🚀 Quick Start

Run your first analysis in under two minutes — no installation, no sign-up, everything runs in your browser.

1

Open mindstat.pro in your browser — every feature is available instantly with no setup.
2

From the main page (Home), pick the module that matches your research and click "Open App".
3

Load your data: import CSV / Excel / SPSS, type it directly, or paste from Excel with Ctrl+V.
4

From the sidebar choose the test, map variables, then press the blue run button or Ctrl+Enter.
5

Read the results, click Verify with R Engine, or open the Statistical Assistant for interpretation.
6

Export from the 📤 Export button (PDF, Word, Excel, CSV) or print with Ctrl+P.

💡 Press ? (question mark) anywhere inside the app to open the keyboard shortcuts modal.

🧩 Modules Hub — What's Inside

The main page (mindstat.pro) is a hub that groups MindStat into 9 specialized modules. Each card opens a dedicated workspace with its own tests, forms, and charts.

📊 Statistical Analysis

The main workspace with 90+ procedures plus Bayesian, Bootstrap, and Mixed Models as built-in panels.

🩺 Biostatistics & Medical

Survival analysis, ROC curves, epidemiology, and clinical trial calculations.

📈 Econometrics

ARIMA, VAR, GARCH, cointegration, panel data, Granger causality, unit root tests.

🗺️ Spatial Statistics

Moran's I, Geary's C, spatial autocorrelation, density maps, SAR/SEM models.

🧠 SEM / CFA Modeling

Structural equation modeling, confirmatory factor analysis, path diagrams, fit indices.

🧪 Experimental Design

CRD, RCBD, Latin Square, Factorial, Split-Plot, ANCOVA, RSM.

🏭 SPC & Quality

Control charts (X̄-R, I-MR, p, np, c, u) and process capability indices.

📋 SPSS Interpreter

Paste any SPSS output table and get an instant plain-language + APA 7 interpretation.

🎯 Psychometrics

Reliability (α, ω), item analysis, IRT basics, scale validation.

💡 Bayesian Statistics, Bootstrap & Permutation, and Mixed Models are not separate hub cards — you access them from inside the Statistical Analysis module's sidebar.

📂 Import Data

Supported Formats

CSV / TSV

UTF-8 files. Separator (comma, semicolon, tab) is auto-detected.

Excel (.xlsx)

Parsed via SheetJS; the first sheet is loaded automatically.

SPSS (.sav)

Read directly in the browser — labels and missing codes are preserved.

Manual Entry

Type directly into the grid, or paste from Excel with Ctrl+V.

Data Formatting Rules

The first row must contain column names (variable headers).
International numeral formats are auto-converted to standard numbers.
Empty cells, 'NA', and 'NaN' are all treated as missing values.
Avoid merged cells, multi-row headers, and hidden sheets in Excel.
Keep datasets under ~10 MB for smooth performance.

🔒 Your data never leaves the browser — parsing, analysis, and storage all happen locally.

🏷️ Variable Types

After import, MindStat auto-detects each column's type. You can override the type at any time by clicking the type badge above the column header.

🔢 Metric — Continuous / numeric 🏷️ Nominal — Unordered categories 📊 Ordinal — Ordered categories

How auto-detection works

Columns where most values are numeric → Metric.
Few unique text values → Nominal.
Integer columns with ≤ 7 distinct values (Likert-like) → Ordinal.

💡 Setting the correct type decides which tests appear as options — categorical unlocks Chi-square and non-parametric tests; metric unlocks t-tests, ANOVA, and regression.

🧰 Data Wrangling (Transform Panel)

Before analyzing, you often need to reshape, clean, or derive new variables. Open the 🛠 Transform panel from the Statistical Analysis sidebar — it bundles six operations:

🔄 Reshape

Pivot long ↔ wide — before running repeated-measures ANOVA or mixed models.

🔍 Filter

Keep only rows matching a condition (e.g., age > 30, group = 'treatment').

🧮 Compute

Create a new variable from a formula (log, sqrt, z-score, BMI…).

✂️ Split & Analyze

Run the current analysis separately for each level of a grouping variable.

🔗 Merge

Join a second dataset on a shared key column (inner, left, outer).

🏷 Recode

Convert values to new ones (e.g., bin continuous variable into groups).

↩️ Every transformation is undoable — Ctrl+Z to roll back, Ctrl+Y / Ctrl+Shift+Z to redo.

▶️ Running Analyses

MindStat ships with 90+ procedures in the core Statistical Analysis module alone, plus dozens more across the specialized modules. The workflow is identical in every module:

1

From the sidebar, open the category you need (Descriptive, Hypothesis, Correlation, Regression, Non-parametric, Mediation, Power…).
2

Pick a specific test from the panel's dropdown.
3

Map variables to the required roles (DV, grouping factor, covariates, time, event…).
4

Press the blue run button (label varies: ▶ Run, ▶ Analyze, ▶ Draw, ▶ Calculate…) or hit Ctrl+Enter.
5

Results appear instantly: tables, interactive Plotly charts, assumption checks, effect sizes, and a plain-language interpretation.

