Watch the video for an overview of the p-value:
Watch this video on YouTube.
Can’t see the video? Click here.
A p value is used in hypothesis testing to help you support or reject the null hypothesis. The p value is the evidence against a null hypothesis. The smaller the p-value, the stronger the evidence that you should reject the null hypothesis.
P values are expressed as decimals although it may be easier to understand what they are if you convert them to a percentage. For example, a p value of 0.0254 is 2.54%. This means there is a 2.54% chance your results could be random (i.e. happened by chance). That’s pretty tiny. On the other hand, a large p-value of .9(90%) means your results have a 90% probability of being completely random and not due to anything in your experiment. Therefore, the smaller the p-value, the more important (“significant“) your results.
When you run a hypothesis test, you compare the p value from your test to the alpha level you selected when you ran the test. Alpha levels can also be written as percentages.
Graphically, the p value is the area in the tail of a probability distribution. It’s calculated when you run hypothesis test and is the area to the right of the test statistic (if you’re running a two-tailed test, it’s the area to the left and to the right).
P Value vs Alpha level
Alpha levels are controlled by the researcher and are related to confidence levels. You get an alpha level by subtracting your confidence level from 100%. For example, if you want to be 98 percent confident in your research, the alpha level would be 2% (100% – 98%). When you run the hypothesis test, the test will give you a value for p. Compare that value to your chosen alpha level. For example, let’s say you chose an alpha level of 5% (0.05). If the results from the test give you:
P Values and Critical Values
The p value is just one piece of information you can use when deciding if your null hypothesis is true or not. You can use other values given by your test to help you decide. For example, if you run an f test two sample for variances in Excel, you’ll get a p value, an f-critical value and a f-value.
In the above image, the results from the f-test show a large p value (.244531, or 24.4531%), so you would not reject the null. However, there’s also another way you can decide: compare your f-value with your f-critical value. If the f-critical value is smaller than the f-value, you should reject the null hypothesis. In this particular test, the p value and the f-critical values are both very large so you do not have enough evidence to reject the null.
What if I Don’t Have an Alpha Level?
In an ideal world, you’ll have an alpha level. But if you do not, you can still use the following rough guidelines in deciding whether to support or reject the null hypothesis:
- If p > .10 → “not significant”
- If p ≤ .10 → “marginally significant”
- If p ≤ .05 → “significant”
- If p ≤ .01 → “highly significant.”
How to Calculate a P Value on the TI 83
To get the p-value on a TI 83, run a hypothesis test. Watch the video for the steps:
Calculate a P Value on the TI 83
Watch this video on YouTube.
Can’t see the video? Click here.
Example question:The average wait time to see an E.R. doctor is said to be 150 minutes. You think the wait time is actually less. You take a random sample of 30 people and find their average wait is 148 minutes with a standard deviation of 5 minutes. Assume the distribution is normal. Find the p value for this test.
- Press STAT then arrow over to TESTS.
- Press ENTER for Z-Test.
- Arrow over to Stats. Press ENTER.
- Arrow down to μ0 and type 150. This is our null hypothesis mean.
- Arrow down to σ. Type in your std dev: 5.
- Arrow down to xbar. Type in your sample mean: 148.
- Arrow down to n. Type in your sample size: 30.
- Arrow to <μ0 for a left tail test. Press ENTER.
- Arrow down to Calculate. Press ENTER. P is given as .014, or about 1%.
The probability that you would get a sample mean of 148 minutes is tiny, so you should reject the null hypothesis.
Note: If you don’t want to run a test, you could also use the TI 83 NormCDF function to get the area (which is the same thing as the probability value).
References
Dodge, Y. (2008). The Concise Encyclopedia of Statistics. Springer.
Gonick, L. (1993). The Cartoon Guide to Statistics. HarperPerennial.
