The field of statistics consists of many ways researchers can prove their hypotheses through numbers and calculations. A very popular method is hypothesis testing, which confronts a null hypothesis with an alternative hypothesis. In some tests you need to compare the significance level to the p-value. The following article revolves around this p-value, its calculation, use, and explanation through an elaborate example.
P-value in a nutshell
The p-value is a statistical measurement that is compared to the significance level to determine whether the null hypothesis should be accepted or rejected.
Definition: P-value
The p-value, which is short for probability value, plays a major role in hypothesis testing, where it decides over accepting or rejecting the null hypothesis. This value is rarely calculated by hand. It generally requires statistical programs, which use the information gathered in the experiment. The probability value is then compared to the previously set significance level. If the p-value is lower than the significance level, the null hypothesis has to be rejected.
Note: The p-value can easily be misinterpreted or misused, which is why many researchers prefer other methods to argue about their null and alternative hypothesis.
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Significance level
The significance level α is a statistical measurement that indicates the probability of rejecting the null hypothesis when it is actually correct. The lower the percentage, the stronger the evidence for or against each hypothesis has to be.
As a standard, the significance level is usually set to 5%, which equals a 5% chance of agreeing with the wrong hypothesis. Depending on your research, a significance level of 10% is also possible, as well as even 1%, which is often used in medical studies since high precision is required.
Technically, as a researcher, you can choose your significance level, even 3%, 12%, or 35%; it is up to your choice. However, the higher the level, the less reliable the findings. Standard significance levels protect you against the accusation of moulding the value into your study to prove your hypothesis, which is considered research bias.
Calculating the p-value
Statistical programmes and software like R and SPSS exist for automatically calculating p-values. Moreover, several tables for approximating the probability value exist online.
The tables depend on the test statistics and degrees of freedom of your test to show how frequently you would anticipate seeing a similar test statistic in the presented null hypothesis.
Note: The probability value calculation usually is contingent on the applied statistical test for hypothesis testing.
This is because:
- Different statistical tests have varying assumptions.
- The quantity of independent variables you have in your test usually changes the size of the test statistic you need to generate the same probability value.
The calculation of the p-value furthermore depends on the method used for hypothesis testing, such as:
- t-Test
- Correlation analysis
- Chi-Square Test
- Linear regression analysis
Use
The p-value is used in hypothesis testing to determine whether the null hypothesis can be rejected or accepted. Therefore, the probability value is compared to the significance level. If the p-value is lower than the significance level, the null hypothesis can be rejected. If not, the null hypothesis has to be accepted or further tested.
For conducting a test and using the p-value, it is necessary to know whether your research is built as a two-tailed test or a one-tailed one. In a one-tailed test, the expectations of the alternative hypothesis only go in one direction, either higher or lower than the null hypothesis. A two-tailed test, on the other hand, has the alternative hypothesis cover both sides outside the null area.
Example
The following example summarizes the previous information.
Example
You want to determine if there is a disparity in lifespan between two groups of rabbits fed on different diets.
- You can label the two diets as X and Y.
- Using a two-tailed statistic test, you can test the difference between diets X and Y.
If the rabbits in your test live longer on either diet, then your test statistic from your test will meticulously match the null hypothesis’ test statistic. Therefore, the subsequent p-value will be near 1 (not exactly one).
In contrast, if there is a variance in the lifespan between the two groups, your test statistic will be more distant from the predicted null hypothesis value. Therefore, the p-value will be on the smaller side.
However, the probability value will never be zero because even in extreme cases, there is a plausibility that the series of observations in your observed data could potentially have occurred coincidentally.
Your comparison of the rabbit results gives you a probability value of less than 0.02. This value is lower than your threshold value of 0.05, meaning that there is a statistically noteworthy variance between the diets. Therefore, the null hypothesis, assuming that the diets do not have any effect, can be rejected.
FAQs
It means that you can anticipate to discover a test statistic as extreme as the one derived by your test only 1 percent of the time.
It is a probability value that tells you how likely your collected figures would have happened under the assumption that your null hypothesis of your study is true.
You can use automatic probability value-calculating programmes or software. The calculation technique depends on the test statistic chosen for your study.
A probability value below the significance threshold (usually p > 0.05) means you can cast off the null hypothesis. However, it does not nasty that the alternative hypothesis is true.
The p-value helps determine whether to accept or reject the null hypothesis. If the p-value is smaller than the significance level, the null hypothesis can be rejected. Otherwise it has to be accepted.
