## What does less p-value mean?

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**Table of contents**

- What does p-value of 0.3 mean?
- What does less p-value mean?
- How do you reject a null hypothesis?
- Why do we use 0.05 level of significance?
- Related questions

A p-value less than 0.05 (typically ≤ 0.05) is **statistically significant**. It indicates strong evidence against the null hypothesis, as there is less than a 5% probability the null is correct (and the results are random). Therefore, we reject the null hypothesis, and accept the alternative hypothesis.

## What does p-value of 0.3 mean?

E.g. a p-value of 0.3 means "**repeating the study many times**, given that the null hypothesis + all other assumptions are true, I would see the result I'm seeing (or a more extreme result) 30% of time, so it wouldn't be super unusual.Mar 24, 2016

## What does less p-value mean?

For the participants, the intuitive null hypothesis is that they have a probability of one-third for guessing the correct cup in each round of the game. The participants were unaware, however, that none of the cups concealed a red button, and that they thus would lose every time. In other words, the intuitive null hypothesis was untrue. The objective of the experiment was to investigate how many times the participants would repeat the game before starting to suspect that something was wrong, meaning that they would doubt the null hypothesis. More than half of the participants were suspicious after six rounds of repeated losses (p = 0.088) and nearly 90 % after eight rounds (p = 0.039). The experiment indicates that many people naturally and intuitively will choose a significance level of approximately 5 %.

## How do you reject a null hypothesis?

Rejecting the Null Hypothesis

Reject the null hypothesis when the p-value is less than or equal to your significance level. Your sample data favor the alternative hypothesis, which suggests that the effect exists in the population. For a mnemonic device, remember—when the p-value is low, the null must go!

Failing to Reject the Null Hypothesis

Conversely, when the p-value is greater than your significance level, you fail to reject the null hypothesis. The sample data provides insufficient data to conclude that the effect exists in the population. When the p-value is high, the null must fly!

Note that failing to reject the null is not the same as proving it. For more information about the difference, read my post about Failing to Reject the Null.

That’s a very general look at the process. But I hope you can see how the path to more exciting findings depends on being able to rule out the less exciting null hypothesis that states there’s nothing to see here!

## Why do we use 0.05 level of significance?

The significance level is the probability of rejecting the null hypothesis when it is true. For example, a significance level of 0.05 indicates a 5% risk of concluding that a difference exists when there is no actual difference. Lower significance levels indicate that you require stronger evidence before you will reject the null hypothesis.

Use significance levels during hypothesis testing to help you determine which hypothesis the data support. Compare your p-value to your significance level. If the p-value is less than your significance level, you can reject the null hypothesis and conclude that the effect is statistically significant. In other words, the evidence in your sample is strong enough to be able to reject the null hypothesis at the population level.

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##### How do you know if the hypothesis is accepted?

The *P*-value approach involves determining "likely" or "unlikely" by determining the probability — assuming the null hypothesis were true — of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed. If the *P*-value is small, say less than (or equal to) *P*-value is large, say more than

If the *P*-value is less than (or equal to) *P*-value is greater than

Specifically, the four steps involved in using the *P*-value approach to conducting any hypothesis test are:

- Specify the null and alternative hypotheses.
- Using the sample data and assuming the null hypothesis is true, calculate the value of the test statistic. Again, to conduct the hypothesis test for the population mean
*μ*, we use the*t*-statisticwhich follows a*t*-distribution with*n*- 1 degrees of freedom. - Using the known distribution of the test statistic, calculate the
*P**-value*: "If the null hypothesis is true, what is the probability that we'd observe a more extreme test statistic in the direction of the alternative hypothesis than we did?" (Note how this question is equivalent to the question answered in criminal trials: "If the defendant is innocent, what is the chance that we'd observe such extreme criminal evidence?") - Set the significance level,, the probability of making a Type I error to be small — 0.01, 0.05, or 0.10. Compare the
*P*-value to. If the*P*-value is less than (or equal to), reject the null hypothesis in favor of the alternative hypothesis. If the*P*-value is greater than, do not reject the null hypothesis.

