The p-value is one of the most significant statistical estimates. The probability value, often known as the p-value, is a figure that, when determined from a statistical test, indicates how likely it was that your results would have been true had the null hypothesis been correct. If the P-value is higher than 0.5, the null hypothesis is assumed to be true; as a result, the P-value is not statistically significant. A P-value of less than 0.5 is statistically significant. So, what exactly is P-Value and why is it so crucial?

P-Value: What Is It?
The probability that a real-valued test statistic is at least as extreme as the value actually obtained is measured by the P-Value, also known as the probability value, in statistical hypothesis testing. Your collection of observations’ P-value indicates how likely it is that they could have happened under the null hypothesis. In statistical hypothesis testing, P-values are used to decide whether to reject the null hypothesis. The likelihood that you should reject the null hypothesis increases as the p-value decreases.

P-values are given as decimal expressions that can be translated into percentages. For instance, a p-value of 0.0237 is equal to 2.37%, which indicates that there is a 2.37% possibility that your results were accidental or random.

Alpha Level A vs. P Value The probability of getting an effect that is at least as strong as what was actually seen in the sample data is indicated by the P-value.

You can determine the likelihood of incorrectly rejecting a true null hypothesis using an alpha level. The level is determined by the researcher by deducting your level of confidence from 100 percent. For instance, if you are 95% confident in your research, the alpha level will be 5% (0.05).

Critical values and P values
You can utilise other numbers provided by your test, in addition to the P-value, to ascertain whether your null hypothesis is accurate.

You will get a p-value, an f-critical value, and an f-value, for instance, if you run an F-test in Excel to compare two variances. The f-value and f-critical value should be compared. You should reject the null hypothesis if the f-critical value is lower.

How is the P-Value determined?
P-values are typically computed manually using p-value tables, spreadsheets, or statistical tools like R, SPSS, etc.

The frequency with which the test statistic will fall under the null hypothesis will depend on the test statistic and degrees of freedom (the number of independent variables divided by the number of observations).

P-Value for Testing Hypotheses
A calculated probability is employed in the P-Value technique to hypotheses testing to determine whether there is sufficient evidence to reject the null hypothesis, also known as the conjecture. The alternative hypothesis determines if the observed population parameter differs from the population parameter value according to the conjecture, whereas the conjecture is the initial assertion regarding a data population.

In essence, the significance level is set in advance to specify the minimum P-value required to reject the null hypothesis. Readers may find it challenging to compare the findings of two distinct tests because the degrees of significance vary from one researcher to the next. P-value is helpful in this situation.

Example
A stockholder claims that the performance of their portfolio of investments is comparable to the Standard & Poor’s (S&P) 500 Index. In order to ascertain this, he does a two-tailed test.

The alternative hypothesis states that the returns of the portfolio and the returns of the S&P 500 are not equivalent, contrary to the null hypothesis, which states that the returns of the portfolio and the returns of the S&P 500 are equal.