P Value Calculator

P Value Calculator

Use this P value calculator to calculate either one or two-tailed P values from statistical scores such as Z score, T score, F ratio score, Pearson (R) score, chi-square value, and Tukey Q score. With that, it automatically determines whether your results are statistically significant or not based on your chosen significance level.

What Is P-Value?

“The P-value is the probability of obtaining results at least as extreme as the observed ones, assuming the null hypothesis is true”

Null Hypothesis (H0):

When there is no difference between the observed value and the expected value, then this condition is known as the null hypothesis. 

Alternative Hypothesis (H1):

This condition shows a difference between the expected and the observed value. Meanwhile, it proposed that there is an effect on the data. 

Significance:

It means your results are so unlikely to happen randomly.

How To Calculate P Value?

There are different statistical tests(Z score, T score, Chi-square, etc) and each test requires different parameters to calculate the p-value. A p-value is based on the probability distribution of the test under the null hypothesis (H₀).

P value from Z Score:

A z score tells you how far a specific point is from the average(mean) value. The Z score depends on the standard normal distribution. It is used to find the difference for both large and small samples until the data follows the normal distribution. 

Z = X- µ σ

How To calculate P Value From Z Score?

• Calculate the z-statistic for deriving the P-value with the given formula
• After getting the calculated test statistic
• Use the z-score table to determine the P-value

P Value From T Score:

A t score, like a z score, is a standardized score used in statistics to know the distance of a point from the mean value. It is expressed in terms of standard deviation. Read on to know how to find p value from t score!

t = X- µ S ÷ n

P value can be easily determind by searching for the t score in a t-Distribution table or by putting it in a p value calculator from t score. 

• Positive T-score: The data point's value is above the mean value. It means the higher the p score, the above the data point is
• Negative T-score: It means that the data point is below the mean value
• T-score of 0: It means that the data point is equal to the mean

P value From Chi-Square (X2):

A chi-square test is used to determine the relationship between the categorical variables. With the help of the chi-square test, you can determine whether there’s a statistically significant difference or not between what you expected and what you observed in your data, especially when analyzing surveys with categorized answers. It helps you understand how likely the results are due to chance. 

If the value of the difference is large, then it suggests a relationship between the variables. It does not provide any information about the direction(positive or negative). You can calculate P value from chi square.

X2 = Σ (O- E)2 E

P Value From F Statistic:

The f statistic is used in conjunction with an F-test to assess the difference between variances of two or more groups (populations or samples). The interpretation of the F text depends upon the resulting p-value. Therefore stay attentive and focused whether you are performing the manual calculation or doing it with the help of the P-value calculator. If the value of p is low, then it means that the variance is likely different. While a greater p score indicates that the null hypothesis of variance can not be rejected. 

F = (s1)2 (s2)2

The degrees of freedom in the nominator is df1 = n1 - 1 and the degree of freedom for denominator is df2 = n2 - 1

Where:

• (s1)2 indicates the first sample variance
• (s2)2 represents the second sample variance

P-Value From Pearson (r) Score:

Pearson (r) score is a statistical measure that finds the degree of linear relationship between two quantitive variables. It gives the value between -1 and +1, indicating the relationship and direction. You can use the number between -1 and +1 and the degree of freedom (N-2) to find the P value from the r score. 

• Strong Positive Correlation: If it gives a value that’s near the +1, then it means on increasing one value, the other value will also increase
• Strong Negative Correlation: When the value is closer to the -1, then it means that on increasing one value the other value will decrease
• Weak or No Linear Correlation: If the value is near 0, then it indicates a weak or no relation between the variables

Finding P value from the Pearson (r) score involves the following steps:

Step #1: Calculate the test statistic (t)

t= r n-2 (1 - r2)

Step #2: Determine the degrees of freedom (df) = n−2

Step #3: Use the t-distribution table to determine the critical t-value and interpolate (if necessary)

y = y + (x - x1)(y2 - y1) x2 - x1

Step #4: Approximate P value

Use a P value table/chart to approximate the P value or get the exact P value effortlessly by using our P value calculator.

P-Value From Tukey q (Studentized Range Distribution) Score:

Tukey's HSD (Honestly Significant Difference) is the test that compares groups in the data and finds significant differences to determine whether they are significant or not. 

To find p value from Tukey q Score:

• Determine the Tukey Q Score: It shows the magnitude of the difference between two groups
• Calculate the Degrees of Freedom(df): It relies upon the number of groups that are compared and the sample size
• Studentized Range Distribution Table: Use the table that contains the calculated q-score and degrees of freedom
• Approximate the interpolation: If the q score does not match with any value of the table then use the interpolation to find p value

While we mentioned how easily you can calculate p-values from various statistics. For more convenient calculations, you can start using our P value calculator. It uses different scores and appropriate distribution to provide you P-value directly. 

How To Interpret P-Value Results?

• When the P-value is lower than the significance, then it means that the result is statically significant
• When the P-value is higher than the significance, then it indicates that the result is not significant and the p-value does not provide the evidence to reject the null hypothesis

References: 

From the source of Wikipedia.org: P-Value.