P-value is often discussed when dealing with science. Especially in scientific journals, you will surely find mentions of the p-value. But what is it, really? Well, if I were to explain it in very simple and concise terms, I would say:
“Imagine formulating a certain hypothesis. For example, we hypothesized that the average height of Italians is over 168 cm. Obviously, we want to know if this hypothesis is true or if the observed value is simply due to chance. To do this, it is necessary to perform a hypothesis test, in which a test statistic is calculated and a p-value is associated with it. These two components, the test statistic and the p-value associated with it, are precisely what we use to decide whether to reject our hypothesis or not. The p-value expresses the probability that the obtained test statistic value is due to chance. Of course, we want the observed result to be true and not just due to pure chance. Therefore, the p-value must be 'low'. But how low? Well, it is necessary to define a p-value threshold which, if exceeded, forces us to say that the p-value, and therefore the probability that the test statistic value is due to chance, is too high to 'accept' the formulated hypothesis. The threshold is usually 0.05 but can vary.”
The test statistic is useful because its recorded value determines the p-value, which graphically represents the area under the probability distribution curve, whose shape varies according to the type of test statistic used, to the right (or/and to the left in the case of two-sided tests) of the test value.
P-value is often discussed when dealing with science. Especially in scientific journals, you will surely find mentions of the p-value. But what is it, really? Well, if I were to explain it in very simple and concise terms, I would say:
“Imagine formulating a certain hypothesis. For example, we hypothesized that the average height of Italians is over 168 cm. Obviously, we want to know if this hypothesis is true or if the observed value is simply due to chance. To do this, it is necessary to perform a hypothesis test, in which a test statistic is calculated and a p-value is associated with it. These two components, the test statistic and the p-value associated with it, are precisely what we use to decide whether to reject our hypothesis or not. The p-value expresses the probability that the obtained test statistic value is due to chance. Of course, we want the observed result to be true and not just due to pure chance. Therefore, the p-value must be 'low'. But how low? Well, it is necessary to define a p-value threshold which, if exceeded, forces us to say that the p-value, and therefore the probability that the test statistic value is due to chance, is too high to 'accept' the formulated hypothesis. The threshold is usually 0.05 but can vary.”
The test statistic is useful because its recorded value determines the p-value, which graphically represents the area under the probability distribution curve, whose shape varies according to the type of test statistic used, to the right (or/and to the left in the case of two-sided tests) of the test value.