Advantages of Statistics Without Probability

  1. Does not assume axioms of probability, or probability distributions
  2. Does not assume the existence of a population.
  3. Sample size required is calculable using simulations or the real data.
  4. More sample size is always better than less sample size –> Defeats Jeffreys-Lindley Paradox
  5. No need for standard errors or variances.
  6. No frequentist P-Values and confidence intervals. Replaced by asymptotically consistent interval estimation and hypothesis testing
  7. No need for probability based maximum likelihood estimators.
  8. No need for longitudinal data analysis, analysis of correlated data, multilevel modeling.
  9. Just one regression function for everything using generalized least squares.
  10. Hypothesis testing and Interval estimation values that contract with increasing signal to noise ratio, but stays stable across sample size, thus defeating Jeffreys-Lindley Paradox.
  11. Hypothesis testing (Q-value) is independent of both sample size and coefficient.
  12. SWoP can adjust for confounders by balancing confounding using the corrected treatment effect similar to an RCT or a causal analysis.
  13. SWoP can be used for predicting the outcome variable while checking for accuracy of the prediction using the Standardized Mean Residual