✅ Every chart is interactive — hover, drag-to-zoom, double-click to reset, and use Plotly's camera icon to save as PNG.

Analysis History

Every analysis you run is logged automatically. Open the 📋 History button in the toolbar to re-open past results or re-run a test.

📦 Batch Analysis & Data Quality

Batch Analysis

Run the same test across many dependent variables at once — perfect for scale reliability, survey batteries, or screening multiple biomarkers.

Pick the test type in the Batch panel.
Select multiple dependent variables (Ctrl/Cmd-click).
Click 📦 Run Batch — results appear in one summary table.
Click 📥 Export to download the full batch report.

Data Quality Dashboard

Before you trust any analysis, check the health of your dataset via the 🔍 Data Quality button:

Missing-value counts and percentages per column
Outlier detection (IQR and z-score rules)
Duplicate row detection
Distribution skewness and kurtosis warnings per numeric variable
Automatic type-mismatch flags

🗺️ Which Test Should I Use?

Use this decision guide to map your research question, data type, sample size, and normality to the correct statistical test.

💡 When in doubt, ask the Statistical Assistant — describe your data and question in plain language and it will recommend the most appropriate test.

t-Tests / Mean Comparisons

Non-parametric

ANOVA Family

Correlation

Regression

Categorical / Chi-Square

Reliability

My research question	Data type	n	Normality	→ Use this test
Compare ONE group to a fixed value	Metric	Any	Normal	One-sample t-test
Compare ONE group to a fixed value	Metric	Any	Non-normal	Wilcoxon Signed-rank
Compare TWO independent groups	Metric	Any	Normal	Independent t-test (Welch)
Compare TWO independent groups	Metric	Any	Non-normal	Mann-Whitney U
Compare TWO related/paired groups	Metric	Any	Normal	Paired t-test
Compare TWO related/paired groups	Metric	Any	Non-normal	Wilcoxon Signed-rank
Compare THREE+ independent groups	Metric	Any	Normal	One-Way ANOVA
Compare THREE+ independent groups	Metric	Any	Non-normal	Kruskal-Wallis
Compare THREE+ related measurements	Metric	Any	Normal	Repeated-Measures ANOVA
Compare THREE+ related measurements	Metric	Any	Non-normal	Friedman Test
Relationship between 2 metric variables	Both Metric	Any	Normal	Pearson r
Relationship between 2 ordinal/non-normal	Ordinal	Any	Any	Spearman ρ
Predict one variable from another	Metric	≥ 20	Normal residuals	Linear Regression
Predict binary outcome	Binary DV	≥ 50	Any	Logistic Regression
Association between categorical variables	Categorical	n ≥ 20	N/A	Chi-Square
Association between categorical variables	Categorical	n < 20	N/A	Fisher's Exact
Scale reliability	Ordinal / Metric	≥ 30	N/A	Cronbach's Alpha

📘 Statistical Reference — Formulas & When to Use

A concise academic reference for the tests you will use most often in MindStat — what each test answers, when it applies, its assumptions, the underlying formula, and how to read the output.

📐 Mathematical formulas are rendered as native MathML. Use this section alongside the Statistical Assistant for deeper explanations.

1 · Descriptive Statistics

Arithmetic Mean M, x̄

The centre of gravity of a numeric variable.

\bar{x} = \frac{1}{n} \sum_{i = 1}^{n} x_{i}

When

Use with metric variables that are roughly symmetric and free of extreme outliers.

Read as

Report with SD: M = 42.3 (SD = 5.1).

Sample Standard Deviation SD, s

Average distance of observations from the mean.

s = \sqrt{\frac{1}{n - 1} \sum_{i = 1}^{n} (x_{i} - \bar{x})^{2}}

Why n-1

Bessel's correction gives an unbiased estimate of the population variance.

Read as

Small SD → clustered near mean; large SD → spread out.

Standard Error of the Mean SE, SEM

S E = \frac{s}{\sqrt{n}}

Meaning

Expected variability of the sample mean across repeated samples — basis of every CI and t-test.

Skewness & Kurtosis

g_{1} = \frac{1}{n} \sum {(\frac{x_{i} - \bar{x}}{s})}^{3} g_{2} = \frac{1}{n} \sum {(\frac{x_{i} - \bar{x}}{s})}^{4} - 3

Rule of thumb

|skew| < 1 and |kurtosis| < 1 is usually normal enough for parametric tests.

2 · Normality & Assumption Checks

Shapiro-Wilk Test W

Gold standard for testing whether a sample comes from a normal distribution.

