Use this P-value calculator to compute exact tail probabilities for common test statistics. This calculator supports Z-scores, t-scores, chi-square (χ²), and F-scores. To use it, select your test statistic from the dropdown menu. Then, enter your degrees of freedom (if required) and observed test statistic value. Click Calculate to see the result. [Read more…] about P-Value Calculator
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T Test Calculator
Use this T Test Calculator to perform a 1-sample, 2-sample, or paired t-test and assess your sample means. All these t-test calculator will find p-values and construction confidence intervals. Just scroll down to find the t-test you need and click to expand it. Simply enter your data into the table. Or copy and paste from a spreadsheet and the table will add rows as needed. You can enter up to 300 data rows, and the calculator automatically ignores incomplete or invalid rows. The editable headers are used in the statistical results. [Read more…] about T Test Calculator
Chi-Square Calculator
Use this chi-square calculator to test relationships between categorical variables. It computes the Pearson’s chi-square statistic by comparing your observed counts to the values you would expect if there were no association between categories. The results include the overall χ² value, degrees of freedom, p-value, and an APA-style results format for publications. [Read more…] about Chi-Square Calculator
Percentile Calculator
Use this percentile calculator to find a specific percentile in your dataset and its quartiles. It also displays a table with the 10th, 25th, 50th, 75th, and 90th percentiles so you can gauge your data’s distribution at a glance. [Read more…] about Percentile Calculator
Percent Error Calculator
The Percent Error Calculator determines how accurate a measurement is by comparing an observed value to a true value. It calculates the absolute difference relative to the true value and expresses it as percent error. For example, measuring 8.5 when the true value is 10 yields a 15% error. [Read more…] about Percent Error Calculator
Percentage Change Calculator
The Percentage Change Calculator quantifies how much one value changes relative to another. It expresses the result as a percent increase or decrease from the initial value. For example, going from 5 books to 10 books represents a 100% increase. Conversely, going from 10 books to 5 represents a 50% decrease. [Read more…] about Percentage Change Calculator
Variance Calculator
This variance calculator makes it easy to measure how spread out your data are. Just enter your numbers in the text box, separated by commas or spaces. Then choose whether you want to calculate the sample variance or the population variance. [Read more…] about Variance Calculator
Permutation Calculator
This permutation calculator finds the number of ways to arrange a sample of items from a larger set when the order matters. Enter the total number of objects (n) and the number of items in your arrangement (r). For example, the permutations calculator can tell you how many ways you can arrange 4 books from a shelf of 10 books. If the order items in the sample does NOT matter, use the Combination Calculator instead. [Read more…] about Permutation Calculator
Combination Calculator
This combination calculator finds the number of ways to choose a sample of items from a larger set when order does not matter. Enter the total number of objects (n) and the number of items in your sample (r). For example, the combination calculator can tell you how many ways you can choose 4 books from a shelf of 10 books. If the order items in the sample does matter, use the Permutation Calculator instead. [Read more…] about Combination Calculator
Correlation Coefficient Calculator
This correlation coefficient calculator measures the strength and direction of a linear relationship between two variables. Simply enter paired data into the table. Or copy and paste from a spreadsheet and the table will add rows as needed. You can enter up to 300 data rows, and the calculator will automatically ignore incomplete or invalid rows. The editable headers are used for the axis labels in the graph. [Read more…] about Correlation Coefficient Calculator
Poisson Distribution Calculator
This Poisson distribution calculator finds the probability of a specific number of events occurring within a fixed interval of time or space, based on a known average rate. Just enter the average rate (λ) and the number of events you’re interested in (x). For example, the Poisson distribution calculator can tell you the probability of receiving 3 emails in an hour if you typically receive 5 emails per hour. [Read more…] about Poisson Distribution Calculator
Binomial Distribution Calculator
Use this binomial distribution calculator to find the probability of a specific number of events occurring in a fixed number of trials. Just enter the probability of a single event (p), the number of trials (n), and the number of events you’re interested in (x). For example, the binomial distribution calculator can tell you the probability of getting 5 heads in 6 coin tosses. [Read more…] about Binomial Distribution Calculator
Confidence Interval Calculator
This confidence interval calculator finds the confidence interval for the mean–just enter several summary values and choose the method. Below the calculator are additional instructions and examples for using it. [Read more…] about Confidence Interval Calculator
Mean Median Mode Calculator
This mean, median, and mode calculator makes it easy to find the center of your data. Just enter your numbers in the text box, separated by commas or spaces. [Read more…] about Mean Median Mode Calculator
Standard Deviation Calculator
This standard deviation calculator makes it easy to measure how spread out your data are. Just enter your numbers in the text box, separated by commas or spaces. Then choose whether you want to calculate the sample standard deviation or the population standard deviation. [Read more…] about Standard Deviation Calculator
Z-Score Calculators
This page has two interactive Z-score calculators. The first calculator computes a Z-score based on your observed value, the mean, and the standard deviation. The second uses a Z-score to find the probability of various ranges under the standard normal distribution. See all my Statistical Calculators! [Read more…] about Z-Score Calculators
Weighted Least Squares (WLS) Explained
What is Weighted Least Squares (WLS)?
Weighted least squares (WLS) is a type of linear regression that assigns different weights to each data point when fitting the model. Instead of minimizing the simple residual sum of squares as ordinary least squares (OLS) does, WLS minimizes the weighted (wi) sum of squared residuals as the summation symbol below indicates:
Sensitivity vs Specificity: Definition, Formulas & Interpreting
Sensitivity and specificity are two key metrics used to evaluate the performance of diagnostic tests or classification systems in statistics, medicine, and machine learning. These measures assess the intrinsic capabilities of a test. [Read more…] about Sensitivity vs Specificity: Definition, Formulas & Interpreting
Marginal Probability: Definition, Formula & Examples
What Is Marginal Probability?
Marginal probability is the chance that an event will happen without considering other variables. Statisticians write this as p(A), denoting the probability of event A. You can think of it as an unconditional probability. It tells you how likely something will happen on its own, independently of other variables. [Read more…] about Marginal Probability: Definition, Formula & Examples
Latin Square Design in Experiments Explained
What Is a Latin Square Design?
A Latin square is an experimental design that tests multiple treatments while controlling for two sources of unwanted variation, known as nuisance variables. These nuisance variables are factors that you are not studying directly but could affect the outcome of your experiment if left uncontrolled. [Read more…] about Latin Square Design in Experiments Explained
