Name: p-value in hypothesis testing
Uploaded: 2025-05-22T09:05:48.000Z
Duration: 1 min 10 s
Channel: JoVE

K12 Standards

Virginia  Standards of Learning

HIgh School

Biology

BIO.1

BIO.1.d

P-value

When a test statistic is calculated from the sample statistic, such as sample proportion, it can be located in a probability distribution.
This value of the test statistic demarcates an area under the curve from the rest of the area.
This area at the tail of the distribution is the P-value, where P stands for probability.
Assuming that the null hypothesis is true, there is always a chance of observing the calculated test statistic, or a value higher than that, in the critical region of the given distribution.
A P-value provides the probability of getting that test statistic value in the critical region just by chance alone.
So, when the P-value is observed to be smaller than a predetermined value&#8212;such as 0.05&#8212;we reject the null hypothesis, as it indicates that the observed outcome is highly unlikely and the evidence against the null hypothesis is stronger.
The P-value can be calculated at the right tail, left tail, or both the tails depending on the hypothesis or the value of the test statistic.

p-value

P-value is one of the most crucial concepts in statistics.
P-value stands for the probability value. &#160;P-value is the probability that, if the null hypothesis is true, the results from another randomly selected sample will be as extreme or more extreme as the results obtained from the given sample.
A large P-value calculated from the data indicates to&#160; not reject the null hypothesis. But a higher P-value does not mean that the null hypothesis is true. The smaller the P-value, the more unlikely the outcome and the stronger the evidence is against the null hypothesis.&#160;&#160; The null hypothesis is rejected if the evidence is strongly against it. Generally, P-value &#60; 0.05 is considered statistically significant, where 0.05 is the pre-decided significance level.
P-value is not a probability of rejecting the null hypothesis. It is neither a permissible statistical error nor a sampling error that may occur while conducting an experiment or collecting data. It is also not an error rate. P-value also does not mean that there is a 95% chance (at a pre-decided 95% significance level) that the observed difference or the outcome is real. P-value does not convey any information about the truth of null or alternative hypotheses.

P-value is one of the most crucial concepts in statistics.
P-value stands for the probability value. &#160;P-value is the probability that, if the null ...

Education

JoVE Core

Statistics

Unit 1

Hypothesis Testing

KEY TERMS AND CONCEPTS

p-value in hypothesis testing

P-value is a key idea in statistics and hypothesis testing. It stands for probability value. It helps show how likely the observed sample results are if the null hypothesis is true.

More exactly, p-value is the probability that another randomly selected sample will produce results as extreme or more extreme than the results from the given sample, assuming the null hypothesis is true. A large p-value suggests that the null hypothesis should not be rejected. However, a larger p-value does not prove that the null hypothesis is true.

A smaller p-value means the outcome is less likely and gives stronger evidence against the null hypothesis. When the evidence is strong enough, the null hypothesis is rejected. In many cases, p-value less than 0.05 is treated as statistically significant, and 0.05 is the pre-decided significance level.

P-value does not mean the probability of rejecting the null hypothesis. It is not a permissible statistical error, a sampling error, or an error rate from collecting data or running an experiment. It also does not mean there is a 95% chance that the observed difference is real at a 95% significance level. P-value does not tell us whether the null hypothesis or the alternative hypothesis is true.

P-Value in Hypothesis Testing

what is a hypothesis?

Testing a Hypothesis with Sample Data

A hypothesis is a statement about a population property or a phenomenon seen in an observation or experiment. It can describe something that is expected or predicted for a group. In statistics, it is a claim that can be tested with data. A hypothesis should be general, but not vague. It should not make a claim with a definite number, quantity, or measurement for a population property. A hypothesis is not judged as right or wrong on its own. It must be examined through data collection and an...

null and alternative hypotheses

Comparing Hypotheses in Statistical Tests

Statistical hypothesis testing starts by comparing two opposing claims. These are the null hypothesis and the alternative hypothesis. They give researchers a way to judge sample data before making a decision. The null hypothesis, written as H0, says there is no difference between the variables. It also says the variables are not related. This idea is often treated as the status quo. The alternative hypothesis, written as H1 or Ha, makes a claim that conflicts with H0. It is the statement the...

critical region, critical values and significance level

critical-region-critical-values-and-significance-level

Rejection Regions and Significance in Tests

Rejection regions and significance level help decide whether to reject the null hypothesis in hypothesis testing. A sample statistic is first turned into a test statistic using the z, t, or chi-square distribution. The critical region is the part of the probability curve where the test statistic leads to rejection of the null hypothesis. This region is also called the rejection region or region of rejection. It can appear in the right tail, left tail, or both tails of the distribution. The...