W = \frac{{(\sum_{i = 1}^{n} a_{i} x_{(i)})}^{2}}{\sum_{i = 1}^{n} (x_{i} - \bar{x})^{2}}

H₀

The data are drawn from a normal distribution.

Decision

p < .05 → reject normality. Valid for 3 ≤ n ≤ 5000.

Caveat

With huge samples it rejects tiny deviations — always inspect a Q-Q plot too.

Levene's Test F

W = \frac{(N - k)}{(k - 1)} \cdot \frac{\sum_{i = 1}^{k} n_{i} ({\bar{z}}_{i \cdot} - {\bar{z}}_{\cdot \cdot})^{2}}{\sum_{i = 1}^{k} \sum_{j = 1}^{n_{i}} (z_{i j} - {\bar{z}}_{i \cdot})^{2}}

Where

z_ij = |x_ij − median_i| (the Brown-Forsythe robust variant MindStat uses).

Purpose

Checks the equal-variances assumption before pooled t-tests or ANOVA. If p < .05 use Welch.

3 · t-Tests (Comparing Means)

One-Sample t-test t

Does a single sample mean differ from a known reference value?

Two-tailed t distribution — red = rejection regions (α/2 each).

t = \frac{\bar{x} - μ_{0}}{s / \sqrt{n}}, d f = n - 1

Assumptions

Metric continuous outcome
Independent observations
Approximately normal distribution (or n ≥ 30)

Effect size

Cohen's d = (x̄ − μ₀) / s · small 0.2, medium 0.5, large 0.8

In MindStat

Hypothesis Tests → "One-sample t-test" (Ctrl+H).

Independent-Samples t-test t

Do two independent groups differ on average?

t = \frac{{\bar{x}}_{1} - {\bar{x}}_{2}}{\sqrt{s_{p}^{2} (\frac{1}{n_{1}} + \frac{1}{n_{2}})}}, s_{p}^{2} = \frac{(n_{1} - 1) s_{1}^{2} + (n_{2} - 1) s_{2}^{2}}{n_{1} + n_{2} - 2}

Welch variant

When variances are unequal (Levene p < .05), MindStat switches to Welch's t automatically.

Effect size

Cohen's d = (x̄₁ − x̄₂) / s_p

Paired-Samples t-test t

Do the same subjects differ between two measurements (pre/post)?

t = \frac{\bar{d}}{s_{d} / \sqrt{n}}, d f = n - 1

Where

d_i = x_{i,2} − x_{i,1}, the per-subject difference.

Use for

Pre-post intervention studies, matched pairs, within-subject designs.

4 · Analysis of Variance (ANOVA)

One-Way ANOVA F

Compares the means of three or more independent groups.

F is right-skewed — only large values reject H₀.

F = \frac{M S_{b e t w e e n}}{M S_{w i t h i n}} = \frac{S S_{B} / (k - 1)}{S S_{W} / (N - k)}

SS between

$SS_B = \sum_{i=1}^{k} n_i (\bar{x}_i - \bar{x})^2$

SS within

$SS_W = \sum_{i=1}^{k}\sum_{j=1}^{n_i} (x_{ij} - \bar{x}_i)^2$

Effect size

η² = SS_B / SS_total · small .01, medium .06, large .14

Post-hoc

On significant F, MindStat runs Tukey HSD or Games-Howell automatically.

Two-Way ANOVA

Tests two factors and their interaction on a single outcome.

Y_{i j k} = μ + α_{i} + β_{j} + (α β)_{i j} + ε_{i j k}

Partition

SS_total = SS_A + SS_B + SS_{AB} + SS_{error}

Read interaction first

If A×B is significant, interpret simple effects — main effects alone lose meaning.

Repeated-Measures ANOVA

Compares 3+ measurements on the same subjects.

F = \frac{M S_{t r e a t m e n t}}{M S_{s u b j e c t \times t r e a t m e n t}}

Sphericity

Mauchly's W — if violated, MindStat applies Greenhouse-Geisser or Huynh-Feldt correction automatically.

Use for

Longitudinal studies, pre/mid/post designs, crossover trials.

ANCOVA

Compares group means after adjusting for continuous covariates.

Y_{i j} = μ + τ_{i} + β (X_{i j} - \bar{X}) + ε_{i j}

Key assumption

Slopes must be equal across groups — tested by the group × covariate interaction.

Output

Adjusted marginal means with 95% CIs + an F test on the adjusted group effect.

MANOVA

Compares group means on multiple correlated dependent variables simultaneously.

Λ_{Wilks} = \frac{| E |}{| H + E |}

Statistics

Wilks' Λ, Pillai, Hotelling-Lawley, Roy's largest root — MindStat reports all four.

Assumption

Multivariate normality + equal covariance matrices (Box's M).

5 · Non-parametric Alternatives

Mann-Whitney U Test U

Non-parametric alternative to the independent-samples t-test.

