## Definition

In statistical hypothesis testing, the p-value or probability value or asymptotic significance is the probability for a given statistical model that, when the null hypothesis is true, the statistical summary would be the same as or of greater magnitude than the actual observed results. The use of p-values in statistical hypothesis testing is common in many fields of research such as physics, economics, finance, political science, psychology, biology, criminal justice, criminology, and sociology. Their misuse has been a matter of considerable controversy.

### What is the 'P-Value'

The p-value is the level of marginal significance within a statistical hypothesis test representing the probability of the occurrence of a given event. The p-value is used as an alternative to rejection points to provide the smallest level of significance at which the null hypothesis would be rejected. A smaller p-value means that there is stronger evidence in favor of the alternative hypothesis.

### Explaining 'P-Value'

P-values are calculated using p-value tables or spreadsheet/statistical software. Because different researchers use different levels of significance when examining a question, a reader may sometimes have difficulty comparing results from two different tests. For example, if two studies of returns from two particular assets were undertaken using two different significance levels, a reader could not compare the probability of returns for the two assets easily.

### P-Value Approach to Hypothesis Testing

The p-value approach to hypothesis testing uses the calculated probability to determine whether there is evidence to reject the null hypothesis. The null hypothesis, also known as the conjecture, is the initial claim about a population of statistics. The alternative hypothesis states whether the population parameter differs from the value of the population parameter stated in the conjecture. In practice, the p-value, or critical value, is stated in advance to determine how the required value to reject the null hypothesis.

### Type I Error

A type I error is the false rejection of the null hypothesis. The probability of a type I error occurring, or rejecting the null hypothesis when it is true, is equivalent to the critical value used. Conversely, the probability of accepting the null hypothesis when it is true is equivalent to 1 minus the critical value.

### Example

Assume an investor claims that her investment portfolio's performance is equivalent to that of the Standard & Poor's (S&P) 500 Index. The investor conducts a two-tailed test. The null hypothesis states that the portfolio's returns are equivalent to the S&P 500's returns over a specified period, while the alternative hypothesis states that the portfolio's returns and the S&P 500's returns are not equivalent. If the investor conducted a one-tailed test, the alternative hypothesis would state that the portfolio's returns are either less than or greater than the S&P 500's returns.

Research Commentary—Too Big to Fail: Large Samples and the
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#### Why do many fields require experiments to have low p values?

Many fields require experiments to have low p values because it shows that there is more evidence against the null hypothesis, and therefore, more evidence for an alternative theory.

#### When must an experiment have a low p-value?

An experiment must have a low p-value in order to be considered evidence of an alternative hypothesis.

#### How do we know whether our sample size was large enough or not ?

We know whether our sample size was large enough or not by calculating effect sizes and confidence intervals . Effect sizes tell us how big our effects are , while confidence intervals tell us what range of values we should

#### How can you determine if your results are statistically significant or not?

You can determine if your results are statistically significant by using statistical software such as SPSS or R .

#### What does the p-value approach to hypothesis testing use?

The p-value approach uses calculated probabilities to determine whether there is evidence to reject the null hypothesis.

#### What happens if you reject null hypotheses too often?

You will have made many type I errors and will have rejected too many true null hypotheses. This could result in your losing credibility with others who may doubt your ability to make accurate decisions based on data analysis and statistics.

#### What is a p-value?

A p-value is the probability that the null hypothesis gives for a specific experimental result to happen.

#### Is it possible for two different studies with similar data sets but different conclusions to both be correct?

Yes, it is possible for two different studies with similar data sets but different conclusions to both be correct. This happens when one study has enough statistical power while another study does not have enough statistical power .

#### What does a low p-value mean?

A low p-value means that there is a higher chance of the null hypothesis being false.

#### How can rejection points be used as opposed to using p-values?

Rejection points can be used instead of using p-values because they provide a more concrete way for determining if something should be rejected or accepted.

#### Can you give me some examples of how statistics can be misused in society today?

Yes, I will give you some examples of how statistics can be misused in society today. One example would be when politicians use misleading statistics about crime rates in their campaigns . Another example would be when people use misleading statistics about gun control laws .

#### What does it mean when you say that you are rejecting or accepting null hypotheses?

Rejecting means that you believe there is enough evidence in favor of an alternative hypothesis, while accepting means that you do not believe there is enough evidence in favor of an alternative hypothesis.

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