What is the p-value and how to calculate it?

The p-value is calculated using the sampling distribution of the test statistic under the null hypothesis, the sample data, and the type of test being done (lower-tailed test, upper-tailed test, or two-sided test). The p-value for: a lower-tailed test is specified by: p-value = P(TS ts | H 0 is true) = cdf(ts)

What is the p-value and why is it important?

The p value is a number, calculated from a statistical test, that describes how likely you are to have found a particular set of observations if the null hypothesis were true . P values are used in hypothesis testing to help decide whether to reject the null hypothesis.

Is P exactly 0.05 statistically significant?

If the p-value is less than 0.05, it is judged as “significant,” and if the p-value is greater than 0.05, it is judged as “not significant.” However, since the significance probability is a value set by the researcher according to the circ*mstances of each study, it does not necessarily have to be 0.05.

Why isn't the p-value enough?

While a P value can inform the reader whether an effect exists, the P value will not reveal the size of the effect . In reporting and interpreting studies, both the substantive significance (effect size) and statistical significance (P value) are essential results to be reported.

What is the p-value in statistics for dummies?

The p-value is used to quantify the result of the test given the null hypothesis . This is done by comparing the p-value to the threshold value also known as significance level referred to by the Greek letter alpha. Typically, the alpha value is 0.05 or 5%. The p-value is compared to the pre-defined alpha value.

Can you calculate p-value on calculator?

You can get a p-value by doing an inference test, which can be done by pressing the stat key followed by two clicks to the right . There will be a list of tests, and by putting in your numbers, the calculator will give you a p-value.

Why is it important to correct the p-values?

That is because the probability of reporting a false positive in a group of independent tests is the sum of the individual p-values . When this is done for hundreds of pathways, we are virtually guaranteed to have some pathways that appear to be significant just by chance.

What is the most significant p-value?

Most authors refer to statistically significant as P < 0.05 and statistically highly significant as P < 0.001 (less than one in a thousand chance of being wrong).

What is the significance of the p-value quizlet?

When is a P-value significant? Alpha (false positive rate) sets the critical level of our P-value to accept or reject the null hypothesis . As P < α we reject the null hypothesis. This difference between groups/time periods is stastically significant.

How do you find the p-value by hand?

To compute a p-value by hand all you do is find the area “outside” of the test ratio value from step 6 in 'normal curve' – that is your p-value. There are two areas “outside” of your test ratio from step 6 – one on each side of the normal curve. The p-value is the area to the “outside” of the z-scores of -2.0 and 2.0.

How to calculate p-value ti 84?

TI-83 or 84 Type in the hypothesized proportion (p0), X, sample size, arrow over to the ≠, <, > sign that is the same in the problems alternative hypothesis statement then press the [ENTER] key, arrow down to [Calculate] and press the [ENTER] key. The calculator returns the z-test statistic and the p-value.

How do you calculate the p-value in Excel?

Use the formula =T. TEST(data_array1, data_array2, tails, type) in the cell where you want to place the P-value result. Enter the data arrays and specify the number of tails and the type of test you want to perform. Press "Enter" to see the result.

P-Value: What It Is, How to Calculate It, and Why It Matters (2024)

What Is P-Value?

In statistics, a p-value is defined as In statistics, a p-value indicates the likelihood of obtaining a value equal to or greater than the observed result if the null hypothesis is true.

The p-value serves as an alternative to rejection points to provide the smallest level of significance at which thenull hypothesis would be rejected. A smaller p-value means stronger evidence in favor of the alternative hypothesis.

P-value is often used to promote credibility for studies or reports by government agencies. For example, the U.S. 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. The Census Bureau also has standards in place stipulating which p-values are acceptable for various publications.

Key Takeaways

A p-value is a statistical measurement used to validate a hypothesis against observed data.
A p-value measures the probability of obtaining the observed results, assuming that the null hypothesis is true.
The lower the p-value, the greater the statistical significance of the observed difference.
A p-value of 0.05 or lower is generally considered statistically significant.
P-value can serve as an alternative to—or in addition to—preselected confidence levels for hypothesis testing.