P-value is a key idea in statistics and hypothesis testing. It stands for probability value. It helps show how likely the observed sample results are if the null hypothesis is true. More exactly, p-value is the probability that another randomly selected sample will produce results as extreme or more extreme than the results from the given sample, assuming the null hypothesis is true. A large p-value suggests that the null hypothesis should not be rejected. However, a larger p-value does not...

types of hypothesis testing

Tail Direction in Hypothesis Tests

Hypothesis tests are classified by the direction of the alternative hypothesis. The null hypothesis is a neutral statement, and the alternative hypothesis is the claim being tested against it. If the null hypothesis says p = 0.5, the alternative can be written as p &gt; 0.5, p 0.5, the critical region lies on the right side of the probability distribution curve. A right-tailed hypothesis test is used in that case. When the claim is p &lt; 0.5, the critical region lies on the left side of the...

decision making: p-value method

Hypothesis Test Results with P-Values

Hypothesis testing with the P-value method uses sample data to judge a claim about a population parameter. The process starts with a clear research question and a simple statement about the population. An opposing statement is also written so the claim can be tested fairly. These statements become the null hypothesis and the alternative hypothesis. The null hypothesis is a neutral statement, while the alternative hypothesis can have a direction. In some cases, the original claim is the...

decision making: traditional method

Hypothesis Tests Using Critical Values

Hypothesis tests using critical values follow a traditional decision process in statistics. Students first state a claim about a population parameter and then write the opposite statement. These become the null hypothesis and the alternative hypothesis. The null hypothesis is neutral, while the alternative hypothesis can show a direction. After the hypotheses are set, they are written in symbols. By convention, the null hypothesis includes the equality symbol. The alternative hypothesis may...

hypothesis: accept or fail to reject?

Fail to Reject the Null Hypothesis

Hypothesis testing helps scientists decide whether to reject or fail to reject the null hypothesis. The decision comes from the data, the test statistic, the confidence level, the critical values, and the P-value. These parts work together to show whether the evidence is strong enough to support the alternative hypothesis. When the evidence is weak, it is not correct to say that the null hypothesis has been accepted as true. In statistics, that wording can suggest the null hypothesis has been...

errors in hypothesis tests

Type I, Type II, and Test Power

Hypothesis testing can lead to four outcomes based on the true state of the null hypothesis and the choice to reject or not reject it. If the null hypothesis is true and the decision is not to reject it, that is a correct decision. If the null hypothesis is true but it is rejected, that is a Type I error. A Type II error happens when the null hypothesis is false, but it is not rejected. This is also an incorrect decision. The correct decision when the null hypothesis is false is to reject it.

testing a claim about population proportion

testing-a-claim-about-population-proportion

Population Proportion Tests with z and Binomial

Population proportion tests use hypothesis testing to check a claim about a binomial result. The data must come from random and unbiased samples. The variable must also have only two outcomes, such as success or failure, selected or not selected, or true or false. One common method uses the sample proportion and a normal approximation to the binomial distribution. This approach works when the sample is large enough, the proportion is close to 0.5, and np is greater than 5. Here, p is the...

testing a claim about mean: known population sd

testing-a-claim-about-mean-known-population-sd

Z Test for Mean with Known SD

The z test for a population mean uses a known population standard deviation and a normal distribution. It is used when random samples are collected without sampling bias. The sample size should be greater than 30, and the population standard deviation must already be known. In many real situations, the population standard deviation is unknown. In the rare cases when it is known, the claim about the population mean can be tested with the normality assumption and the z distribution. The null...

testing a claim about mean: unknown population sd

testing-a-claim-about-mean-unknown-population-sd

Using the t Test for a Population Mean

Testing a population mean with an unknown standard deviation uses the t test. This method helps estimate a mean when the population standard deviation is not known. It is common in real situations, so the sample standard deviation is used instead. The data should come from randomly selected samples with no sampling bias. The samples should also be approximately normally distributed. There is no specific requirement for sample size, but a different approach is used when the sample size is less...

testing a claim about standard deviation

Chi-Square Test for Standard Deviation Claims

Chi-square hypothesis testing is used to check a claim about population standard deviation or population variance. The data and samples must be random and unbiased. The population distribution must also be normal. The test starts by stating the null and alternative hypotheses clearly and in symbolic form. The claim usually gives a specific value for the population standard deviation or variance. A sample standard deviation or variance is then used to calculate the test statistic. The critical...

key terms and concepts

Learn how p-value is used in hypothesis testing, what a small or large p-value means, and why it does not prove a hypothesis true or false.

P-Value in Hypothesis Testing | JoVE K12

statistics

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Chemistry

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BIO.1.f

P-Value in Hypothesis Testing

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