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##### How do you test the hypothesis at 0.05 level of significance?

The significance level determines how far out from the null hypothesis value we'll draw that line on the graph. To graph a significance level of 0.05, we need to shade the 5% of the distribution that is furthest away from the null hypothesis.

In the graph above, the two shaded areas are equidistant from the null hypothesis value and each area has a probability of 0.025, for a total of 0.05. In statistics, we call these shaded areas the *critical region* for a two-tailed test. If the population mean is 260, we’d expect to obtain a sample mean that falls in the critical region 5% of the time. The critical region defines how far away our sample statistic must be from the null hypothesis value before we can say it is unusual enough to reject the null hypothesis.

Our sample mean (330.6) falls within the critical region, which indicates it is statistically significant at the 0.05 level.

We can also see if it is statistically significant using the other common significance level of 0.01.

###### Related

##### Does a lower p-value mean more significant?

But on the other hand, p-values are dependent on sample size. They are not an absolute measure. Thus we cannot simply say 0.001593 is *more significant* than 0.0439. Yet this what would be implied in Fisher's framework: we would be more surprised to such an extreme value. There's even discussion about the term *highly significant* being a misnomer: Is it wrong to refer to results as being "highly significant"?

I've heard that p-values in some fields of science are only considered important when they are smaller than 0.0001, whereas in other fields values around 0.01 are already considered highly significant.

*Related questions:*

- Is the "hybrid" between Fisher and Neyman-Pearson approaches to statistical testing really an "incoherent mishmash"?
- When to use Fisher and Neyman-Pearson framework?
- Is the exact value of a 'p-value' meaningless?
- Frequentist properties of p-values in relation to type I error
- Confidence intervals vs P-values for two means
- Why are lower p-values not more evidence against the null? Arguments from Johansson 2011 (as provided by @amoeba)

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##### How do you know if p-value is significant?

How small is small enough? The most common threshold is *p <* 0.05; that is, when you would expect to find a test statistic as extreme as the one calculated by your test only 5% of the time. But the threshold depends on your field of study – some fields prefer thresholds of 0.01, or even 0.001.

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

Reporting *p*-values

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

Caution when using *p*-values

*P*-values are often interpreted as your risk of rejecting the null hypothesis of your test when the null hypothesis is actually true.

In reality, the risk of rejecting the null hypothesis is often higher than the *p*-value, especially when looking at a single 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 pattern completely by accident.

###### Related

##### How do you reject the null hypothesis in t test?

If the absolute value of the t-value is greater than the critical value, you reject the null hypothesis. If the absolute value of the t-value is less than the critical value, you fail to reject the null hypothesis. You can calculate the critical value in Minitab or find the critical value from a t-distribution table in most statistics books. For more information calculating the critical value in Minitab, go to Using the inverse cumulative distribution function (ICDF) and click *Use the ICDF to calculate critical values*.

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##### How do I know if I reject or fail to reject?

Suppose that you do a hypothesis test. Remember that the decision to reject the null hypothesis (H*0*) or fail to reject it can be based on the p-value and your chosen significance level (also called α). If the p-value is less than or equal to α, you reject H*0*; if it is greater than α, you fail to reject H*0*.

Your decision can also be based on the confidence interval (or bound) calculated using the same α. For example, the decision for a test at the 0.05 level of significance can be based on the 95% confidence interval:

- If the reference value specified in H
*0*lies outside the interval (that is, is less than the lower bound or greater than the upper bound), you can reject H*0*. - If the reference value specified in H
*0*lies within the interval (that is, is not less than the lower bound or greater than the upper bound), you fail to reject H*0*.

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##### What does P less than 0.05 mean?

- P > 0.05 is the probability that the null hypothesis is true.
- 1 minus the P value is the probability that the alternative hypothesis is true.
- A statistically significant test result (P ≤ 0.05) means that the test hypothesis is false or should be rejected.
- A P value greater than 0.05 means that no effect was observed.