U_{1} = n_{1} n_{2} + \frac{n_{1} (n_{1} + 1)}{2} - R_{1}, U = min (U_{1}, U_{2})

Use when

Data are ordinal, skewed, or contain outliers.

Effect size

r = Z / √N

Wilcoxon Signed-Rank Test W

Non-parametric paired t-test alternative.

W^{+} = \sum_{i = 1}^{n} 1 (d_{i} > 0) \cdot rank (| d_{i} |)

Use when

Paired differences are not normal, or the outcome is ordinal.

Kruskal-Wallis Test H

Non-parametric one-way ANOVA for 3+ groups.

H = \frac{12}{N (N + 1)} \sum_{i = 1}^{k} \frac{R_{i}^{2}}{n_{i}} - 3 (N + 1)

Post-hoc

Dunn's test with Bonferroni adjustment (auto-run on significance).

6 · Correlation

Pearson Correlation r

Strength and direction of a linear relationship.

Four scatter plots: strong positive → none → strong negative.

r = \frac{\sum_{i = 1}^{n} (x_{i} - \bar{x}) (y_{i} - \bar{y})}{\sqrt{\sum_{i = 1}^{n} (x_{i} - \bar{x})^{2} \sum_{i = 1}^{n} (y_{i} - \bar{y})^{2}}}

Range

−1 ≤ r ≤ +1

Interpretation

|r| ≈ 0.1 weak, 0.3 moderate, 0.5 strong, 0.7+ very strong.

Warning

Correlation ≠ causation. Inspect the scatter plot first.

Spearman's ρ ρ

ρ = 1 - \frac{6 \sum_{i = 1}^{n} d_{i}^{2}}{n (n^{2} - 1)}

Use when

Variables are ordinal, monotonic-but-nonlinear, or have outliers.

7 · Regression

Simple Linear Regression OLS

Predict Y from a single predictor X.

OLS minimizes the sum of squared residuals (red segments).

{\hat{y}}_{i} = β_{0} + β_{1} x_{i}, β_{1} = \frac{\sum (x_{i} - \bar{x}) (y_{i} - \bar{y})}{\sum (x_{i} - \bar{x})^{2}}

Fit quality

$R^2 = 1 - \dfrac{SS_{res}}{SS_{tot}}$ — proportion of variance in Y explained by X.

Assumptions

Linearity between X and Y
Normally distributed residuals
Homoscedasticity
Independence of observations

Multiple Linear Regression

\hat{β} = (X^{⊤} X)^{- 1} X^{⊤} y

Multicollinearity

Check VIF: values > 5 (strict > 10) → predictors are redundant. MindStat reports VIF per coefficient.

Adj. R²

$R_{adj}^2 = 1 - (1 - R^2)\dfrac{n - 1}{n - k - 1}$

Logistic Regression

Predict a binary (0/1) outcome.

Pr (Y = 1 ∣ X) = \frac{1}{1 + e^{- (β_{0} + β_{1} x_{1} + \dots + β_{k} x_{k})}}

Odds ratio

$OR = e^{\beta_j}$ — multiplicative change in odds per one-unit ↑ in X_j.

Fit check

Hosmer-Lemeshow + ROC / AUC (auto-reported).

Ordinal Logistic Regression polr

Predict an ordinal outcome (≥ 3 levels) — proportional odds model.

\log \frac{P (Y \leq j ∣ x)}{P (Y > j ∣ x)} = α_{j} - x^{'} β, j = 1, \dots, J - 1

Brant test

H₀: common β across binary logits. p < .05 → violation.

Use when

Outcome has a natural order (e.g., Likert scale, pain level 1–5).

Multinomial Logistic Regression multinom

Predict a nominal outcome (≥ 3 unordered categories).

\log \frac{P (Y = j ∣ x)}{P (Y = 0 ∣ x)} = α_{j} + x^{'} β_{j}, j = 1, \dots, J - 1

IIA assumption

IIA tested via Hausman-McFadden (reported in output).

Use when

Outcome has 3+ unordered categories (party choice, transport mode, etc.).

ZIP / ZINB

Count regression with excess zeros — structural + sampling-zero mixture.

P (Y = 0) = π + (1 - π) e^{- μ}, P (Y = k) = (1 - π) \frac{e^{- μ} μ^{k}}{k!}, k \geq 1

Model selection

Vuong test (vs Poisson) + LR test (ZIP vs ZINB). AIC reported automatically.

Use when

Count data (Y ≥ 0 integer) with excess zeros (e.g., doctor visits, claims).

Variance Inflation Factor VIF

Quantifies multicollinearity in a regression model.

V I F_{j} = \frac{1}{1 - R_{j}^{2}}

Where

$R_j^2$ = R² when X_j is regressed on all other predictors.

Cut-offs

< 5 OK · 5-10 concern · > 10 serious — drop or combine variables.

