I Built 32 Free Statistics Calculators for Thesis Students: How I Verified the Maths

Ali Haider — Thu, 29 Oct 2026 04:37:56 +0000

Every semester, thousands of students reach the same wall in their thesis: the statistics chapter. They need a sample size, a reliability check for their questionnaire, the right test, and a results paragraph in APA style, and the usual options are an SPSS licence, a steep R learning curve, or online calculators that print a number without explaining it.

So I built SolveGrid: a set of free, browser-based statistics calculators that cover the whole research workflow, from planning the sample to writing up the result. Here is how it is put together and, more importantly, how I made sure the numbers are right.

What it covers

The site follows the order a student actually works in:

Plan the study: a statistical test chooser, Slovin and Cochran sample size, and an a priori power analysis for t-tests, ANOVA, correlation and chi-square.
Check the questionnaire: Cronbach's alpha, Likert weighted means, Cohen's kappa and ICC.
Run the test: t-tests, one-way ANOVA with Tukey HSD, chi-square, correlation, multiple regression, and the non-parametric family (Mann-Whitney, Wilcoxon, Kruskal-Wallis, Friedman, McNemar), plus Shapiro-Wilk for normality.
Report it: every calculator writes an APA-style sentence, and there are guides such as how to report regression in APA style.

The stack

It is a Next.js App Router site where every calculator page is statically pre-rendered. The calculators themselves are small client components; all of the statistics live in one plain TypeScript module of pure functions, so they can be tested outside React. Nothing is sent to a server: the data a student pastes in never leaves the browser.

The hard parts

Most of the formulas are textbook, but a few distributions needed real numerical work:

Exact p-values for t, F and chi-square use the regularised incomplete beta and gamma functions (continued fractions and series expansions).
Tukey HSD needs the studentized range distribution. I compute its CDF with a double numerical integral (Simpson's rule over the range of normals, then over the chi distribution of the denominator), and invert it by bisection for the critical value.
Power analysis needs noncentral t, F and chi-square distributions. The noncentral F and chi-square use Poisson mixtures of central distributions; the noncentral t uses a single integral over the chi distribution.
Shapiro-Wilk uses Royston's 1995 approximation, and the Mann-Whitney and Wilcoxon tests switch to exact distributions for small samples without ties.

How I verified it

Every function was checked against SciPy before it shipped. For each test I wrote a small script that runs the same sample data through my TypeScript and through scipy.stats, and compares the statistic, degrees of freedom, p-value and confidence interval. Examples that had to match:

Welch's t-test: t = 4.0548, df = 18.30, p = .00072
One-way ANOVA with Tukey: F(2, 21) = 38.85, all three pairwise p-values and intervals
Multiple regression: coefficients, standard errors, VIF, Durbin-Watson and Cook's distance
Power analysis: 64 per group for d = 0.5 at alpha = .05 and 80% power, the same as G*Power

Where I use an approximation (for example the Fisher z method for correlation power, which can differ from G*Power's exact method by one participant), the page says so.

What I learned

Building statistics tools is mostly an exercise in being honest about edge cases: ties, tiny samples, perfect collinearity, a column with no variance. Each one needed a clear error message rather than a silent NaN.