If you answered “none of the above,” you may understand this slippery concept better than many researchers. The ASA panel defined the *P* value as “the probability under a specified statistical model that a statistical summary of the data (for example, the sample mean difference between two compared groups) would be equal to or more extreme than its observed value.”

Why is the exact definition so important? Many authors use statistical software that presumably is based on the correct definition. “It’s very easy for researchers to get papers published and survive based on knowledge of what statistical packages are out there but not necessarily how to avoid the problems that statistical packages can create for you if you don’t understand their appropriate use,” said Barnett S. Kramer, M.D., M.P.H., *JNCI*’s former editor in chief and now director of the National Cancer Institute’s Division of Cancer Prevention. (Kramer was not on the ASA panel.)

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##### Do you reject the null hypothesis at the 0.05 significance level?

In the majority of analyses, an alpha of 0.05 is used as the cutoff for significance. If the p-value is less than 0.05, we reject the null hypothesis that there's no difference between the means and conclude that a significant difference does exist. If the p-value is larger than 0.05, we *cannot* conclude that a significant difference exists.

That's pretty straightforward, right? Below 0.05, significant. Over 0.05, *not* significant.

"Missed It By *That* Much!"

In the example above, the result is clear: a p-value of 0.7 is so much higher than 0.05 that you can't apply any wishful thinking to the results. But what if your p-value is really, *really* close to 0.05?

*Like, what if you had a p-value of 0.06? *

That's not significant.

*Oh. Okay, what about 0.055?*

Not significant.

*How about 0.051?*

It's *still* not statistically significant, and data analysts should not try to pretend otherwise. A p-value is not a negotiation: if p > 0.05, the results are not significant. *Period.*

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##### Why reject null hypothesis when p-value is small?

A crucial step in null hypothesis testing is finding the likelihood of the sample result if the null hypothesis were true. This probability is called the . A low *p* value means that the sample result would be unlikely if the null hypothesis were true and leads to the rejection of the null hypothesis. A high *p* value means that the sample result would be likely if the null hypothesis were true and leads to the retention of the null hypothesis. But how low must the *p* value be before the sample result is considered unlikely enough to reject the null hypothesis? In null hypothesis testing, this criterion is called and is almost always set to .05. If there is less than a 5% chance of a result as extreme as the sample result if the null hypothesis were true, then the null hypothesis is rejected. When this happens, the result is said to be . If there is greater than a 5% chance of a result as extreme as the sample result when the null hypothesis is true, then the null hypothesis is retained. This does not necessarily mean that the researcher accepts the null hypothesis as true—only that there is not currently enough evidence to conclude that it is true. Researchers often use the expression “fail to reject the null hypothesis” rather than “retain the null hypothesis,” but they never use the expression “accept the null hypothesis.”

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##### What does a p-value of 0 mean in statistics?

The

**p**-value**is**conditional upon the null hypothesis being true**is**unrelated to the truth or falsity of the research hypothesis. A**p**-value higher**than 0**.**05**(>**0**.**05**)**is**not statistically significant and indicates weak evidence against the null hypothesis.

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##### What does p value is 1 minus P mean?

P > 0.05 is the probability that the null hypothesis is true. 1 minus the P value is the probability that the alternative hypothesis is true. A statistically significant test result (P ≤ 0.05) means that the test hypothesis is false or should be rejected.

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##### What if the p value is less than the critical value?

To your point, the p value could be less than 0.05 and we could still have the test statistic be less than the critical value. This would mean our chosen α was smaller than 0.05, and would mean we would fail to reject the null. Thanks for contributing an answer to Cross Validated!

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##### What happens if the p-value is not less than 5?

If the

**p**-value**is**not**less than**.**05**, then we fail to reject the null hypothesis and conclude that we do not have sufficient evidence to say that the alternative hypothesis**is**true. The following examples explain how to interpret a**p**-value**less than**.**05**and how to interpret a**p**-value greater**than**.**05**in practice.

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