Abstract:

A large proportion of researchers in fields such as medicine, biology, and sociology commit basic errors in statistical interpretation throughout their professional careers. This problem largely originates from deficient statistical teaching, common even in developed countries, where a high percentage of university professors who use the p-value are unaware of what it actually measures. We propose that the solution lies in shifting the focus from mathematical complexity and formulas towards the basic logic that governs statistical inference.

Statistical inference is based on a logical mechanism identical to the one people constantly and correctly use in their daily lives. Understanding the fundamental concepts requires no mathematical knowledge:
1. The p-Value: Far from being a complex mathematical index, the p-value is simply a relative frequency (proportion) that indicates the probability of obtaining a specific result (or a more extreme one) if the null hypothesis were true in the population. Statistical logic consists of rejecting a hypothesis if the result is hardly compatible with it. This reasoning is identical to deciding on guilt: the presence of the accused on another continent makes the data incompatible with the hypothesis of guilt, which is then rejected. The p-value simply quantifies this degree of incompatibility.
2. The Logical Error of Conclusion: The most serious and frequent error is assuming that a hypothesis is true because insufficient evidence was found to reject it. A large p-value indicates that the result is compatible with the null hypothesis, accepting it as possible, but not as certain. If one starts from the hypothesis that a hidden animal is a tiger and it is known to have four legs, it can be concluded that it might be a tiger, but also any quadruped. In a clinical trial, a large p-value only demonstrates that a new drug has not been proven to be better than the old one, and prematurely affirming that it is useless can lead to the abandonment of potentially beneficial research.
3. Sample Size: The calculation of sample size is surrounded by the myth of the existence of an "adequate" or "correct" size justified by a formula. However, just as there is no "adequate" amount of money when buying a bicycle, there is no single sample size for research. Formulas depend on flexible parameters and can yield almost any size value using reasonable parameter values. The logical approach is for the researcher to choose a size that fits their resources, knowing that the larger the size, the greater the probability of finding a smaller p-value. Formulas can be more useful for detecting insufficient or unnecessarily large sizes.

The complexity of statistical inference is neither intellectual nor mathematical; rather, it lies in the lack of pedagogical clarity. If it is taught that the p-value is a proportion that quantifies the incompatibility of the data with the null hypothesis, that its logic is the same as that used in everyday judgments (like an alibi), and that there is no unique sample size just as there are no unique quantities in other aspects of common life, false conclusions would be avoided, and fruitful and effective research would be promoted.

Keywords:

Education, statistical inference, p-value, sample size.