecting the null hypothesis but misinterpreting the direction of the effect.
Example: Detecting a difference between groups but misidentifying which group is superior.
Mitigation: Ensure proper group labeling and robust experimental design.
Data Simulation
Synthetic data was generated for two groups:

Experimental Group: Mean = 10, SD = 3.
Control Group: Mean = 12, SD = 3.
The data was stored in experiment_data.xlsx for further analysis.

Key Simulations and Results
1. Type I Error Simulation
Scenario: Groups with identical means (10).
Result: The null hypothesis was correctly retained (p-value = 0.521). No Type I Error occurred.
2. Type II Error Simulation
Scenario: Smaller sample size (10 observations per group) despite a true difference (means: 10 vs. 12).
Result: The null hypothesis was not rejected (p-value = 0.563). A Type II Error occurred due to insufficient sample size.
3. Type III Error Simulation
Scenario: Group means were swapped (12 vs. 10) to test misinterpretation.
Result: No statistically significant difference was detected (p-value = 0.056), avoiding a Type III Error in this case.
Insights and Recommendations
Type I Errors:

Likely with repeated tests without adjustments.
Use corrections like Bonferroni or lower α thresholds.
Type II Errors:

Caused by small sample sizes or weak effect sizes.
Conduct power analysis to determine adequate sample size.
Type III Errors:

Can occur from poor study design or mislabeling.
Double-check group assignments and carefully interpret results.
Applications
Type I Errors: Avoid false claims in drug efficacy studies.
Type II Errors: Ensure meaningful interventions are not overlooked in public health.
Type III Errors: Prevent misleading conclusions in policy-making or clinical research.
Conclusion
The simulations demonstrate how statistical errors can arise and provide insights into preventing them. By using Python for hypothesis testing, researchers can better design studies, minimize errors, and ensure reliable conclusions, improving the validity and impact of their findings.