How to calculate p value

How to calculate P Value?

P-value, also referred to as probability value is a statistical measure used to determine whether to accept or reject the Null Hypothesis, considering the Null Hypothesis to be True.
For calculating the p-value, we perform an experiment and based on the observations of the test-statistic we make decisions, i.e., if the measure is statistically below the significance level, the Null Hypothesis is rejected, specifying that the Null Hypothesis is very less likely to occur.

How it works?
Consider, there is a magazine that says, on an average there are 12% Indian employees in a company in US.

Assumptions:

Methods to determine P Value

By Simulation
We simulate the situation and take samples that provide our Null Hypothesis to be True. In the above example, we take 20 samples of 50 employees each, and in each sample, there are 12% of Indian employees (Null Hypothesis). We re-sample 20 samples of 50 employees each from the above-collected samples.
Below are the results of the simulation:

There are 5 samples out of 20 which had more than 20% employees as Indian.
Hence, the p-value would be 5/20 = 0.25.
Since the significance level was 5% and after simulation, the value obtained 25%, we cannot reject the Null Hypothesis.

z Statistic
To perform z-test, three conditions are required to be met for the samples we collect:

Note: When considering means, t-test is used, and when considering proportions, z test is used.

P-Value

Skylar Clarine is a fact-checker and expert in personal finance with a range of experience including veterinary technology and film studies.

What Is P-Value?

In statistics, the p-value is the probability of obtaining results at least as extreme as the observed results of a statistical hypothesis test, assuming that the null hypothesis is correct. The p-value serves 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.

P-value is often used to promote credibility for studies or reports by government agencies. For example, the United States Census Bureau stipulates 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 what p-values are acceptable for various publications.

Key Takeaways

Click Play to Learn How P-Value Is Calculated

How Is P-Value Calculated?

P-values are usually found using p-value tables or spreadsheets/statistical software. These calculations are based on the assumed or known probability distribution of the specific statistic tested. P-values are calculated from the deviation between the observed value and a chosen reference value, given the probability distribution of the statistic, with a greater difference between the two values corresponding 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.

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-sided test.

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. 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 in order 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.

For example, suppose a study comparing returns from two particular assets was undertaken by different researchers who used the same data but different significance levels. The researchers might come to opposite conclusions regarding whether the assets differ.

If one researcher used a confidence level of 90% and the other required a confidence level of 95% to reject the null hypothesis and the p-value of the observed difference between the two returns was 0.08 (corresponding to a confidence level of 92%), then the first researcher would find that the two assets have a difference that is statistically significant, while the second would find no statistically significant difference between the returns.

To avoid this problem, the researchers could report the p-value of the hypothesis test and allow readers to interpret the statistical significance themselves. This is called a p-value approach to hypothesis testing. Independent observers could note the p-value and decide for themselves whether that represents a statistically significant difference or not.

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

An investor claims that their investment portfolio’s performance is equivalent to that of the Standard & Poor’s (S&P) 500 Index. To determine this, 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.

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 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?

A p-value of 0.001 indicates that if the null hypothesis tested were indeed true, 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 Two 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.

Correction–April 2, 2022: A previous version incorrectly described the p-value as the probability of results arising through random chance.

Excel P-Value

By Madhuri Thakur

Excel P-Value (Table of Content)

P-Value in Excel

Null hypothesis:

Excel functions, formula, charts, formatting creating excel dashboard & others

How to Calculate P-Value in Excel?

Let’s understand how to calculate P-Value in Excel by using relevant examples.

P-Value in Excel – Example #1

In this example, we will calculate P-Value in Excel for the given data.

Now to find P-Value for this particular expression, the formula for that is TDIST(x, deg_freedom, tails).

P-Value in Excel – Example #2

Similarly, you can find the P-Values by this method when values of x, n, and tails are provided.

P-Value in Excel – Example #3

Here we will see how to calculate P-Value in excel for Correlation.

=t.dist.2t(t, degree_freedom)

A/B testing:

Test: 1 Expected Data:

Total Visitors: 5,000

Test: 2 Observed Data:

Total Visitors: 7,000

Things To Remember About P-Value in Excel

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P Value Formula

What is the P-Value Formula?

