PhD Nest

# P-value: Definition, Formula, Table and Calculation

## Definition of p –value

Calculated probabilities such as p-values can be utilised to detect the least possible level of significance for rejecting the null hypothesis.

• Under ideal circumstances, the test results will be identical to what was observed, assuming the null hypothesis is true.
• An extremely low p-value suggests that the outcome is conceivable, but unlikely.
• p-values is used instead of rejection points since they provide the lowest level of significance under which the null hypothesis is not true.
• The statistical significance of a hypothesis test is provided by the p-value.
• A p-value is primarily used to assess if the null hypothesis can be rejected or not.
• p-value may be found by using other essential statistical tests such as the t-test, Z-score, and the chi-score test, therefore it facilitates readers from around the world to speak with one another using a common language. ## p-value formula

• You can calculate p-values either by hand or with statistical software, depending on your preference.
• The z-score, t-score, or chi-square value acquired from different tests is used to calculate P-values.
• The p-value is calculated for each score after the scores have been acquired.
• For t-scores, z-scores, and chi-squares, there are p-value tables that can be used to calculate the value.
• It is possible to download the P-value Formula Excel Template and use it to calculate the p-values in spreadsheets depending on the score and the level of significance.

#### What is the best way to determine the p value?

• In order to discover the p-values, researchers must compare the test results to the p-value table for various scores.
• The p-values are derived by adding the results from the various tests in the various tables.
• If the test stats are positive, the probability which is less than the test score can be found by consulting the matching p-value table value. The p-value is obtained by multiplying the probability by two.
• It is possible to calculate the chance that a test score is greater than zero by using the p-value table, but this is rare. To get the answer, the likelihood is multiplied by two.

#### p- value  table

Tables of p-values vary depending on the hypothesis test being used.

As you can see from the table below, the p-value can be calculated using the t-score.

 P-value Decision P-value > 0.05 The result is not statistically significant and hence don’t reject the null hypothesis. P-value < 0.05 The result is statistically significant. Generally, reject the null hypothesis in favour of the alternative hypothesis. P-value < 0.01 The result is highly statistically significant, and thus rejects the null hypothesis in favour of the alternative hypothesis.

#### p- value significance

• P-values are significant because they translate the test results into a common language.
• Comparing results from two experiments can be challenging since researchers employ varying thresholds of significance when evaluating hypotheses.
• The statistical importance of the data can be inferred using p-values, which can be calculated in certain situations.
• The P-value method of hypothesis testing makes use of probability values to assess whether or not the null hypothesis should be rejected.
• P-value is a statistical significance test used to decide that a hypothesis is valid or not.
• It is possible to utilise a p-value to assess the statistical significance of research findings.

#### p-value less than 0.05

• Smaller than 0.05 p-values imply important proof that the null hypothesis is incorrect.
• The null hypothesis is thus rejected.
• As a result, the null hypothesis is rejected and the alternative hypothesis is accepted for hypothesis with p-values less than 0.05.
• This signifies that the research/findings study’s are significant statistically.

#### p-value greater than 0.05

• Weak evidence against the null hypothesis is indicated by a high p-value (> 0.05).
• Consequently, we can say that the null hypothesis is not ruled out in this situation
• Because the null hypothesis is not rejected when the p-value is greater than 0.05, the alternative hypothesis is also not accepted.
• This suggests that the study’s findings aren’t worth pursuing further.

#### When performing a t-test, how do I determine the p-value?

• The t-test must first be run to get the t-score value before calculating the p-value from the t-test.
• After then, d.f = (n-1) is used to calculate the degree of freedom.
• With the obtained degree of freedom, enter the table and read along the row until you find the closest value to the t-score.
• The probability value associated with each entry in the table is then recorded. This is the p-value for the hypothesis if it is a one-tailed hypothesis.
• The p-value for a certain t-score is obtained by doubling the probability value if the hypothesis is a two-tailed one.
• The t-score on p-value calculators can also be used to derive the p-value.

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

• The z-test must first be run to get the z-score value before calculating the p-value from the z-test.
• The z-score is then compared to the table, with the negative values of the tenth and hundredth positions of the score being compared to the table’s column and the oneth place being compared to the table’s row. If the z-score is 1.83, for example, -1.8 will be selected in the column while 0.03 will be selected in the row.
• Based on z-score, the value is found by traversing the column and row.
• The p-value is derived from the tally result and stored in a database.
• In addition, p-value calculators may deduce the z-score from the p-value to get the p-value.

#### How do you calculate the chi-square test’s p-value?

• Prior to determining the p-value from the chi-square test, the chi-square test must be conducted to determine the chi-square value. The degree of freedom is also determined while running the test using the formula d.f = (c-1)(r-1) where c and r are the number of columns and rows, respectively.
• It’s now possible to find the value of the chi-square in the chi-square distribution table by entering the acquired degree of freedom. The range of the chi-square value is used if the exact value cannot be discovered.
• The p-value is determined by taking the likelihood that each of the numeric values is true.
• Similarly, p-value calculators may derive the p-value from the t-score.

#### p-value Citations

• https://online.stat.psu.edu/statprogram/reviews/statistical-concepts/hypothesis-testing/p-value-approach
• https://www.thoughtco.com/degrees-of-freedom-in-two-way-table-3126402
• https://www.itl.nist.gov/div898/handbook/eda/section3/eda3674.htm
• https://www.investopedia.com/terms/p/p-value.asp