P-value calculator: How to calculate p-value
Is your data sufficient to reject the null hypothesis? Calculate p-value with our calculator.
P-value calculator
Z Score
Test Type
Significance Level
The p-value is
0
The result is not significant at p ≥
0.05
Picture this: you're diving deep into the world of analytics and statistics, trying to make sense of all those numbers and data points. Suddenly, you stumble upon a little gem called the p-value. It's like a secret code that researchers use to unlock the mysteries of hypothesis testing and significance.
The primary use of the p-value is for decision-making in hypothesis testing. It helps researchers assess if the observed data is enough to reject the null hypothesis for an alternative hypothesis. Researchers also use the p-value to compare groups or test for correlations.
Gather answers using the SurveyMonkey p-value calculator above.
What is a p-value?
The p-value stands for probability value. It measures the likelihood of a result, assuming the null hypothesis is true. It's a probability gauge showing how likely your result is, assuming no real difference (the null hypothesis).
The p-value quantifies the strength of evidence against the null hypothesis. It is typically compared to a predetermined level of significance, such as 0.05. When the p-value is low, it tells you, "This result probably didn't happen by chance!" This gives you the green light to reject the null hypothesis and consider that your hypothesis might be true.
The p-value is important because researchers use it to decide whether to accept or reject the null hypothesis. Some examples of research questions that can use the p-value are:
- “Do men and women differ in customer satisfaction?”
- “Is satisfaction with training programs associated with employee satisfaction?”
A low p-value suggests there are differences among the groups you tested. It also indicates that real, predictable relationships among variables may exist.
Researchers can then interpret the significance of their findings and communicate the strength of evidence to stakeholders and peers.
How to calculate p-value
To calculate a p-value, first determine the probability of obtaining your data if the null hypothesis were true. Then, compare this probability to your chosen significance level (usually 0.05) to decide if your results are statistically significant.
Calculate the p-value from z-score
To calculate a p-value from a z-score, look up the z-score in a standard normal distribution table. Alternatively, use software to find the corresponding probability. This probability represents the likelihood of observing a value as extreme as the z-score under the null hypothesis.
The following formulas give the p-value:
- Left-tailed z-test: p-value = P(Zscore)
- Right-tailed z-test: p-value = 1 - P(Zscore)
- Two-tailed z-test: p-value = 2 × P(−|Zscore|) or 2 - 2 × P(|Zscore|)
Here’s the step-by-step guide on how to calculate the p-value from a z-score:
- Understand the problem: You have data and want to know how likely it is to get that result. You also want to see how likely something more extreme would be, assuming the null hypothesis is true.
- Find the z-score: Start by finding the z-score of your data. This tells you how many standard deviations away from the mean your data point is. Find your z-score by leveraging statistical software (like R or SPSS) or look up the deviation in a table (like this one).
- Determine the direction: Choose a one-tailed test (extreme values in one direction) or a two-tailed test (in both directions). If you expect the difference to be significantly smaller or larger, use a one-tailed test—the left- or right-tailed test. If you don’t have a hypothesis about which direction the difference will be, use a two-tailed test.
- Look up the z-score: Using a standard normal table, software, or a p-value calculator, find the cumulative probability.
- Calculate the p-value by leveraging the p-value calculator above or:
- For a one-tailed test: If the z-score is positive (right-tailed test), subtract the cumulative probability from 1. If the z-score is negative (left-tailed test), use the cumulative probability directly.
- For a two-tailed test: Double the cumulative probability to account for both tails. Then, subtract it from 1 if the z-score is positive.
- Interpret the p-value: If the p-value is very small (usually less than 0.05), it suggests that your data is unlikely under the null hypothesis, indicating statistical significance. You can also use our p-value calculator above to interpret the p-value based on the confidence level.
Calculate the p-value from t-score
To calculate a p-value from a t-score, first, determine the t-score representing the difference between your sample mean and the population mean. Then, use a t-distribution table or software to find the probability of observing that t-score. This indicates the likelihood of obtaining your sample results under the null hypothesis.
The following formula gives the p-value from the t-score.
- Left-tailed t-test: p-value = cdft,d(tscore)
- Right-tailed t-test: p-value = 1 - cdft,d(tscore)
- Two-tailed t-test: p-value = 2 × cdft,d(−|tscore|) or p-value = 2 - 2 × cdft,d(|tscore|)
Where cdft,d represents the cumulative distribution function of the t-Student distribution with d degrees of freedom.
Here’s the step-by-step guide on how to calculate the p-value from a t-score:
- Understand the situation: You have sample data and want to know how likely it is to get your results. This assumes there's no actual difference in the population.
- Calculate the t-score: This measurement tells you how different your sample mean is from the population mean.
- Determine degrees of freedom: This is based on your sample size. It helps you look up the correct probability in the t-distribution table.
- Check the t-distribution table: Look up your calculated t-score in the table. This provides the probability of observing that difference or more if there is no actual difference in the population.
- Interpret the result: If the p-value is very small, your sample results are unlikely under the null hypothesis. This suggests your results might be significant.
Calculate the p-value from the Pearson Correlation
To obtain the p-value for a Pearson correlation coefficient, first use the calculated coefficient to derive a t-statistic. Then, you can find its associated p-value using the t-distribution with degrees of freedom (n - 2).
The formula to get the t-statistic from a Pearson correlation coefficient is below:
Where:
- r is the Pearson correlation coefficient.
- n is the sample size.
After obtaining the z-score, you can calculate the p-value using the cumulative distribution function of the t-distribution. This uses n - 2 degrees of freedom, where n is the sample size.
Here's the general process:
- Understand the situation: You have some sample data and want to see if two variables are correlated.
- Calculate the t-statistic: Convert the correlation coefficient (r) to a t-statistic using the formula above.
- Determine the degrees of freedom: Calculate the degrees of freedom (df). Use the formula 𝑑𝑓 = n - 2, where n is the sample size.
- Find the p-value: Once you have the t-statistic and degrees of freedom, you can use a t-distribution table or a statistical software package to find the p-value associated with the calculated t-statistic.
- Interpret the result: If the p-value is less than your chosen significance level (commonly 0.05), you reject the null hypothesis and conclude that there is a statistically significant correlation between the two variables. Otherwise, you fail to reject the null hypothesis.