Durbin-Watson DW

Detects first-order autocorrelation in regression residuals.

D W = \frac{\sum_{t = 2}^{n} (e_{t} - e_{t - 1})^{2}}{\sum_{t = 1}^{n} e_{t}^{2}}

Interpretation

DW ≈ 2 → no autocorrelation · < 1.5 positive · > 2.5 negative.

Use when

Data are ordered in time — independent-error assumption is critical.

Breusch-Pagan χ²

Detects heteroscedasticity in regression residuals.

B P = n \cdot R_{e^{2} \sim X}^{2}

Procedure

Regress squared residuals on predictors; BP ~ χ²(k).

Remedy

p < .05 → use White / HC3 robust standard errors (one-click switch in MindStat).

8 · Tests for Categorical Data

Chi-Square of Independence χ²

Are two categorical variables associated?

χ^{2} = \sum_{i = 1}^{r} \sum_{j = 1}^{c} \frac{(O_{i j} - E_{i j})^{2}}{E_{i j}}, E_{i j} = \frac{R_{i} \cdot C_{j}}{N}

(r − 1)(c − 1)

Assumption

E ≥ 5 in 80%+ of cells — else MindStat switches to Fisher's exact test.

Effect size

Cramér's V = √(χ² / (N · min(r−1, c−1)))

Fisher's Exact Test

p = \frac{(\binom{a + b}{a}) (\binom{c + d}{c})}{(\binom{n}{a + c})}

Use when

2×2 table with small / zero expected counts — exact p, no approximation.

McNemar's Test

Paired χ² — for matched 2×2 dichotomous data (pre/post yes-no).

χ_{M c N}^{2} = \frac{(| b - c | - 1)^{2}}{b + c}

b, c

Off-diagonal cells (discordant pairs: yes→no and no→yes).

Use for

Diagnostic test agreement, pre/post treatment success-failure, case-control pairs.

Kolmogorov-Smirnov KS, D

Compares an empirical distribution against a reference (or two samples).

D_{n} = sup_{x} | F_{n} (x) - F (x) |

Use for

Normality check (alt. to Shapiro-Wilk) or two-sample distribution comparison.

9 · Survival Analysis (Biostatistics)

Kaplan-Meier Estimator

Survival drops at each event; upward ticks mark censored subjects.

\hat{S} (t) = \prod_{t_{i} \leq t} (1 - \frac{d_{i}}{n_{i}})

Where

d_i = events at t_i, n_i = subjects at risk just before t_i.

Output

A stepped survival curve with 95% CI bands and a risk table.

Log-rank Test χ²

Compares survival curves of 2 or more groups.

χ_{L R}^{2} = \sum_{i = 1}^{k} \frac{(O_{i} - E_{i})^{2}}{E_{i}}

Assumption

Proportional hazards — hazard ratio is constant over time.

Cox Proportional-Hazards

h (t ∣ X) = h_{0} (t) \cdot \exp (β_{1} x_{1} + β_{2} x_{2} + \dots + β_{k} x_{k})

Hazard ratio

$HR = e^{\beta_j}$ — HR > 1 ↑ risk, HR < 1 ↓ risk.

10 · Reliability & Psychometrics

Cronbach's Alpha α

Internal-consistency reliability for a set of items.

α = \frac{k}{k - 1} (1 - \frac{\sum_{i = 1}^{k} s_{i}^{2}}{s_{t o t a l}^{2}})

Acceptable

α ≥ .70 — research scale; ≥ .80 — clinical use; ≥ .90 — individual decisions.

Alternative

McDonald's ω is preferred for unequal loadings — also in the Psychometrics module.

Friedman Test χ²_r

Non-parametric alternative to Repeated-Measures ANOVA — compares 3+ related measurements by ranks.

χ_{r}^{2} = \frac{12}{n k (k + 1)} \sum_{j = 1}^{k} R_{j}^{2} - 3 n (k + 1)

Where

n = number of subjects, k = number of conditions, R_j = column rank sum for condition j.

k − 1

Post-hoc

Wilcoxon Signed-rank tests with Bonferroni correction for pairwise comparisons.

Use when

Data are ordinal, RM-ANOVA assumptions violated, or distributions are non-normal.

In MindStat

Non-parametric → Friedman Test.

Intraclass Correlation (ICC) ICC

Measures reliability of ratings when multiple raters assess the same subjects.

I C C (A, 1) = \frac{M S_{B M S} - M S_{W M S}}{M S_{B M S} + (k - 1) \cdot M S_{W M S}}

Where

MS_BMS = MS between subjects; MS_WMS = MS within subjects; k = number of raters.

Interpretation

< 0.50 poor · 0.50–0.75 moderate · 0.75–0.90 good · > 0.90 excellent (Koo & Mae 2016).

Variants

ICC(1,1) one-way random; ICC(2,1) two-way random; ICC(3,1) two-way fixed. Always report the model.

