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NI FEATURE: CENTS (CONCEPTS, ERGONOMICS, NUANCES, THERBLIGS, SHORTCOMINGS)  COMMENTARY 



Year : 2019  Volume
: 67
 Issue : 4  Page : 1086 
Know Some Vital Statistics: What is P Value?
Kameshwar Prasad
Department of Neurology, All India Institute of Medical Sciences, New Delhi, India
Date of Web Publication  10Sep2019 
Correspondence Address: Dr. Kameshwar Prasad Professor of Neurology, Department of Neurology, Former Head (Neurology) and Chief, Neurosciences Centre, All India Institute of Medical Sciences, New Delhi India
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/00283886.266277
How to cite this article: Prasad K. Know Some Vital Statistics: What is P Value?. Neurol India 2019;67:1086 
The P value is meant to answer the question: Are the observed results likely to have occured by chance or design? Some of us clinicians might think it may be impossible to determine this. We are right to some extent, but our statistician “gurus” have worked out a number (literally hundreds) of formulae to suit all kinds of observations over the last 100 years.^{[1]} Let us take an example to determine whether a treatment has some effect. Prior to applying the formulae, they start with a hypothesis which assumes that the treatment has no effect (or that there is no difference between the two groups). This is called “null hypothesis.” This strategy may remind you of the widely held assumptions in many criminal justice systems that a person is innocent until proven otherwise.
The next step is to check under the assumption of no effect or no difference, for the probability of obtaining a result equal to (or more extreme than) what was actually observed in the study. There are many steps in the calculation, but you need not worry about that. If this probability is very small, conventionally taken as 5% (0.05), then a decision is taken to reject the null hypothesis and consider that the treatment has an effect that is unlikely by chance. This is the P value (P stands for “probability”). P value of <0.05 suggests that the observed result is unlikely to be due to chance.
To summarize, the P (Probability) value is the probability that the difference observed (or more extreme difference) between two groups has occurred by chance, if the groups were really not different (i.e., under null hypothesis).^{[2]}
In most biomedical and epidemiologic research, a study results where probability value (P value) is less than 5% (P < 0.05) are considered sufficiently unlikely to have occurred by chance to justify the designation of statistical significance.^{[3]}
But why 5% is the cutoff value? This is truly arbitrary, but you may agree that it is reasonable. To understand this, let us conduct a hypothetical experiment. Five friends A, B, C, D, and E gather to decide who will get a free dinner tonight. Everybody is given a similar coin and asked to toss it, stopping when they get a “tail.” Whosoever got the highest number of heads before getting a tail will get a free dinner tonight. A got first head and then tail. B got Head–Head–Head–Tail. C got Head–Head–Tail. D got Head–Head–Head–Head–Tail. Would you believe D or reject him?. Many of you might think he was doing some tricks, but some may accept it as just good luck. What about E? He got Head–Head–Head–Head–Head–Tail. A majority, if not all, will reject him thinking that he may have cheated, etc. But the fact is that according to the law of probability there is a definite, though small, probability that it has all happened by chance. This probability is ½ × ½ × ½ × ½ × ½ = 0.03 (3%). Thus, you see that when the use (probability) of an event happening by chance is as low as 3%, a majority of people would reject it. Based on similar logic, early statisticians decided that if probability of something happening under null hypothesis is <5%, then they recommended to reject the null hypothesis and accept the alternative hypothesis. Such a result was termed, 'statistically significant.' The clinical relevance of this result will be discussed later writeup in this series.
» References   
1.  Fisher RA. Statistical Methods for Research Workers. Edinburgh, UK: Oliver and Boyd; 1925. 
2.  Schervish MJ. P values: What they are and what they are not. Am Stat 1996;50:2036. 
3.  Neyman J, Pearson E. On the problem of the most efficient tests of statistical hypotheses. Philos Trans R Soc Lond A 1933;231:289337. 
