A p-value is a metric used to measure the degree of statistical significance. It tells you how rare a result is compared to the null hypothesis, the idea that there is no difference between groups. A low p-value indicates that the numbers would be very unlikely to occur by chance alone and may lead researchers to believe that the null hypothesis is false.
The p-value is a measure of the chance that a particular test statistic is extreme. It is commonly written as Pr(data), H0 (hypothesis), and is expressed in the following way mentioned in the blog.
Using a p-value in the statistical analysis of data is an important part of conducting a statistical analysis. However, a p-value is expressed in decimals but usually converted to percentages. A p-value of 0.0254 means that there is a 2.54% chance that the observed values are random. The smaller the p-value is, the higher the importance of outcomes.
The p-value is a predefined significance level based on a statistical test statistic. It is not derived from the data but is chosen beforehand. A p-value of 0.001 means that the null hypothesis is not true. If the p-value is large, then the alternative hypothesis is weak. But it does not mean that the alternative hypothesis is not true.
What is the p-value?
P-Value is the probability value. It is a number that depicts the probability of obtaining results not less than the extreme of the observed effects of the hypothesis testing, presuming that the null hypothesis is valid. P-value describes the likelihood of our data being occurred just by chance.
You must understand the null hypothesis and hypothesis testing to understand the p-value.
What is hypothesis testing?
A hypothesis is a sophisticated guess based on observed data. A data analyst or scientist is required to draw insights from a given data. To test his result, he makes a hypothesis statement with design criteria. This statement is tested either by experiment or observation. Researchers usually establish it based on prior research and their knowledge. A hypothesis statement has ‘if’ and ‘then.’ It also includes both dependent and independent variables.
Hypothesis testing is used to determine whether the results were coincidental or correct. If the results happened just by chance, you can reject the hypothesis and move on to the valid results.
There are two types of hypotheses:
- Null hypothesis
- Alternative hypothesis
What is a Null hypothesis?
A null hypothesis is an idea that nothing is happening or zero. In other technical words, a null hypothesis is a statement that states that there is no statistical significance in the given set of data. Also, there is no association between the two groups of dependant and independent variables.
A null hypothesis is by default true until there is proof to deny its veracity. It assumes that whatever we are trying to prove did not happen. The null hypothesis intends to test the validity of the data, and H₀ denotes it.
What is an alternative hypothesis?
This hypothesis comes into the picture when the null hypothesis gets rejected. It is the opposite of the null hypothesis. It says that the dependent variable depends on the independent variable. And it says that whatever we are trying to prove happened, not just by chance. It is denoted by
Let’s consider an example. The problem statement: If group 1 has blood type O positive and group 2 has blood type O negative. Is there any significant difference in the blood pressure between group 1 and group 2?
The null hypothesis of the above problem will say that there is no difference in the blood pressures of group 1 and group 2.
On the other hand, the alternative hypothesis will say that there is a difference in the blood pressures of group 1 and group 2 since they have different blood groups.
How to calculate the p-value?
It is calculated using statistical programs on your data. There are also tables for the estimation of p-values. Based on the degree of freedom and test statistic, these tables show how frequently the test statistics are under the null hypothesis.
The p-value can also be calculated mathematically, using integral calculus, from the area under the probability distribution curve for all data points. The data points should be at least as distant from the reference value as the observed value.
The calculation of the p-value depends on the statistical test and the number of independent variables you choose and include. P-value is the statistical significance that lies between 0 and 1.
P-value is generally written in points like 0.023 or 0.67. To understand it better, you should convert it into a percentage. Now it is 2.3%, which is quite nominal, right? So there is only 2.3% evidence in the favor or null hypothesis. On the other hand, 0.67 is 67%, which is a considerable amount that will lead to the failure of rejection of the null hypothesis.
The null hypothesis is rejected if the p-value is less than the threshold value. This threshold value is referred to as the alpha level or significance level. The researcher predefines this alpha level before examining the data, and the most common alpha value is 0.05.
P-value ≤ 0.05
A P-value less than 0.05 is statistically significant. It shows that there is less than a 5% probability that the null hypothesis is valid. It indicates strong evidence against the null hypothesis. Thus, it forms the base of the rejection of the null hypothesis. However, this does not give any proof that the alternative hypothesis is true.
Just as a p-value less than 0.05 is statistically significant, a p-value less than 0.001 is statistically highly significant. It shows that there is only one possibility out of 1000 observations that the null hypothesis is true. So, this is regarded as the rarest chance or just a random happening. And in this case, the null hypothesis is undoubtedly rejected.
P-value ≥ 0.05
P-value more than 0.05 is not statistically significant. It shows more than a 5% probability that the null hypothesis is valid. It indicates strong evidence in favor of the null hypothesis. So, in this case, one has failed to reject the null hypothesis.
There is no such thing as acceptance of a null hypothesis. You can only reject or fail to reject the null hypothesis. 5% probability serves as the threshold value for the rejection or failure of rejection of the null hypothesis.
What are the factors affecting the p-value?
- Size of the sample: The larger the sample, the more the likelihood of detecting a difference.
- Spread of the data: The spread of observations in a data set is commonly measured with standard deviation. The bigger the standard deviation, the more the spread of observations and the lower the P value.
What is the significance of the p-value?
P-value serves as the rejection point to render the slightest degree of significance at which you would rule out the null hypothesis.
The smaller the p-value, the stronger the indication favoring the alternative hypothesis.
P-value can not establish that the research hypothesis is correct because it requires 100% certainty. It only provides evidence in support or against the research hypothesis.
Conclusion
P-value plays a crucial role in statistical analysis. It is used in hypothesis testing. It can assist you in deciding whether you should reject the null hypothesis or not. The smaller the p-value, the more the likelihood of rejecting the null hypothesis.
The hypothesis is an educated guess you make during your research or analysis based on your observations. There are two types of hypothesis, null hypothesis, and alternative hypothesis. The null hypothesis assumes that your research statement is incorrect and your results are just by chance. The alternative hypothesis is just the opposite of that.
P-value does not approve or validate your alternative hypothesis. It can just form the basis of rejection of the null hypothesis. Rejecting the null hypothesis does not mean that the null hypothesis is false, and the alternative hypothesis is true. P-value does not establish the probability of the hypothesis. It can only help you in moving forward in the analysis.