Use for

Inter-rater reliability, test-retest reliability, instrument calibration.

Cohen's Kappa κ

Categorical agreement between two raters, corrected for chance.

κ = \frac{P_{o} - P_{e}}{1 - P_{e}}

Where

P_o = observed proportion of agreement; P_e = expected agreement by chance.

Interpretation

< 0.20 slight · 0.21–0.40 fair · 0.41–0.60 moderate · 0.61–0.80 substantial · > 0.80 almost perfect.

Use for

Diagnostic agreement, coding reliability in qualitative research, clinical judgment studies.

Caveat

Kappa is sensitive to class imbalance — consider weighted kappa for ordinal categories.

Effect Size Reference Guide

Benchmarks for interpreting effect magnitude, independent of n and significance.

Guide

Statistic	Test family	Small	Medium	Large
Cohen's d	t-tests	0.20	0.50	0.80
Pearson r	Correlation	0.10	0.30	0.50
η² (eta-squared)	ANOVA	0.01	0.06	0.14
Cohen's f	ANOVA / Power	0.10	0.25	0.40
Cohen's w	Chi-Square	0.10	0.30	0.50
Cramér's V	Chi-Square (2×2)	0.10	0.30	0.50
R²	Regression	0.02	0.13	0.26

Note

Cohen (1988) benchmarks are discipline-independent guidelines. A 'small' effect may still be clinically or practically important depending on context.

11 · SEM / CFA Fit Indices

Model χ²

Tests whether model-implied covariance = observed covariance.

χ^{2} = (n - 1) \cdot F_{M L} (S, Σ (\hat{θ}))

Caveat

Very sensitive to large n — always inspect CFI/TLI/RMSEA/SRMR together.

CFI / TLI

C F I = 1 - \frac{max (χ_{M}^{2} - d f_{M}, 0)}{max (χ_{M}^{2} - d f_{M}, χ_{B}^{2} - d f_{B}, 0)}

T L I = \frac{(χ_{B}^{2} / d f_{B}) - (χ_{M}^{2} / d f_{M})}{(χ_{B}^{2} / d f_{B}) - 1}

Cut-offs

≥ .90 acceptable · ≥ .95 good fit (Hu & Bentler 1999).

Difference

CFI vs baseline · TLI adds complexity penalty.

RMSEA

R M S E A = \sqrt{max (\frac{χ^{2} - d f}{d f (n - 1)}, 0)}

Cut-offs

≤ .05 close · ≤ .08 reasonable · > .10 poor. Always report the 90% CI.

SRMR

S R M R = \sqrt{\frac{2}{p (p + 1)} \sum_{i = 1}^{p} \sum_{j = 1}^{i} {(\frac{s_{i j} - {\hat{σ}}_{i j}}{s_{i i}^{1 / 2} s_{j j}^{1 / 2}})}^{2}}

Cut-off

< .08 indicates acceptable fit — less sensitive to n than χ².

In MindStat

SEM / CFA module reports all indices + AIC/BIC on every model fit.

12 · Time Series (Econometrics)

ACF / PACF

First step in diagnosing AR / MA structure of a time series.

ρ_{k} = \frac{\sum_{t = k + 1}^{n} (y_{t} - \bar{y}) (y_{t - k} - \bar{y})}{\sum_{t = 1}^{n} (y_{t} - \bar{y})^{2}}

Reading

ACF spikes → MA(q) · PACF spikes → AR(p). Bars inside the 95% band are non-significant.

ARIMA(p, d, q)

The workhorse of univariate time-series forecasting.

(1 - \sum_{i = 1}^{p} ϕ_{i} L^{i}) (1 - L)^{d} y_{t} = (1 + \sum_{j = 1}^{q} θ_{j} L^{j}) ε_{t}

p, d, q

p = AR order · d = differencing for stationarity · q = MA order.

Model selection

Use auto.arima() (AIC/BIC minimization) — MindStat also checks residual white-noise.

ADF Test

Unit-root test — stationary or needs differencing?

Δ y_{t} = α + β t + γ y_{t - 1} + \sum_{i = 1}^{p} δ_{i} Δ y_{t - i} + ε_{t}

H₀

γ = 0, series has a unit root (non-stationary).

Decision

p < .05 → reject non-stationarity. Safe to fit a stationary model.

Granger Causality F

Does X's past help predict Y beyond Y's own past?

y_{t} = α + \sum_{i = 1}^{p} ϕ_{i} y_{t - i} + \sum_{j = 1}^{p} β_{j} x_{t - j} + ε_{t}

H₀

All β_j = 0 → X does not Granger-cause Y. F-test restricted vs unrestricted.

Caveat

'Causality' is statistical prediction, not true cause-effect.

13 · Statistical Process Control (SPC)

Shewhart X̄-R Limits

3σ control limits for the sample mean using subgroup range.

