# P-value- definition, formula, table, finding p-value, significance

## p-value definition

The p-value or the calculated probability is the best probability to provide the smallest level of significance at which the null hypothesis is not true.

• It is the best-case scenario under which the test results will be the same as the results actually observed under the condition that the null hypothesis is correct.
•  A small p-value indicates the result is possible but not very likely under the null hypothesis.
• P-value works as an alternate for the rejections point as they provide the smallest level of significance under which the null hypothesis is not true.
• P-value provides the statistical significance to the results of a hypothesis testing.
• The primary interpretation of the p-value is to test whether there is enough evidence to reject the null hypothesis.
• Because p-value can be obtained from all other important statistical tests like the t-test, the z-score, and the chi-score test, it helps to provide a universal language for readers from all over the world. ## p-value formula

• P-values are calculated either manually from the p-value tables or through spreadsheets or statistical software.
• P-values are calculated from the z-score, t-score, or chi-square value obtained from various tests.
• Once the scores are obtained, the values are used to determine the p-value for that specific score.
• There are p-value tables for t-score, z-score, and chi-square which can be used to determine the value from the respective scores.
• In spreadsheets, P-value Formula Excel Template can be downloaded for Excel to determine the p-values based on the score and the level of significance.

## How to find p-value?

• P-values are found by comparing the test scores against the p-value table for different scores.
• The scores calculated from the corresponding tests are then tallied in the respective tables to determine the p-values.
• In the case where the test statics in positive, the probability that is less than the test score is determined from the corresponding value on the p-value table. This probability is then doubled to find the p-value.
• In the case where the test statics is negative, the probability greater than the test score is determined from the corresponding value on the p-value table. This probability is then doubled to get the result.

## p-value table

P-value tables are different for different tests that are performed for hypothesis testing.

The table below is the p-value table to obtain the p-value from the t-score. The table below is the table for p-value from z-score. The table below is the p-value table from chi-square values. ## p-value significance

• P-values are important as they provide a universal language to the test results.
• As different researchers use different levels of significance while testing a hypothesis, it might be difficult to compare the result from two tests.
• In such cases, p-values can be determined and used to interpret the statistical significance of the results.
• The P-value approach to hypothesis testing uses the probability values to determine if there is enough evidence to reject the null hypothesis.
• P-value is considered as a test to determine the statistical significance of the hypothesis.
• A p-value is a number between 0 and 1 that can be used to determine the statistical significance of the results can be interpreted.

### p-value less than 0.05

• If the p-value is small (< 0.05), it indicates a piece of strong evidence against the null hypothesis.
• As a result, the null hypothesis is rejected.
• Thus for a hypothesis with a p-value less than 0.05, the null hypothesis is rejected, and the alternative hypothesis is accepted.
• This means that the results of the research/ study are statistically significant.

### p-value greater than 0.05

•  If the p-value is large (> 0.05), it indicates weak evidence against the null hypothesis.
• As a result, the null hypothesis is not rejected.
• Thus for a hypothesis with a p-value greater than 0.05, the null hypothesis is not rejected, and the alternative hypothesis is not accepted.
• This means that the results of the research/ study are not statistically significant.

## How to find p-value from t-test?

• In order to find the p-value from the t-test, at first, the t-test is to be performed to obtain the t-score value.
• Then the degree of freedom is determined as d.f = (n-1) where n is the number of samples.
• After entering the table with the obtained degree of freedom and reading along the row, the value closest to the t-score is found.
• The value of probability corresponding to the value from the table is then noted down. If it is a one-tailed hypothesis, this value is the p-value for the hypothesis.
• Now, if the hypothesis is a two-tailed hypothesis, the probability value is then doubled to obtain the p-value for the particular t-score.
• Additionally, the p-value can also be derived from the t-score on p-value calculators.

## How to find p-value from z-test?

• In order to find the p-value from the z-test, at first, the z-test is to be performed to obtain the z-score value.
• The z-score obtained is then tallied against the table where the negative of the tenth and hundredth position of the score is tallied against the column of the table while the oneth position is tallied against the row.  For, e.g., if the z-score is 1.83, -1.8 is selected on the column while 0.03 is selected on the row.
• The value is found after moving through the column and row based on the value of the z-score.
• The number obtained after the tally is then collected as the p-value.
• Besides, the p-value can also be derived from the z-score on p-value calculators.

## How to find the p-value from the chi-square test?

• In order to find the p-value from the chi-square test, at first, the chi-square test is to be performed to obtain the chi-square value. While performing the test, the degree of freedom is also calculated by the formula, d.f = (c-1)(r-1) where c is the number of columns and r is the number of rows.
• Now the chi-square distribution table is entered, with the obtained degree of freedom, and the value of the chi-square is found in the table. If the exact value is not found, we select the range between which the chi-square value lies.
• The probability corresponding to those values is then selected as the p-value.
• Similarly, the p-value can also be derived from the t-score on p-value calculators.

## References and Sources

• C.R. Kothari (1990) Research Methodology. Vishwa Prakasan. India.
• 2% – https://online.stat.psu.edu/statprogram/reviews/statistical-concepts/hypothesis-testing/p-value-approach
• 1% – https://www.thoughtco.com/degrees-of-freedom-in-two-way-table-3126402
• 1% – https://www.itl.nist.gov/div898/handbook/eda/section3/eda3674.htm
• 1% – https://www.investopedia.com/terms/p/p-value.asp
• 1% – https://towardsdatascience.com/hypothesis-testing-in-3-steps-c23789e92a09
• 1% – https://towardsdatascience.com/how-to-understand-p-value-in-layman-terms-80a5cc206ec2
• 1% – https://sixsigmastats.com/null-and-alternative-hypothesis/