what is the p-value if the claim is modified to state that the proportion is equal to 0.5

Understanding P-values | Definition and Examples

Published on July 16, 2020 by Rebecca Bevans. Revised on January 7, 2021.

The p-value is a number, calculated from a statistical test, that describes how probable y'all are to take establish a item set up of observations if the null hypothesis were true.

P-values are used in hypothesis testing to aid decide whether to reject the nada hypothesis. The smaller the p-value, the more likely you are to reject the zero hypothesis.

What is a zero hypothesis?

All statistical tests accept a zippo hypothesis. For most tests, the zip hypothesis is that in that location is no human relationship between your variables of involvement or that in that location is no difference among groups.

For example, in a 2-tailed t-exam, the cipher hypothesis is that the deviation between two groups is zero.

Case: Aught and culling hypothesis

You lot want to know whether in that location is a deviation in longevity between 2 groups of mice fed on different diets, diet A and diet B. You can statistically test the deviation between these 2 diets using a two-tailed t exam.

• Null hypothesis: there is no departure in longevity between the 2 groups.
• Alternative hypothesis: there is a difference in longevity betwixt the 2 groups.

What exactly is a p-value?

The p -value, or probability value, tells you how likely it is that your data could accept occurred under the nothing hypothesis. It does this by computing the likelihood of your examination statistic, which is the number calculated by a statistical test using your data.

The p-value tells yous how often you would wait to see a exam statistic as extreme or more extreme than the one calculated past your statistical test if the cypher hypothesis of that examination was true. The p-value gets smaller as the test statistic calculated from your data gets further away from the range of test statistics predicted past the zippo hypothesis.

The p-value is a proportion: if your p-value is 0.05, that means that 5% of the time you would see a exam statistic at least as extreme every bit the one you constitute if the nix hypothesis was true.

Example: Test statistic and p-value

If the mice live equally long on either diet, then the examination statistic from your t-exam will closely match the test statistic from the aught hypothesis (that there is no difference betwixt groups), and the resulting p-value will be close to 1. It likely won't reach exactly ane, because in existent life the groups will probably not exist perfectly equal.

If, however, at that place is an average difference in longevity between the two groups, and so your test statistic will move further abroad from the values predicted by the nothing hypothesis, and the p-value will get smaller. The p-value will never reach zilch, because there's always a possibility, even if extremely unlikely, that the patterns in your data occurred by hazard.

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Encounter an example

How exercise yous calculate the p-value?

P-values are ordinarily automatically calculated by your statistical program (R, SPSS, etc.).

Y'all can also find tables for estimating the p-value of your exam statistic online. These tables show, based on the test statistic and degrees of liberty (number of observations minus number of contained variables) of your examination, how oftentimes you lot would expect to come across that examination statistic under the null hypothesis.

The calculation of the p-value depends on the statistical test you lot are using to test your hypothesis:

• Different statistical tests have different assumptions and generate different test statistics. Yous should choose the statistical test that best fits your data and matches the effect or relationship y'all want to test.
• The number of independent variables you include in your examination changes how big or small the test statistic needs to exist to generate the same p-value.

Instance: Choosing a statistical test

If you lot are comparison merely ii different diets, then a ii-sample t-test is a practiced mode to compare the groups. To compare three different diets, utilise an ANOVA instead – doing multiple pairwise comparisons will upshot in artificially low p-values and lets y'all overestimate the significance of the deviation between groups.

No thing what test yous use, the p-value always describes the same thing: how ofttimes you can wait to see a examination statistic every bit extreme or more extreme than the one calculated from your test.

P-values and statistical significance

P-values are most often used by researchers to say whether a certain pattern they accept measured is statistically pregnant.

Statistical significance is another fashion of maxim that the p-value of a statistical test is minor enough to pass up the nil hypothesis of the examination.

How small is small enough? The most common threshold is p < 0.05; that is, when you would wait to find a test statistic as extreme every bit the one calculated by your exam only five% of the fourth dimension. But the threshold depends on your subject – some fields adopt thresholds of 0.01, or even 0.001.

The threshold value for determining statistical significance is also known every bit the alpha value.

Example: Statistical significance

Your comparison of the two mouse diets results in a p-value of less than 0.01, below your blastoff value of 0.05; therefore you lot determine that in that location is a statistically meaning difference between the two diets.

Reporting p-values

P-values of statistical tests are usually reported in the results section of a research newspaper, forth with the central information needed for readers to put the p-values in context – for example, correlation coefficient in a linear regression, or the average divergence between treatment groups in a t-test.

Instance: Reporting the results

In our comparing of mouse diet A and mouse diet B, we found that the lifespan on diet A  (hateful = 2.1 years; sd = 0.12) was significantly shorter than the lifespan on nutrition B (mean = 2.6 years; sd = 0.1), with an average difference of 6 months (t(fourscore) = -12.75; p < 0.01).

Caution when using p-values

P-values are oftentimes interpreted equally your risk of rejecting the null hypothesis of your test when the zero hypothesis is really true.

In reality, the risk of rejecting the goose egg hypothesis is often higher than the p-value, especially when looking at a unmarried study or when using small sample sizes. This is because the smaller your frame of reference, the greater the chance that you stumble across a statistically significant blueprint completely by accident.

P-values are besides oft interpreted as supporting or refuting the alternative hypothesis. This is not the case. Thep-value can simply tell you whether or not the nil hypothesis is supported. It cannot tell you lot whether your alternative hypothesis is true, or why.

Frequently asked questions about p-values

How do y'all calculate a p-value?

P-values are usually automatically calculated by the program you utilise to perform your statistical test. They can also be estimated using p-value tables for the relevant test statistic.

P-values are calculated from the null distribution of the exam statistic. They tell yous how frequently a test statistic is expected to occur under the zero hypothesis of the statistical exam, based on where it falls in the null distribution.

If the test statistic is far from the mean of the aught distribution, and then the p-value volition be modest, showing that the test statistic is not probable to have occurred under the zero hypothesis.

What is statistical significance?

Statistical significance is a term used past researchers to state that it is unlikely their observations could accept occurred under the null hypothesis of a statistical test. Significance is unremarkably denoted past a p-value, or probability value.

Statistical significance is arbitrary – it depends on the threshold, or alpha value, chosen by the researcher. The most common threshold is p < 0.05, which means that the data is probable to occur less than five% of the time nether the nothing hypothesis.

When the p-value falls beneath the chosen alpha value, then we say the effect of the test is statistically meaning.

Does a p-value tell you whether your alternative hypothesis is true?

No. The p-value only tells you how probable the data yous have observed is to take occurred under the nada hypothesis.

If the p-value is beneath your threshold of significance (typically p < 0.05), then you can reject the zero hypothesis, but this does not necessarily mean that your alternative hypothesis is true.

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