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Statistics calculators cover descriptive and inferential statistics: ANOVA, linear regression and correlation, confidence intervals, hypothesis tests, distributions, percentiles and margin of error. Each tool states the formula, the assumptions it requires, and the interpretation of the result, with worked examples from real data sets. The methods follow standard statistical references, and where a test depends on assumptions such as normality or equal variance, the page flags it and suggests alternatives. Outputs include the intermediate values so you can trace the calculation. These tools support coursework and data analysis; they run in your browser and nothing you enter is stored. The statistics pages walk through the output of each test step by step, so the result includes the evidence you would need to report the analysis.
Worked scenarios
Illustrative examples. Every figure was calculated with the tools linked at the foot of each scenario, using the formula each tool documents, so the numbers can be reproduced. They are not client results and they are not advice.
A survey with a 5% margin of error at 95% confidence needs 385 responses when the expected result is near 50%. Tighten the margin to 3% and the requirement more than doubles to 1,068. If the analysis has to be split into four groups, each group needs the full sample, so the practical target is about 1,540.
Worked with: Sample Size Calculator, Margin of Error Calculator
Twelve exam scores give a mean of 77.4 and a sample standard deviation of 8.0. The standard error is 2.3 and the 95% confidence interval runs from 72.9 to 81.9. Reporting the mean alone, 77.4, hides the range. The interval is what tells a reader how much the next class average could move.
Worked with: Standard Deviation Calculator, Confidence Interval Calculator, Mean / Median / Mode Calculator
Worked case studies: academic
Three scenarios, each with the inputs stated and the result computed. Every figure was calculated with the tools linked at the foot of the study, using the formula each tool documents, so it can be reproduced by entering the same values. They are illustrative examples, not client results, and they are not advice.
A student has to approximate the integral of sin(x) between 0 and pi, where the exact answer is 2, and can choose between the trapezoidal rule and Simpson's rule. Both runs use the same number of subintervals.
Inputs: f(x) = sin(x) on the interval 0 to pi. Four subintervals first, then eight.
Result: At four subintervals the trapezoidal rule returns 1.896119, an error of 0.103881, while Simpson's rule returns 2.004560, an error of 0.004560. At eight subintervals the values are 1.974232 and 2.000269.
What it means: At the same node count Simpson's rule lands more than twenty times closer to the answer, so the choice of method buys more here than doubling the work does.
Worked with: Simpson's Rule Calculator, Trapezoidal Rule Calculator
A surveyor measures the three sides of a triangular plot as 13 m, 14 m and 15 m. There is no right angle to work from and no convenient height to measure.
Inputs: Sides a = 13 m, b = 14 m, c = 15 m.
Result: Heron's formula gives an area of 84 square metres and a perimeter of 42 m. The three angles are 53.13, 59.49 and 67.38 degrees.
What it means: An awkward-looking triangle comes out on an exact whole number of square metres, which is the reason Heron's formula earns its place when nothing can be measured from a right angle.
Worked with: Triangle Calculator, Area Calculator
A poll of 1,000 respondents puts one candidate at 47% and the report calls it a lead. The question is whether the sample supports that word.
Inputs: 1,000 respondents, a proportion of 47%, and 95% confidence. Then 500 and 1,500 respondents for comparison.
Result: The standard error is 1.58 percentage points, so the margin is 3.09 points and the interval runs from 43.91% to 50.09%. At 500 respondents the margin widens to 4.37 points, and at 1,500 it narrows to 2.53 points.
What it means: At 1,000 responses the interval crosses 50%, so the poll does not establish a lead, and the extra precision from a bigger sample arrives slowly.
Worked with: Margin of Error Calculator, Confidence Interval Calculator, Sample Size Calculator
Available now
Percentile rank and inverse percentile with six interpolation methods.
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One-proportion z-test and one-sample t-test (or z-test with known ฯ) for means, test statistic, p-value, critical value, and confidence interval.
Pearson r, Spearman ฯ, and Kendall ฯ for paired data.
Chi-square test for independence or goodness of fit with observed vs expected frequencies.
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