P-Value: What It Is, How to Calculate It, and Why It Matters (1)

Understanding P-Value

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. While the sample size influences the reliability of the observed data, the p-value approach to hypothesis testing specifically involves calculating the p-value based on the deviation between the observed value and a chosen reference value, given the probability distribution of the statistic. A greater difference between the two values corresponds to a lower p-value.

Mathematically, the p-value is calculated using integral calculus from the area under the probability distribution curve for all values of statistics that are at least as far from the reference value as the observed value is, relative to the total area under the probability distribution curve. Standard deviations, which quantify the dispersion of data points from the mean, are instrumental in this calculation.

The calculation for a p-value varies based on the type of test performed. The three test types describe the location on the probability distribution curve: lower-tailed test, upper-tailed test, or two-tailed test. In each case, the degrees of freedom play a crucial role in determining the shape of the distribution and thus, the calculation of the p-value.

In a nutshell, the greater the difference between two observed values, the less likely it is that the difference is due to simple random chance, and this is reflected by a lower p-value.

The 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. This determination relies heavily on the test statistic, which summarizes the information from the sample relevant to the hypothesis being tested. The null hypothesis, also known as the conjecture, is the initial claim about a population (or data-generating process). The alternative hypothesis states whether the population parameter differs from the value of the population parameter stated in the conjecture.

In practice, the significance level is stated in advance to determine how small the p-value must be to reject the null hypothesis. Because different researchers use different levels of significance when examining a question, a reader may sometimes have difficulty comparing results from two different tests. P-values provide a solution to this problem.

Even a low p-value is not necessarily proof of statistical significance, since there is still a possibility that the observed data are the result of chance. Only repeated experiments or studies can confirm if a relationship is statistically significant.

Example of P-Value

Aninvestorclaims that their investment portfolio’s performance is equivalent to that of the . To determine this, the investor conducts atwo-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.

The p-value hypothesis test does not necessarily make use of a preselected confidence level at which the investor should reset the null hypothesis that the returns are equivalent. Instead, it provides a measure of how much evidence there is to reject the null hypothesis. The smaller the p-value, the greater the evidence against the null hypothesis.

Thus, if the investor finds that the p-value is 0.001, there is strong evidence against the null hypothesis, and the investor can confidently conclude that the portfolio’s returns and the S&P 500’s returns are not equivalent.

Although this does not provide an exact threshold as to when the investor should accept or reject the null hypothesis, it does have another very practical advantage. P-value hypothesis testing offers a direct way to compare the relative confidence that the investor can have when choosing among multiple different types of investments or portfolios relative to a benchmark such as the S&P 500.

For example, for two portfolios, A and B, whose performance differs from the S&P 500 with p-values of 0.10 and 0.01, respectively, the investor can be much more confident that portfolio B, with a lower p-value, will actually show consistently different results.

Is a 0.05 P-Value Significant?

A p-value less than 0.05 is typically considered to be statistically significant, in which case the null hypothesis should be rejected. A p-value greater than 0.05 means that deviation from the null hypothesis is not statistically significant, and the null hypothesis is not rejected.

What Does a P-Value of 0.001 Mean?

Ap-value of 0.001 indicates that if the null hypothesis tested were indeed true, then there would be a one-in-1,000 chance of observing results at least as extreme. 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.

How Can You Use P-Value to Compare 2 Different Results of a Hypothesis Test?

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. Beyond this simplified example, you could compare a 0.04 p-value to a 0.001 p-value. Both are statistically significant, but the 0.001 example provides an even stronger case against the null hypothesis than the 0.04.

The Bottom Line

The p-value is used to measure the significance of observational data. When researchers identify an apparent relationship between two variables, there is always a possibility that this correlation might be a coincidence. A p-value calculation helps determine if the observed relationship could arise as a result of chance.