Common Statistical Constants and Their Interpretations

1. Significance Levels (α)

p = 0.05 (5%): Standard significance level in most fields

p = 0.01 (1%): More stringent significance level

p = 0.10 (10%): Sometimes used in exploratory research

p = 0.001 (0.1%): Very strict significance level

2. Interquartile Range (IQR) Outlier Detection

1.5 × IQR: Standard for potential outliers (mild outliers)

3.0 × IQR: Often used for extreme outliers

3. Standard Deviation Thresholds

1σ (68.27%): Contains ~68% of data in normal distribution

2σ (95.45%): Contains ~95% of data in normal distribution

3σ (99.73%): Contains ~99.7% of data in normal distribution (Three-sigma rule)

6σ (Six Sigma): 99.99966% of defect-free outcomes

4. Z-score Thresholds

z = ±1.96: 95% confidence interval for two-tailed test

z = ±2.58: 99% confidence interval for two-tailed test

z = ±1.645: 95% confidence interval for one-tailed test

z = ±2.33: 99% confidence interval for one-tailed test

5. Effect Size Interpretation (Cohen's d)

0.2: Small effect

0.5: Medium effect

0.8: Large effect

6. Correlation Coefficient (r) Interpretation

0.1-0.3: Weak correlation

0.3-0.5: Moderate correlation

0.5-0.7: Strong correlation

0.7-0.9: Very strong correlation

0.9-1.0: Nearly perfect correlation

7. Variance Inflation Factor (VIF) for Multicollinearity

VIF > 5: Moderate multicollinearity concern

VIF > 10: Serious multicollinearity problem

8. R-squared Thresholds (context-dependent)

0.25: Weak explanation

0.50: Moderate explanation

0.75: Strong explanation

9. Cronbach's Alpha (Reliability)

0.7: Minimum acceptable

0.8: Good

0.9: Excellent

10. Critical Values for Durbin-Watson Test

Close to 0: Positive autocorrelation

Close to 2: No autocorrelation

Close to 4: Negative autocorrelation

11. Bootstrap Resampling

1,000 resamples: Typical minimum

10,000 resamples: More precise estimates

12. Degrees of Freedom Adjustments

Welch-Satterthwaite adjustment for t-tests

*Greenhouse-Geisser and Huynh-Feldt corrections for ANOVA

These constants serve as conventional reference points in statistical analysis, though their appropriateness may vary depending on the specific field, research question, and data characteristics.