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{"appState":{"pageLoadApiCallsStatus":true},"articleState":{"article":{"headers":{"creationTime":"2016-03-26T15:32:55+00:00","modifiedTime":"2022-08-10T17:20:31+00:00","timestamp":"2022-08-10T18:01:05+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"//dummies-api.dummies.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Math","_links":{"self":"//dummies-api.dummies.com/v2/categories/33720"},"slug":"math","categoryId":33720},{"name":"Statistics","_links":{"self":"//dummies-api.dummies.com/v2/categories/33728"},"slug":"statistics","categoryId":33728}],"title":"How to Calculate a P-Value When Testing a Null Hypothesis","strippedTitle":"how to calculate a p-value when testing a null hypothesis","slug":"how-to-determine-a-p-value-when-testing-a-null-hypothesis","canonicalUrl":"","seo":{"metaDescription":"Learn how to come up with a p-value (a probability associated with your critical value) by using z-tables.","noIndex":0,"noFollow":0},"content":"In statistics, when you <a href=\"//www.dummies.com/education/math/statistics/how-to-set-up-a-hypothesis-test-null-versus-alternative/\" target=\"_blank\" rel=\"noopener\">test a hypothesis</a> about a <a href=\"//www.dummies.com/education/math/statistics/how-to-test-a-null-hypothesis-based-on-one-population-proportion/\" target=\"_blank\" rel=\"noopener\">population</a>, you find a p-value and use your test statistic to decide whether to reject the null hypothesis, H<sub>0</sub>.\r\n\r\nA <a href=\"//www.dummies.com/article/academics-the-arts/math/statistics/what-a-p-value-tells-you-about-statistical-data-169734/\" target=\"_blank\" rel=\"noopener\"><em>p-value</em></a> is a probability associated with your critical value. The critical value depends on the probability you are allowing for a Type I error. It measures the chance of getting results at least as strong as yours if the claim (H<sub>0</sub>) were true.\r\n\r\nThe following figure shows the locations of a test statistic and their corresponding conclusions.\r\n<div class=\"imageBlock\" style=\"width: 535px;\">\r\n\r\n[caption id=\"\" align=\"alignnone\" width=\"535\"]<img src=\"//sg.cdnki.com/how-to-calculate-p-value-in-research---aHR0cHM6Ly93d3cuZHVtbWllcy5jb20vd3AtY29udGVudC91cGxvYWRzLzM2MjUyMS5pbWFnZTAuanBn.webp\" alt=\"\"Decisions\" width=\"535\" height=\"213\" /> Decisions for Ha: not-equal-to[/caption]\r\n\r\n<div class=\"imageCaption\"></div>\r\n</div>\r\nNote that if the alternative hypothesis is the less-than alternative, you reject H<sub>0</sub> only if the test statistic falls in the left tail of the distribution (below –2). Similarly, if H<sub>a</sub> is the greater-than alternative, you reject H<sub>0</sub> only if the test statistic falls in the right tail (above 2).\r\n\r\nTo find the<i> p-</i>value for your test statistic:\r\n<ol class=\"level-one\">\r\n \t<li>\r\n<p class=\"first-para\">Look up your test statistic on the appropriate distribution — in this case, on the standard normal (<i>Z-</i>) distribution (see the following <i>Z</i>-tables).<img class=\"alignnone wp-image-287021 size-full\" src=\"//sg.cdnki.com/how-to-calculate-p-value-in-research---aHR0cHM6Ly93d3cuZHVtbWllcy5jb20vd3AtY29udGVudC91cGxvYWRzL3otc2NvcmUtdGFibGUtMS5wbmc=.webp\" alt=\"z-score table 1\" width=\"535\" height=\"933\" />\r\n<img class=\"alignnone wp-image-287022 size-full\" src=\"//sg.cdnki.com/how-to-calculate-p-value-in-research---aHR0cHM6Ly93d3cuZHVtbWllcy5jb20vd3AtY29udGVudC91cGxvYWRzL3otc2NvcmUtdGFibGUtMi5wbmc=.webp\" alt=\"z-score table 2\" width=\"535\" height=\"912\" /></p>\r\n</li>\r\n \t<li>\r\n<p class=\"first-para\">Find the probability that <i>Z</i> is beyond (more extreme than) your test statistic:</p>\r\n\r\n<ol class=\"level-two\">\r\n \t<li>\r\n<p class=\"first-para\">If H<sub>a</sub> contains a less-than alternative, find the probability that <i>Z</i> is less than your test statistic (that is, look up your test statistic on the <i>Z</i>-table and find its corresponding probability). This is the<i> p-</i>value. (Note: In this case, your test statistic is usually negative.)