Points beyond the 3σ limits (red) signal an out-of-control process.

U C L_{\bar{X}} = \bar{\bar{X}} + A_{2} \bar{R}, L C L_{\bar{X}} = \bar{\bar{X}} - A_{2} \bar{R}

U C L_{R} = D_{4} \bar{R}, L C L_{R} = D_{3} \bar{R}

Constants

A₂, D₃, D₄ are from SPC tables, depending on subgroup size n (MindStat looks them up).

Out-of-control rules

Flags any of the 8 Western Electric / Nelson rules automatically.

Cp / Cpk / Pp / Ppk

Does the process fit inside its spec limits?

C_{p} = \frac{U S L - L S L}{6 σ}, C_{p k} = min (\frac{U S L - μ}{3 σ}, \frac{μ - L S L}{3 σ})

Benchmarks

Cpk ≥ 1.33 OK · 1.67 good · 2.00 Six Sigma (≈ 3.4 DPMO).

Cp vs Cpk

Cp ignores centring; Cpk penalizes drift.

14 · Spatial Statistics

Moran's I

Global measure of spatial autocorrelation.

I = \frac{n}{\sum_{i} \sum_{j} w_{i j}} \cdot \frac{\sum_{i} \sum_{j} w_{i j} (x_{i} - \bar{x}) (x_{j} - \bar{x})}{\sum_{i} (x_{i} - \bar{x})^{2}}

Range

−1 (dispersion) ≤ I ≤ +1 (clustering), expected value ≈ −1/(n−1).

Test

Z-statistic vs the expected value under spatial randomness.

15 · Item Response Theory

2-PL IRT Model

Probability of a correct response given ability θ, difficulty b, discrimination a.

P (X_{i} = 1 ∣ θ) = \frac{1}{1 + e^{- a_{i} (θ - b_{i})}}

a — discrimination

How sharply the item separates high vs low ability. a ≥ 1 adequate.

b — difficulty

Ability level where P = 0.5. b ≈ 0 is medium-difficulty.

Output

Item Characteristic Curves + information functions (Psychometrics module).

16 · Power Analysis

Power & Sample Size

Pre-study planning — how large a sample do I need?

n \approx \frac{2 {(z_{1 - α / 2} + z_{1 - β})}^{2}}{d^{2}}

Defaults

α = .05, power (1−β) = .80, small/medium/large d as per Cohen.

In MindStat

Power Analysis panel computes required n for t-tests, ANOVA, correlations, χ², regression.

📚 This reference is intentionally concise. For deeper derivations or worked examples, ask the Statistical Assistant — it can walk you through any formula step by step.

🟢 Verify Results with the R Engine

MindStat embeds a real R interpreter (R 4.5.1) compiled to WebAssembly via WebR — re-compute any analysis with real R code, all inside your browser, with no R installation.

1

Look for the green ✓ Verify with R Engine button below each supported result.
2

First click downloads the R engine (~30 MB, one-time). Expect 30-60 seconds on first use.
3

Once ready the badge becomes '🟢 R 4.5.1 Ready' — subsequent clicks run instantly.
4

R results are shown side-by-side with JavaScript results — green ✓ means both engines agree.

⚠️ The initial download needs internet. After the first successful load, R runs entirely locally for the rest of the session.

R packages loaded on demand

Packages are installed only on demand to keep first-load small. Typical ones include:

stats / car

t-tests, ANOVA, linear regression, Levene's test, diagnostics

survival

Kaplan-Meier, Cox proportional hazards

pwr

Power analysis and sample size calculations

lavaan

SEM, CFA, path analysis, fit indices

💡 Not every test has a Verify button — only tests where R gives meaningful cross-validation. If the button is absent, JavaScript is the single source of truth for that test.

💬 Statistical Assistant

The built-in Statistical Assistant is a specialized statistical interpretation engine. It interprets results, drafts APA 7 write-ups, suggests the right test, and explains assumptions — all in Arabic or English.

✅ No setup, no API key, no sign-up — the assistant is ready the moment you open the app.

Where to find it

The Assistant has three entry points inside the app:

The floating chat button in the bottom corner — a blue rectangle labeled "Statistical Assistant".
An "Interpret Results" button inside every result panel — sends the current result context automatically.
The "Ask the Advisor" link in the sidebar — useful for general questions before running a test.

Four things it does well

📖 Interpret Results

Plain-language explanation of p-values, CIs, effect sizes, and what they mean for your research.

📝 APA 7 Write-up

Generates a publication-ready results paragraph in correct APA 7 format.

🧭 Suggest a Test

Describe your data in natural language; get a recommended test plus alternatives.

🧪 Check Assumptions

Explains assumptions, flags violations in your data, and suggests remedies.

💡 Inside the chat, press Ctrl+Enter (or Cmd+Enter) to send. Clear prompts like "Write this in APA 7" or "Is my sample normal enough?" give the best answers.