P is a statistical measure that helps researchers to determine whether their hypothesis is correct. It helps determine the significance of results. The null hypothesis Null Hypothesis Null hypothesis presumes that the sampled data and the population data have no difference or in simple words, it presumes that the claim made by the person on the data or population is the absolute truth and is always right. So, even if a sample is taken from the population, the result received from the study of the sample will come the same as the assumption. read more is a default position that there is no relationship between two measured phenomena. It is denoted by H_{0. An alternative} hypothesis is the one you would believe if the null hypothesis is concluded to be untrue. Its symbol is H₁ or H_a.

P-value in excel P-value In Excel P-value is used in correlation and regression analysis in Excel to determine whether the result obtained is feasible or not and which data set from the result to work with. It’s value ranges from 0 to 1. read more is a number between 0 and 1. There are tables, spreadsheet programs, and statistical software to help calculate the p-value. The level of significance (α) is a pre-defined threshold set by the researcher. It is generally 0.05. A very small p-value, which is lesser than the level of significance, indicates that you reject the null hypothesis. P-value, which is greater than the level of significance, indicates that we fail to reject the null hypothesis.

Table of contents

Explanation of the P-Value Formula

The formula for the calculation of the p-value can be derived by using the following steps:

Calculating P-Value from a Z Statistic

Step 1: We need to find out the test statistic z

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For eg:
Source: P Value Formula (wallstreetmojo.com)

Step 2: We need to find the corresponding level of p from the z value obtained. For this purpose, we need to look at the z table.

For instance, let us find the value of p corresponding to z ≥ 2.81. Since the normal distribution is symmetric, negative values of z are equal to its positive values. 2.81 is a sum of 2.80 and 0.01. Look at 2.8 in the z column and the corresponding value of 0.01. We get p = 0.0025.

Examples of P-Value Formula (with Excel Template)

Let’s see some simple to advanced examples of the P-Value equation to understand it better.

Example #1

a) P-value is 0.3015. If the level of significance is 5%, find if we can reject the null hypothesis.

b) P-value is 0.0129. If the level of significance is 5%, find if we can reject the null hypothesis.

Solution:

Use the following data for the calculation of P-Value.

a) Since the p-value of 0.3015 is greater than the level of significance of 0.05 (5%), we fail to reject the null hypothesis.

b) Since the p-value of 0.0129 is less than the level of significance of 0.05, we reject the null hypothesis.

Example #2

27% of people in India speak Hindi as per a research study. A researcher is curious if the figure is higher in his village. Hence, the frames the null and alternate hypotheses. He tests H_0: p = 0.27. H_a: p > 0.27. Here, p is the proportion of people in the village who speak Hindi. He commissions a survey in his village to find out the number of people who can speak Hindi. He finds that 80 out of 240 people sampled can speak Hindi. Find out the approximate p-value for the researcher’s test if we were to assume that the necessary conditions are met, and the significance level is 5%.

Solution:

Use the following data for the calculation of P-Value.

Here, the sample size n = 240,

p₀ is the population proportion. We will have to find the sample proportion

= 80 / 240

= 0.33

Z Statistic

Calculation of Z Statistic

=0.33 – 0.27 / √ 0.27 * (1 – 0.27 ) / 240

Z Statistic will be –

Z = 2.093696

P-Value = P (z ≥ 2.09)

P Value = 0.0183

Since the p-value is less than the significant level of 0.05 (5%), we reject the null hypothesis.

Note: In Excel, the p-value is coming as 0.0181

Example #3

Studies show that a higher number of flight tickets are bought by males as compared to females. They are bought by males and females in the ratio of 2:1. The research was carried out at a particular airport in India to find the distribution of air tickets among males and females. Out of 150 tickets, 88 tickets were bought by males and 62 by females. We need to find out if the experimental manipulation causes the change in the results, or we are observing a chance variation. Calculate the p-value assuming the degree of significance is 0.05.

