p-value definition

The p-value, or calculated probability, is the likelihood that provides the least significant level during which the null hypothesis is not true.

• In the best-case scenario, if the null hypothesis is true, the test findings will match the outcomes that were actually observed.
• A low p-value denotes the possibility of the outcome, but not its likelihood under the null hypothesis.
• The minimum significance level below which the null hypothesis cannot be true is provided by the p-value, which serves as a substitute for the reject point.
• The p-value indicates the statistical significance of a hypothesis test’s results.
• The primary function of the p-value is to evaluate if sufficient evidence exists to reject the null hypothesis.
• p-value may be obtained from all other important statistical tests, such as the t-test, the z-score, and the chi-score test, which contribute to the creation of a universal language for readers throughout the world.

p-value formula

• P-values can be manually calculated using the p-value tables, using spreadsheets, or by using statistical software.
• P-values are derived from the results of various tests using the z-score, t-score, or chi-square value.
• After acquiring the scores, the values are used to determine the p-value for every score.
• To determine the value from the corresponding scores, use the p-value tables for the t-score, z-score, and chi-square.
• To calculate the p-values in spreadsheets depending on the score and degree of significance, download the P-value Formula Excel Template.

How to find the p-value?

• Values are calculated by comparing test findings to a database containing the p-values for several test outcomes.
• The p-values are then obtained by adding the scores computed from the appropriate tests in the corresponding tables.
• In the case where the test statistics remain positive, the probability that is less than the test score is derived from the corresponding number on the p-value table. The p-value is then calculated by doubling this probability.
• In the event that the test statistics are negative, the probability of exceeding the test score is computed using the corresponding number from the p-value table. The outcome is then obtained by doubling this probability.

p-value table

Various tests used for hypothesis testing have different P-value tables.

p-value significance

• Values are significant because they give a consistent vocabulary for test outcomes.
• It could be challenging to compare the results of two studies, since different researchers employ various thresholds of significance when evaluating a hypothesis.
• In these circumstances, p-values can be calculated and applied to assess the data’s statistical significance.
• The probability values are used in the P-value method of hypothesis testing to assess whether there is sufficient data to deny the null hypothesis.
• P-value is considered a test to determine the statistical significance of a hypothesis.
• A p-value is a number between 0 and 1 which may be utilized to evaluate the statistical significance of the data.

p-value less than 0.05

• The null hypothesis is refuted by strong evidence if the p-value is modest (0.05).
• The null hypothesis is thus disproved.
• The additional hypothesis is thus accepted if the p-value for the null hypothesis is less than 0.05.
• This indicates that the research’s or study’s findings are statistically significant.

p-value greater than 0.05

• The null hypothesis has weak evidence against it if the p-value is high (> 0.05).
• The null hypothesis is thus not disproved.
• The null hypothesis is not disproved, and the alternative hypothesis is not accepted for a hypothesis with a p-value higher than 0.05.
• This indicates that the research’s or study’s findings are not statistically significant.

How to find p-value from t-test?

• The t-test must first be run to determine the t-score value in order to determine the p-value from the t-test.
• When n is the number of samples, d.f = (n-1) is used to calculate the degree of freedom.
• Entering the table with the obtained degree of freedom and going along the column reveals the value that is closest to the t-score.
• The probability value that corresponds to the value from the table is then recorded. This figure represents the p-value for the hypothesis in the case of a one-tailed hypothesis.
• The probability value is now divided by two to get the p-value for the specific t-score if the hypothesis is a two-tailed one.
• On p-value calculators, the t-score may also be used to get the p-value.

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

• First, the z-test must be run to determine the z-score value in order to determine the p-value from the z-test.
• The acquired z-score is then compared to the table, with the one position being compared to the row and the negative of the tenth and hundredth positions being compared to the column. For instance, if the z-score is 1.83, -1.8 is chosen for the column and 0.03 for the row.
• On the basis of the z-score value, the value is discovered after traversing the column and row.
• The p-value is then calculated using the result of the tally.
• On p-value calculators, the z-score may also be used to get the p-value.

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

• The chi-square test must first be run to determine the chi-square value in order to determine the p-value from the chi-square test. The formula d.f = (c-1) (r-1) is used to determine the degree of freedom when running the test, where c denotes the number of columns and r is the number of rows.
• The gained degree of freedom is now entered into the chi-square distribution table, and the value of the chi-square is discovered in the table. In the absence of an exact number, we choose the range in which the chi-square value falls.
• The p-value is then chosen to be the probability corresponding to those values.
• On p-value calculators, the t-score may also be used to get the p-value.

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/