📤 Export, Print & Share

After an analysis, the Export button in the results panel offers four file formats plus native printing and a shareable link:

📄 PDF

Full report with tables and charts, ready for submission.

📝 Word (.docx)

Editable Word document — tables and text preserved for thesis/paper insertion.

📊 Excel (.xlsx)

Numerical results and data tables as a real multi-sheet .xlsx.

📋 CSV

Plain-text export of any single table — ideal for R/Python/SPSS re-import.

🖨 Print (Ctrl+P)

Native browser print with a dedicated print stylesheet.

🔗 Share Analysis

Copy a link that reopens the current analysis with the same data and settings.

🎨 Theme & Language

Dark / Light Theme

Click the 🌙 / ☀️ button in the top-right of any page to switch between dark and light themes. Your choice is saved and reapplied automatically next visit.

Arabic / English

The 🌐 button toggles the whole interface between Arabic (RTL) and English (LTR), including statistical interpretation replies. You can also force a language via URL (e.g., ?lang=ar).

✨ When switching to Arabic, Noto Naskh Arabic is auto-loaded for crisp typography.

⌨️ Keyboard Shortcuts

Press ? inside the app any time to pop up this same list.

Ctrl + Enter

Run the current analysis

Ctrl + N

New session — reset everything

Ctrl + S

Save session (data + analyses) locally

Ctrl + D

Jump to Descriptive Statistics panel

Ctrl + H

Jump to Hypothesis Tests panel

Ctrl + R

Jump to Correlation panel

Ctrl + P

Print results (uses print stylesheet)

Ctrl + Z

Undo the last data change

Ctrl + Y

Redo

Ctrl + Shift + Z

Redo — alternative to Ctrl+Y

Ctrl + V

Paste data from Excel into the active grid cell

Alt + ←

Go back to the previous panel / view

Esc

Close the active dialog, modal, or loading spinner

Show the full keyboard shortcuts modal

💡 Shortcuts are disabled while focus is inside a text field — click outside first if they don't respond. On macOS, substitute Cmd (⌘) for Ctrl.

💾 Offline Mode & Auto-save

Everything saves automatically

MindStat writes your data, variable types, and settings into the browser's localStorage on every change. Close the tab, come back later — your session is still there.

Offline Mode (PWA)

MindStat is a Progressive Web App — a service worker caches the entire app shell on first visit. After that you can:

Open the app fully offline and run any JavaScript analysis.
Install the app to your desktop or home screen.
Keep data private — nothing is uploaded, ever.

⚠️ Two features need internet: (1) the one-time WebR engine download, and (2) the Statistical Assistant interpretation engine. Everything else runs locally.

💬 FAQ

Does the app save data automatically?

Yes — MindStat auto-saves to localStorage on every change. Ctrl+S creates a named checkpoint.

Does my data ever leave the browser?

No. Everything runs client-side. The only exception is the Statistical Assistant, which sends your message + results context to the interpretation engine when you use it.

Does the app work offline?

Yes, mostly. 90+ JS procedures, charts, and exports all work offline. Internet is only needed for the first WebR download and the Statistical Assistant.

Why do my R results differ slightly from JavaScript results?

Tiny differences (4-5th decimal) are normal (floating-point). Bigger discrepancies are flagged — usually caused by missing values or wrong variable types.

How do I export my results?

From the 📤 Export button: PDF, Word, Excel, CSV, or print with Ctrl+P. You can also copy a Share link.

Can I cite MindStat in my thesis or paper?

Yes — cite as MindStat Suite (v1.2). Academic Statistical Analysis Platform. https://mindstat.pro. For R-verified analyses, also cite R Core Team and the relevant R package.

Can I use MindStat on mobile?

Yes — responsive design works on tablets and phones. Desktop is recommended for large datasets or SEM / mixed models.

How do I report a bug or request a feature?

Open the About page for contact details. Include your browser version, a screenshot, and reproduction steps.

❓ User Guide

🚀 Quick Start

🧩 Modules Hub — What's Inside

📂 Import Data

Supported Formats

Data Formatting Rules

🏷️ Variable Types

How auto-detection works

🧰 Data Wrangling (Transform Panel)

▶️ Running Analyses

Analysis History

📦 Batch Analysis & Data Quality

Batch Analysis

Data Quality Dashboard

🗺️ Which Test Should I Use?

📘 Statistical Reference — Formulas & When to Use

🟢 Verify Results with the R Engine

R packages loaded on demand

💬 Statistical Assistant

Where to find it

Four things it does well

📤 Export, Print & Share

🎨 Theme & Language

Dark / Light Theme

Arabic / English

⌨️ Keyboard Shortcuts

💾 Offline Mode & Auto-save

Everything saves automatically

Offline Mode (PWA)

💬 FAQ