### What is a 'P-Test'

A statistical method used to test one or more hypotheses within a population or a proportion within a population. When testing a hypothesis about a population proportion (p) within a large population (one in which the sample size, "n", is not greater than 5% of the overall population), the formula is:

x = (m/n-P) / SqRt[P(1-P)/n]
m= "yes" response
n = random sample size
p = proportion
P = population

This formula is used to test three hypotheses:

### Explaining 'P-Test'

For example, a polling group contacted a group of investors and asked if they felt that the economy would fall into a recession. Of the 1000 people contacted, 700 said that they thought that the economy was heading toward recession. The researchers then applied the P-Test to determine if p ≤ 0.60, p ≥ 0.60, or p = 0.60; basically, what percentage of the population believe that the economy will fall into a recession.

Financial development and economic growth: evidence from panel unit root and cointegration tests
www.sciencedirect.com [PDF]
… tests may be quite low given the sample sizes and time spans typically available in economics … Provided all variables involved are integrated of order one, or I(1), valid economic inferences can be … The P test is distributed as χ 2 with degrees of freedom twice the number of cross … A cointegration test for market efficiency
search.proquest.com [PDF]
… tests may be quite low given the sample sizes and time spans typically available in economics … Provided all variables involved are integrated of order one, or I(1), valid economic inferences can be … The P test is distributed as χ 2 with degrees of freedom twice the number of cross … Stock prices response to real economic variables: the case of Germany
www.emerald.com [PDF]
… tests may be quite low given the sample sizes and time spans typically available in economics … Provided all variables involved are integrated of order one, or I(1), valid economic inferences can be … The P test is distributed as χ 2 with degrees of freedom twice the number of cross … Financial development and economic growth in India: some evidence from non-linear causality analysis
… tests may be quite low given the sample sizes and time spans typically available in economics … Provided all variables involved are integrated of order one, or I(1), valid economic inferences can be … The P test is distributed as χ 2 with degrees of freedom twice the number of cross … Using economic value added as a portfolio separation criterion
www.jstor.org [PDF]
… tests may be quite low given the sample sizes and time spans typically available in economics … Provided all variables involved are integrated of order one, or I(1), valid economic inferences can be … The P test is distributed as χ 2 with degrees of freedom twice the number of cross … Stationarity tests for financial time series
www.sciencedirect.com [PDF]
… tests may be quite low given the sample sizes and time spans typically available in economics … Provided all variables involved are integrated of order one, or I(1), valid economic inferences can be … The P test is distributed as χ 2 with degrees of freedom twice the number of cross … The financial impact of boycotts and threats of boycott
www.sciencedirect.com [PDF]
… tests may be quite low given the sample sizes and time spans typically available in economics … Provided all variables involved are integrated of order one, or I(1), valid economic inferences can be … The P test is distributed as χ 2 with degrees of freedom twice the number of cross … Impact of financial/economic crisis on demand for hotel rooms in Hong Kong
www.sciencedirect.com [PDF]
… tests may be quite low given the sample sizes and time spans typically available in economics … Provided all variables involved are integrated of order one, or I(1), valid economic inferences can be … The P test is distributed as χ 2 with degrees of freedom twice the number of cross … Regional economic disparity, financial disparity, and national economic growth: Evidence from China
onlinelibrary.wiley.com [PDF]
… tests may be quite low given the sample sizes and time spans typically available in economics … Provided all variables involved are integrated of order one, or I(1), valid economic inferences can be … The P test is distributed as χ 2 with degrees of freedom twice the number of cross …

#### How do you calculate a p-value?

You take your sample statistic (for example, your test score) and compare it with what's expected given your null hypothesis (the average score). If this comparison yields something unlikely, then you reject H0.

#### What are some common misconceptions about p-values?

Some people think that if their study has found no significant differences between groups, they don't need to report any effect sizes or confidence intervals because they "already know" there was no effect. This isn't true! Reporting effect sizes and confidence intervals helps readers interpret how large an effect size might be if it were real; reporting just one number doesn't help them understand how big or small this number really is in relation to other numbers they may see in research literature or elsewhere. Another misconception about p-values has been articulated by Daniel Kahneman in his book "Thinking Fast and Slow"

#### Where would someone find information on how they can apply this formula?

They could look online for information on how they can apply this formula and/or contact their local library for assistance with finding resources related to applying the P-test statistic in general.

#### What does it mean to test a hypothesis about a population proportion (p) within a large population (one in which the sample size, "n", is not greater than 5 of the overall population)?

It means that you are testing p for three different values.

Yes

#### How do you determine if p = .6, p = .6, or p < .6?

You use the formula x = (mn-P) SqRt[P(1-P)n] and solve for x.

#### What is the null hypothesis significance testing?

The null hypothesis significance testing is a statistical method used to determine if an observed difference between two or more groups is likely due to chance.

#### How small must a p-value be in order for you to reject H0?

If a p-value is less than 0.05, then there's only a 5% chance that we would have obtained our result by random chance alone and therefore we can reject H0.

#### What does p-value mean?

A p-value means the probability of obtaining test results at least as extreme as the results actually observed, under the assumption that the null hypothesis is correct.

#### Who might use this formula?

Anyone who wants an easy way of testing multiple hypotheses at once could potentially use this formula.

#### What is the P-Test?

The P-Test is a statistical method used to test one or more hypotheses within a population or proportion within a population.

#### What are three possible outcomes from using this formula?

Three possible outcomes are that x could be less than 0, equal to 0, or greater than 0. If x is less than 0 then there isn't enough evidence to reject H0; if x equals 0 then there isn't enough evidence to accept either H0 or HA; and if x is greater than 0 then there is enough evidence to reject H0.

#### Why would someone want to use this formula?

Someone might want to use this formula because it allows them to test multiple hypotheses at once without having too many variables.

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