p-values Explained in Plain English with Visuals

A p-value of 0.06 means there’s only a 6% chance your results would occur if there’s truly no effect—still relatively low. This is often interpreted as strong evidence against the null hypothesis. It’s important to consider the entire body of evidence and not rely solely on p-values when interpreting research findings. Other factors like sample size, study design, and measurement precision can influence the p-value. There could still be a real effect or difference, https://www.karmagrup.com/2024/01/08/download-free-monthly-p-l-template-2024-edition/ but it might be smaller or more variable than the study was able to detect. No, a non-significant p-value does not necessarily indicate that there is no effect or difference in the data.

“There is enough statistical evidence to conclude that the mean normal body temperature of adults is lower than 98.6 degrees F.” We use the known value of the sample statistic to learn about the unknown value of the population parameter. This is where samples and statistics come in to play. And how does the t-value from your sample data compare to those expected t-values? How different could you expect the t-values from many random samples from the same population to be?

If you have two different results, one with a p-value of 0.04 and one with a p-value of 0.06, the result with a p-value of 0.04 will be considered more statistically significant than the p-value of 0.06. A p-value greater than 0.05 means that https://megahomepros.com/2025/05/08/economic-order-quantity-eoq-definition-formula/ deviation from the null hypothesis is not statistically significant, and the null hypothesis is not rejected. A p-value less than 0.05 is typically considered to be statistically significant, in which case the null hypothesis should be rejected. Independent observers could note the p-value and decide for themselves whether that represents a statistically significant difference or not.

For example, in the medical field it’s common for researchers to set the alpha level at 0.01 because they want to be highly confident that the results of a hypothesis test are reliable. Thus, we would conclude that we have sufficient evidence to say the alternative hypothesis is true. Second, it is also used to abbreviate “expect value”, which is the expected number of times that one expects to obtain a test statistic at least as extreme as the one that was actually observed if one assumes that the null hypothesis is true. Fisher also underlined the interpretation of p, as the long-run proportion of values at least as extreme as the data, assuming the null hypothesis is true. It is usual and convenient for experimenters to take 5 per cent as a standard level of significance, in the sense that they are prepared to ignore all results which fail to reach this standard, and, by this means, to eliminate from further discussion the greater part of the fluctuations which chance causes have introduced into their experimental results.

Under the null, any differences in results are attributed to chance, not to the factor you are investigating. Common cutoffs for statistical significance are 0.05 and 0.01. A smaller p-value means the results are less consistent with the null and may support the alternative hypothesis. They also do not prove a hypothesis true or false. A large p-value suggests the data are consistent with the null hypothesis. A small p-value suggests the results are unlikely if the null hypothesis is correct.

This sentiment was further supported by a comment in Nature Human Behaviour, that, in response to recommendations to redefine statistical significance to P ≤ 0.005, have proposed that “researchers should transparently report and justify all choices they make when designing a study, including the alpha level.” Although p-values are helpful in assessing how incompatible the data are with a specified statistical model, contextual factors must also be considered, such as “the design of a study, the quality of the measurements, the external evidence for the phenomenon under study, and the validity of assumptions that underlie the data analysis”. While correlation value helps us understand the strength and direction of relationships, p-value helps us determine the likelihood of obtaining the observed results under the null hypothesis. It is important to consider the practical significance of the results in addition to the statistical significance when drawing conclusions from a study. A low p-value (typically less than 0.05) suggests that the observed results are unlikely to have occurred by chance, leading to the rejection of the null hypothesis in favor of the alternative hypothesis.

Next… Confidence intervals and hypothesis tests

Explore theories, classic studies, ADHD, autism, mental health, relationships, and self-care to support both learning and wellbeing. If consistent with existing literature, your result could still be meaningful. Assess if there were methodological limitations or biases (like measurement error or uncontrolled variables) that may have weakened your results. If your confidence interval is narrow and mostly suggests a meaningful effect, this increases confidence that the result may still have practical value. Sample size can impact the interpretation of p-values.

Remember, rejecting the null hypothesis doesn’t prove the alternative hypothesis; it just suggests that the alternative hypothesis may be plausible given the observed data. A statistically significant result cannot prove that a research hypothesis is correct (which implies 100% certainty). Specifically, a p-value of 0.001 means there is only a 0.1% chance of obtaining a result at least as extreme as the one observed, assuming the null hypothesis is correct.

A p-value less than or equal to your significance level (typically ≤ 0. is statistically significant.

The t-distribution example shown above is based on a one-tailed t-test to determine whether the mean of the population is greater than a hypothesized value. Consider them simply different ways to quantify the “extremeness” of your results under the null hypothesis. It’s much more likely that this sample comes from different population, one with a mean greater than 5. It’s more likely this sample doesn’t come from this population (with the hypothesized mean of 5). Given that the probability of obtaining a t-value this high or higher when sampling from this population is so low, what’s more likely? In other words, the probability of obtaining a t-value of 2.8 or higher, when sampling from the same population (here, a population with a hypothesized mean of 5), is approximately 0.006.

🤔 The p-value is the probability of getting results at least as extreme as yours, assuming the null hypothesis is true. A p-value is the probability of observing results at least as extreme as the ones you got, if the null hypothesis were true. While a p-value less than 0.05 is commonly used to indicate statistical significance, it is not a definitive threshold and should be interpreted in the context of the specific research question and study design. One of the key advantages of p-value is that it provides a formal and quantitative measure of the significance of results in a statistical test. P-value, on the other hand, is a measure of the strength of evidence against the null hypothesis in a statistical test.