Solution:

Use the following data for the calculation of P-Value.

Step 1: The observed value is 88 for males and 62 for females.

Step 2: Find out chi-square

=((88-100) 2 )/100 + (62-50) 2 /50

Chi-Square (X^2)

Chi-Square(X^2) will be –

Chi-Square(X^2) = 4.32

Step 3: Find the degrees of freedom

Since there are 2 variables – males and females, n=2

Degrees of freedom = n-1 = 2-1 = 1

Step 4: From the p-value table, we look at the first row in the table as the degree of freedom is 1.We can see that the p-value is between 0.025 and 0.05. Since the p-value is less than the degree of significance of 0.05, we reject the null hypothesis.

P Value = 0.037666922

Note: Excel directly gives the p-value using the formula:

CHITEST (actual range, expected range)

Example #4

It is known that 60% of the people who enter apparel stores in a city purchase something. An apparel shop owner wanted to find if the number is higher for the apparel shop owned by him. He already had the results of a study conducted for his shop. 128 out of 200 people who entered his shop purchased something. The shop owner denoted pas the proportion of people who entered his apparel shop and purchased something. The null hypothesis framed by him was p = 0.60, and the alternate hypothesis was p > 0.60. Find the p-value for the research at a significance level of 5%.

Solution:

Use the following data for the calculation of P-Value.

Here, the sample size n = 200. We will have to find the sample proportion

= 0.64

Z Statistic

Calculation of Z Statistic

= 0.64 – 0.60 / √ 0.60 * (1 – 0.60) /200

Z Statistic will be –

Z Statistic =1.1547

P Value = P (z ≥ 1.1547)

NORMSDIST Function in Excel NORMSDIST Function In Excel NORMDIST or normal distribution is an inbuilt statistical function of excel that calculates the normal distribution of a data set with mean and standard deviation provided. read more

NORMSDIST will be –

NORMSDIST = 0.875893461

There is an inbuilt function to calculate a p-value from a z statistic in Excel. It is known as the NORMSDIST function. The Excel NORMSDIST function calculates the Standard Normal Cumulative Distribution Function from a supplied value. Its format is NORMSDIST(z). Since z statistic value is in cell B2, the function used is = NORMSDIST(B2).

P Value will be –

Since we have to find the area to the right of the curve,

p-value = 1 – 0.875893 = 0.124107

Since p-value of 0.124107 is more than a significant level of 0.05, we fail to reject the null hypothesis.

Relevance and Use

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Comments

Amit says

Thank you for great explanation!
After going through a lot of sites finally my quest has ended now.

Dheeraj Vaidya says

How to Calculate a P-Value from a Z-Score by Hand

In most cases, when you find a z-score in statistics you can simply use a Z Score to P-Value Calculator to find the corresponding p-value.

However, sometimes you may be forced to calculate a p-value from a z-score by hand. In this case, you need to use the values found in a z table.

The following examples show how to calculate a p-value from a z-score by hand using a z-table.

Example 1: Find P-Value for a Left-Tailed Test

Suppose we conduct a left-tailed hypothesis test and get a z-score of -1.22. What is the p-value that corresponds to this z-score?

To find the p-value, we can simply locate the value -1.22 in the z table:

Example 2: Find P-Value for a Right-Tailed Test

Suppose we conduct a right-tailed hypothesis test and get a z-score of 1.43. What is the p-value that corresponds to this z-score?

To find the p-value, we can first locate the value 1.43 in the z table:

Since we’re conducting a right-tailed test, we can then subtract this value from 1.

So our final p-value is: 1 – 0.9236 = 0.0764.

Example 3: Find P-Value for a Two-Tailed Test

Suppose we conduct a two-tailed hypothesis test and get a z-score of -0.84. What is the p-value that corresponds to this z-score?

To find the p-value, we can first locate the value -0.84 in the z table:

Since we’re conducting a two-tailed test, we can then multiply this value by 2.

So our final p-value is: 0.2005 * 2 = 0.401.

Additional Resources

The following tutorials explain how to calculate p-values from z-scores using various statistical software: