

BRIEF REPORT 

Year : 2014  Volume
: 5
 Issue : 1  Page : 2728 

Concept of Pvalue
Areej Abdul Ghani Al Fattani
Department of Pediatrics, King Faisal Specialist Hospital and Research Center, Riyadh, Saudi Arabia
Date of Web Publication  2May2014 
Correspondence Address: Areej Abdul Ghani Al Fattani Department of Pediatrics, MBC58, King Faisal Specialist Hospital and Research Center, P. O. Box 3354, Riyadh 11211 Saudi Arabia
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/16585127.131823
P value has been criticized because it is widely misunderstood and don't tell the researchers what they want to know. Many clinical researches mistaken the conclusion of a significant Pvalue and may be exaggerate small and unimportant difference. In this regard, understanding of meaning and concept of Pvalue is critical to investigators as well as to readers. In brief, Pvalue is the probability of observing a difference equals or more extreme than what was actually observed, if the null hypothesis is true. It is not the proportion of chance that might cause the difference. Pvalue is not the probability of rejecting the null hypothesis, that probability called α (Type1 error). The smaller the Pvalue, the stronger the evidence against null hypothesis. Keywords: Hypothesis, interpretation, Pvalue, significance
How to cite this article: Al Fattani AG. Concept of Pvalue. J Appl Hematol 2014;5:278 
Definition and interpretation   
The 'P' stands for probability; 'P value' is the probability of observing a difference equals or more extreme than what was actually observed, if the nullhypothesis is true. That story starts when you collect data from two groups; for example, each sample having a different mean and you want to know if that difference is happened due to chance or due to underling cause. There is no way ever to know that for sure, and what you can do is to calculate probabilities.
The P value usually considered being significant at 0.05 level, in epidemiological studies, but iis an arbitrary choice in origin. Calculation of statistical significance was started in 1770 by PierreSimon Laplace, but was first defined in 1920 by Ronald Fisher who suggested 1/20 or 0.05 as convenient level of chance to obtain a coincidence false result in 20 successful trials. Later on it was recommended by Statistical Methods and Scientific Inference Book, published by Cambridge University. ^{[1]}
Researchers should not confuse the P value with type I error (or called α), which is the probability of rejecting the nullhypothesis when it is true, which usually sets as 5%. The P value or the critical value then obtained using 't' or 'z' distribution tables depending on α and σ (sample mean) in this case equals 1.96. Then, a result considered as statistically significant when its P value is less than α, 0.05. Consequently, we would reject the nullhypothesis. Note that the smaller the P value, stronger the evidence against nullhypothesis.
In a normal distribution curve of given data, we will observe the means in repeating experiments located most likely in 95% of the area under the curve. Experiments with P value more than 0.05 will be in this area, which is also called also the 'nonrejection area'. The remaining 5% of the area comprises the rejection region. This happens when an experiment had extreme results than what was observed in case of similar groups and a difference that is unlikely due to chance. This 5% split can be around the sides with 0.025 in each side (twotailed), or can be 0.05 in one side (onetailed) [Figure 1].
Important points in the interpretations of P value. ^{[2],[3]}  Figure 1: Graphical illustration to the relation between Alpha and Pvalue (Brandon Foltz. Mar 2014, http://youtu.be/NQWZefn41VY)
Click here to view 
 With the P value 0.03, common misinterpretation when researcher says there is 97% of chance that the difference he observed is due to real difference between populations, and 30% of chance that the difference is due to chance. Correct interpretation would be that: There is a 3% probability that you will observe a difference as large as what you got when the two population are identical (the nullhypothesis is true)
 P value does not tell if the difference is due to sampling error, as it is calculated based on the assumption. It also does not tell if the nullhypothesis is correct for the same reason
 P value is not the probability of rejecting the nullhypothesis, but α (Type 1 error) is that, you set the value of α as part of experimental design, and based on that significance level of α, you define the cutoff limit of P value. The two are not the same
 When a researcher gets a small P value, there are three possibilities for interpretation. First, the difference is real between population. Second, the difference is real but it is so small to consider clinically or for practical change. Third, the difference is not real, it happened just by an error in sampling or mistake in definition of prior probability
 If the P value is larger than α, we do not reject the nullhypothesis, but we cannot conclude that it is true. All what we can say is that we do not have sufficient evidence to reject the assumed nullhypothesis
 Confidence interval gives much more reliable information than P value alone
 Finally, Interpretation of P value is a matter of general sense, logic, and wisdom clinical judgment.
References   
1.  Quinn GR. Keough MJ. Experimental Design and Data Analysis for Biologists. 1 ^{st} ed. Cambridge: Cambridge University Press; 2002. p. 466 9. 
2.  Nuzzo R. Scientific method: Statistical errors. Nature 2014;506:1502. [PUBMED] 
3.  Kirkwood BR, Sternc JA, Malden MA. Essential Medical Statistics. 2 ^{nd} ed. Blackwell Publishing; 2003. 
[Figure 1]