• I’m passionate about statistics, machine learning, and data visualization and I created Statology to be a resource for both students and teachers alike.
• We use the known value of the sample statistic to learn about the unknown value of the population parameter.
• When the null-hypothesis is composite (or the distribution of the statistic is discrete), then when the null-hypothesis is true the probability of obtaining a p-value less than or equal to any number between 0 and 1 is still less than or equal to that number.
• According to the ASA, there is widespread agreement that p-values are often misused and misinterpreted.
• This leads the observer to reject the null hypothesis because either a highly rare data result has been observed or the null hypothesis is incorrect.
• The null hypothesis, also known as the conjecture, is the initial claim about a population (or data-generating process).

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• Statistical significance and p-value have long been recognized and are highly popular in scientific researches, but misuse and interpretation remain to be common (1).
• It is usual and convenient for experimenters to take 5 per cent as a standard level of significance, in the sense that they are prepared to ignore all results which fail to reach this standard, and, by this means, to eliminate from further discussion the greater part of the fluctuations which chance causes have introduced into their experimental results.
• Imagine a magical dart that could be thrown to land randomly anywhere under the distribution curve.
• This can make an effect seem real when it’s actually just a statistical fluke.
• The Census Bureau also has standards in place stipulating which p-values are acceptable for various publications.
• A p-value is a number that helps us judge how surprising our results are if there really were no effect.

It is used in multiple hypothesis testing to maintain statistical power while minimizing the false positive rate. This and other work by Arbuthnot is credited as “… the first use of significance tests …” the first example of reasoning about statistical significance, and “… perhaps the first published report of a nonparametric test …”, specifically the sign test; see details at Sign test § History. As an example of a statistical test, an experiment is performed to determine whether a coin flip is fair difference between p&l and balance sheet (equal chance of landing heads or tails) or unfairly biased (one outcome being more likely than the other). Today, this computation is done using statistical software, often via numeric methods (rather than exact formulae), but, in the early and mid 20th century, this was instead done via tables of values, and one interpolated or extrapolated p-values from these discrete valuescitation needed. Thus computing a p-value requires a null hypothesis, a test statistic (together with deciding whether the researcher is performing a one-tailed test or a two-tailed test), and data. As such, the test statistic follows a distribution determined by the function used to define that test statistic and the distribution of the input observational data.

If your sample size is small or your study has low statistical power (below 80%), you may have missed detecting an actual effect. It means that the observed data do not provide strong enough evidence to reject the null hypothesis. Statistical significance depends on factors like the study design, sample size, and the magnitude of the observed effect.

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The null hypothesis, also known as the conjecture, is the initial claim about a population (or data-generating process). This determination relies heavily on the test statistic, which summarizes the information from the sample relevant to the hypothesis being tested. The p-value approach to hypothesis testing uses the calculated probability to determine whether there is evidence to reject the null hypothesis. Census Bureau stipulates that any analysis with a p-value greater than 0.10 must be accompanied by a statement that the difference is not statistically different from zero. A smaller p-value means stronger evidence in favor of the alternative hypothesis.

A larger sample size provides more reliable and precise estimates of the population, leading to narrower confidence intervals. A p-value below 0.05 means there is evidence against the null hypothesis, suggesting a real effect. Commonly used significance levels are 0.01, 0.05, and 0.10.

If your p-value is less than or equal to 0.05 (the significance level), you would conclude that your result is statistically significant. The significance level is the probability of rejecting the null hypothesis when it is true. In statistical hypothesis testing, you reject the null hypothesis when the p-value is less than or equal to the significance level (α) you set before conducting your test. When researchers run many statistical tests on the same dataset, the chance of finding a “significant” result purely by luck increases. Any data point landing in these extreme regions would be considered statistically significant at the 0.05 level, leading you to reject the null hypothesis.

It indicates the probability of obtaining the observed results, or more extreme results, if the null hypothesis is true. As a whole, summarizing statistical comparisons to statistical significance or non-significance is one of the highly popular statistical misinterpretations of p-values and hypothesis testing. Another assumption that has been used in computing the p–value is that any deviation of the observed data from the null hypothesis was produced by chance, so it is clear that when only chance affects the deviation of the null hypothesis in the calculation of the p-value, it cannot be the probability of operating of the chance (7,8). P-values are usually calculated using statistical software or p-value tables based on the assumed or known probability distribution of the specific statistic tested. An alpha level is the probability of incorrectly rejecting a true null hypothesis.

Different p-values based on independent sets of data can be combined, for instance using Fisher’s combined probability test. The p-value is the probability under the null hypothesis of obtaining a real-valued test statistic at least as extreme as the one obtained. All other things being equal, smaller p-values are taken as stronger evidence against the null hypothesis. If we state one hypothesis only and the aim of the statistical test is to see whether this hypothesis is tenable, but not to investigate other specific hypotheses, then such a test is called a null hypothesis test. Even though reporting p-values of statistical tests is common practice in academic publications of many quantitative fields, misinterpretation and misuse of p-values is widespread and has been a major topic in mathematics and metascience.

For comparison, the probability of being dealt 3-of-a-kind in a 5-card poker hand is over three times as high (≈ 0.021). What’s the chance it would land in the shaded region? Imagine a magical dart that could be thrown to land randomly anywhere under the distribution curve. For example, the shaded region represents the probability of obtaining a t-value of 2.8 or greater. T values of larger magnitudes (either negative or positive) are less likely.