</p>\r\n</li>\r\n \t<li>\r\n<p class=\"first-para\">If H<sub>a</sub> contains a greater-than alternative, find the probability that <i>Z</i> is greater than your test statistic (look up your test statistic on the <i>Z</i>-table, find its corresponding probability, and subtract it from one). The result is your<i> p-</i>value. (Note: In this case, your test statistic is usually positive.)</p>\r\n</li>\r\n \t<li>\r\n<p class=\"first-para\">If H<sub>a</sub> contains a not-equal-to alternative, find the probability that <i>Z</i> is beyond your test statistic and double it. There are two cases:</p>\r\n<p class=\"child-para\">If your test statistic is negative, first find the probability that <i>Z</i> is less than your test statistic (look up your test statistic on the <i>Z</i>-table and find its corresponding probability). Then double this probability to get the<i> p-</i>value.</p>\r\n<p class=\"child-para\">If your test statistic is positive, first find the probability that <i>Z </i>is greater than your test statistic (look up your test statistic on the <i>Z</i>-table, find its corresponding probability, and subtract it from one). Then double this result to get the<i> p-</i>value.</p>\r\n</li>\r\n</ol>\r\n</li>\r\n</ol>\r\nSuppose you are testing a claim that the percentage of all women with varicose veins is 25%, and your sample of 100 women had 20% with varicose veins. Then the sample proportion p=0.20. The standard error for your sample percentage is the square root of p(1-p)/n which equals 0.04 or 4%. You find the test statistic by taking the proportion in the sample with varicose veins, 0.20, subtracting the claimed proportion of all women with varicose veins, 0.25, and then dividing the result by the standard error, 0.04.\r\n\r\nThese calculations give you a test statistic (standard score) of –0.05 divided by 0.04 = –1.25. This tells you that your sample results and the population claim in H<sub>0</sub> are 1.25 standard errors apart; in particular, your sample results are 1.25 standard errors below the claim.\r\n\r\nWhen testing H<sub>0</sub>:<i> p </i>= 0.25 versus H<sub>a</sub>:<i> p </i>< 0.25, you find that the<i> p-</i>value of -1.25 by finding the probability that Z is less than -1.25. When you look this number up on the above <i>Z</i>-table, you find a probability of 0.1056 of Z being less than this value.\r\n\r\nNote: If you had been testing the two-sided alternative,\r\n\r\n<img src=\"//sg.cdnki.com/how-to-calculate-p-value-in-research---aHR0cHM6Ly93d3cuZHVtbWllcy5jb20vd3AtY29udGVudC91cGxvYWRzLzM2MjUyNC5pbWFnZTMucG5n.webp\" alt=\"image3.png\" width=\"91\" height=\"24\" />\r\n\r\nthe <i>p</i>-value would be 2 ∗ 0.1056, or 0.2112.\r\n<p class=\"Warning\">If the results are likely to have occurred under the claim, then you fail to reject H<sub>0</sub> (like a jury decides not guilty). If the results are unlikely to have occurred under the claim, then you reject H<sub>0</sub> (like a jury decides guilty).</p>","description":"In statistics, when you <a href=\"//www.dummies.com/education/math/statistics/how-to-set-up-a-hypothesis-test-null-versus-alternative/\" target=\"_blank\" rel=\"noopener\">test a hypothesis</a> about a <a href=\"//www.dummies.com/education/math/statistics/how-to-test-a-null-hypothesis-based-on-one-population-proportion/\" target=\"_blank\" rel=\"noopener\">population</a>, you find a p-value and use your test statistic to decide whether to reject the null hypothesis, H<sub>0</sub>.\r\n\r\nA <a href=\"//www.dummies.com/article/academics-the-arts/math/statistics/what-a-p-value-tells-you-about-statistical-data-169734/\" target=\"_blank\" rel=\"noopener\"><em>p-value</em></a> is a probability associated with your critical value. The critical value depends on the probability you are allowing for a Type I error. It measures the chance of getting results at least as strong as yours if the claim (H<sub>0</sub>) were true.\r\n\r\nThe following figure shows the locations of a test statistic and their corresponding conclusions.\r\n<div class=\"imageBlock\" style=\"width: 535px;\">\r\n\r\n[caption id=\"\" align=\"alignnone\" width=\"535\"]<img src=\"//www.dummies.com/wp-content/uploads/362521.image0.jpg\" alt=\"\"Decisions\" width=\"535\" height=\"213\" /> Decisions for Ha: not-equal-to[/caption]\r\n\r\n<div class=\"imageCaption\"></div>\r\n</div>\r\nNote that if the alternative hypothesis is the less-than alternative, you reject H<sub>0</sub> only if the test statistic falls in the left tail of the distribution (below –2). Similarly, if H<sub>a</sub> is the greater-than alternative, you reject H<sub>0</sub> only if the test statistic falls in the right tail (above 2).\r\n\r\nTo find the<i> p-</i>value for your test statistic:\r\n<ol class=\"level-one\">\r\n \t<li>\r\n<p class=\"first-para\">Look up your test statistic on the appropriate distribution — in this case, on the standard normal (<i>Z-</i>) distribution (see the following <i>Z</i>-tables).<img class=\"alignnone wp-image-287021 size-full\" src=\"//www.dummies.com/wp-content/uploads/z-score-table-1.png\" alt=\"z-score table 1\" width=\"535\" height=\"933\" />\r\n<img class=\"alignnone wp-image-287022 size-full\" src=\"//www.dummies.com/wp-content/uploads/z-score-table-2.png\" alt=\"z-score table 2\" width=\"535\" height=\"912\" /></p>\r\n</li>\r\n \t<li>\r\n<p class=\"first-para\">Find the probability that <i>Z</i> is beyond (more extreme than) your test statistic:</p>\r\n\r\n<ol class=\"level-two\">\r\n \t<li>\r\n<p class=\"first-para\">If H<sub>a</sub> contains a less-than alternative, find the probability that <i>Z</i> is less than your test statistic (that is, look up your test statistic on the <i>Z</i>-table and find its corresponding probability). This is the<i> p-</i>value. (Note: In this case, your test statistic is usually negative.)</p>\r\n</li>\r\n \t<li>\r\n<p class=\"first-para\">If H<sub>a</sub> contains a greater-than alternative, find the probability that <i>Z</i> is greater than your test statistic (look up your test statistic on the <i>Z</i>-table, find its corresponding probability, and subtract it from one). The result is your<i> p-</i>value. (Note: In this case, your test statistic is usually positive.)</p>\r\n</li>\r\n \t<li>\r\n<p class=\"first-para\">If H<sub>a</sub> contains a not-equal-to alternative, find the probability that <i>Z</i> is beyond your test statistic and double it. There are two cases:</p>\r\n<p class=\"child-para\">If your test statistic is negative, first find the probability that <i>Z</i> is less than your test statistic (look up your test statistic on the <i>Z</i>-table and find its corresponding probability). Then double this probability to get the<i> p-</i>value.</p>\r\n<p class=\"child-para\">If your test statistic is positive, first find the probability that <i>Z </i>is greater than your test statistic (look up your test statistic on the <i>Z</i>-table, find its corresponding probability, and subtract it from one). Then double this result to get the<i> p-</i>value.</p>\r\n</li>\r\n</ol>\r\n</li>\r\n</ol>\r\nSuppose you are testing a claim that the percentage of all women with varicose veins is 25%, and your sample of 100 women had 20% with varicose veins. Then the sample proportion p=0.20. The standard error for your sample percentage is the square root of p(1-p)/n which equals 0.04 or 4%. You find the test statistic by taking the proportion in the sample with varicose veins, 0.20, subtracting the claimed proportion of all women with varicose veins, 0.25, and then dividing the result by the standard error, 0.04.\r\n\r\nThese calculations give you a test statistic (standard score) of –0.05 divided by 0.04 = –1.25. This tells you that your sample results and the population claim in H<sub>0</sub> are 1.25 standard errors apart; in particular, your sample results are 1.25 standard errors below the claim.\r\n\r\nWhen testing H<sub>0</sub>:<i> p </i>= 0.25 versus H<sub>a</sub>:<i> p </i>< 0.25, you find that the<i> p-</i>value of -1.25 by finding the probability that Z is less than -1.25. When you look this number up on the above <i>Z</i>-table, you find a probability of 0.1056 of Z being less than this value.\r\n\r\nNote: If you had been testing the two-sided alternative,\r\n\r\n<img src=\"//www.dummies.com/wp-content/uploads/362524.image3.png\" alt=\"image3.png\" width=\"91\" height=\"24\" />\r\n\r\nthe <i>p</i>-value would be 2 ∗ 0.1056, or 0.2112.\r\n<p class=\"Warning\">If the results are likely to have occurred under the claim, then you fail to reject H<sub>0</sub> (like a jury decides not guilty). If the results are unlikely to have occurred under the claim, then you reject H<sub>0</sub> (like a jury decides guilty).</p>","blurb":"","authors":[{"authorId":9121,"name":"Deborah J. Rumsey","slug":"deborah-j-rumsey","description":" <p><b>Deborah J. Rumsey, PhD,</b> is Professor of Statistics and Statistics Education Specialist at The Ohio State University. She is the author of <i>Statistics Workbook For Dummies, Statistics II For Dummies,</i> and <i>Probability For Dummies</i>. 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A p-value is a probability associated with your critical value. The critical value depends on the probability you are allowing for a Type I error. It measures the chance of getting results at least as strong as yours if the claim (H0) were true.
The following figure shows the locations of a test statistic and their corresponding conclusions.
To find the p-value for your test statistic:
-
Look up your test statistic on the appropriate distribution — in this case, on the standard normal (Z-) distribution (see the following Z-tables).
-
Find the probability that Z is beyond (more extreme than) your test statistic:
-
If Ha contains a less-than alternative, find the probability that Z is less than your test statistic (that is, look up your test statistic on the Z-table and find its corresponding probability). This is the p-value. (Note: In this case, your test statistic is usually negative.)
-
If Ha contains a greater-than alternative, find the probability that Z is greater than your test statistic (look up your test statistic on the Z-table, find its corresponding probability, and subtract it from one). The result is your p-value. (Note: In this case, your test statistic is usually positive.)
-
If Ha contains a not-equal-to alternative, find the probability that Z is beyond your test statistic and double it. There are two cases:
If your test statistic is negative, first find the probability that Z is less than your test statistic (look up your test statistic on the Z-table and find its corresponding probability). Then double this probability to get the p-value.
If your test statistic is positive, first find the probability that Z is greater than your test statistic (look up your test statistic on the Z-table, find its corresponding probability, and subtract it from one). Then double this result to get the p-value.
-
These calculations give you a test statistic (standard score) of –0.05 divided by 0.04 = –1.25. This tells you that your sample results and the population claim in H0 are 1.25 standard errors apart; in particular, your sample results are 1.25 standard errors below the claim.
When testing H0: p = 0.25 versus Ha: p < 0.25, you find that the p-value of -1.25 by finding the probability that Z is less than -1.25. When you look this number up on the above Z-table, you find a probability of 0.1056 of Z being less than this value.
Note: If you had been testing the two-sided alternative,
the p-value would be 2 ∗ 0.1056, or 0.2112.
If the results are likely to have occurred under the claim, then you fail to reject H0 (like a jury decides not guilty). If the results are unlikely to have occurred under the claim, then you reject H0 (like a jury decides guilty).