BioMedStatX User Guide

BioMedStatX runs the entire statistical pipeline from assumption checks to HTML report generation. You supply the data and the mapping; the application selects the appropriate test. No code required.

0. First-Time Orientation

One concept determines everything in BioMedStatX: the division of labour between the application and the user.

BioMedStatX decides	You decide
Which statistical test fits the design	Which columns map to which bucket
Which assumption checks to run	Whether to accept an offered transformation
Parametric vs. nonparametric route	Which post-hoc procedure to use when prompted
Which plots and tables to generate	Which number format your CSV uses (for import)
Whether the result meets $\alpha = 0.05$	Which group subset to include in the analysis

A complete analysis run follows this order:

Load the file; select the worksheet.
Assign columns to the Smart Mapping buckets.
Click Start Auto Analysis.
Respond to any prompts (transformation, post-hoc method).
Review the HTML report, opened in your browser when analysis completes.

1. Launching the Application

Double-click the BioMedStatX application icon. The main window opens.

Developer note: if running from source, launcher scripts are available at the repository root. This has no bearing on normal usage.

2. Importing Data

Click Load Data File. Supported formats: Excel (.xlsx, .xls) and CSV (.csv).

Select the Worksheet from the dropdown (Excel files may contain multiple sheets). The Table Preview displays the first twelve rows so you can verify the import before proceeding.

For CSV files the application asks you to declare the number format instead of guessing it: the column separator (comma, semicolon, tab, or pipe), the decimal mark (dot or comma), and the thousands separator (none, dot, comma, or space). This is deliberate, since a wrong guess on a European file (for example reading 1.234,56 with a dot decimal) silently turns numbers into missing values. Set the three fields to match your file; the preview updates so you can confirm the columns parsed correctly.

Minimum data requirements

Requirement	Rationale
One row = one observation	Required for all supported workflows
At least one numeric measurement column	Needed for the Dependent Variable
At least one grouping or predictor column	Drives test selection
Subject ID column for repeated designs	Links multiple rows to the same individual
$\geq 2$ levels in the grouping factor	Required for any comparison

Prepare your file with a single header row, unique column names, no merged cells, and consistent categorical labels. WT and wt are treated as different levels.

Wide-format data

Wide-format files (one column per condition, e.g. Value_Pre, Value_Post) are detected and pivoted to long format before analysis. A notice confirms the pivot, lists the detected condition columns, and names the design it built — a paired design for two conditions, a repeated-measures design for three or more. Which test then runs is still decided by the assumption checks, so a repeated-measures design may end up as an RM-ANOVA or as Friedman.

Every row needs a subject ID. If the subject column has a blank cell the file is refused with a message rather than loaded in part, because rows without an ID drop out of the checks that decide repeated-measures structure.

Select Data Ranges

For raw Excel sheets that are not organized in tidy tabular format (such as custom plate exports, side-by-side matrices, or replicate blocks), click Select Data Ranges… to open the interactive spreadsheet selector.

1. Choose your experimental design

The dialog offers three design modes depending on how your experiment was structured:

Separate groups (Between-subjects): Each group consists of independent samples (e.g., Control vs. Treated, WT vs. KO). Routes to Welch's/Student's $t$-test or One-Way ANOVA.
Same samples, measured repeatedly (Paired): Each row corresponds to the same sample or animal measured across different conditions (e.g., Pre vs. Post). Enforces equal row height and preserves subject alignment, routing to a paired $t$-test or Repeated-Measures ANOVA.
Two measurements, related (Bivariate): Mark an $X$-block (e.g., dose or predictor) and a $Y$-block (response). Aligns data pairs for Linear Regression and Correlation.

2. Biological vs. Technical Replicates (Between-subjects)

Biological — each cell is an independent sample: Every selected numeric cell counts as $1,n$.
Technical — multiple readings per sample (averaged): Used when samples were measured in duplicates or triplicates:
- Samples in rows (replicates across columns) (Default): Standard laboratory layout where each row is an individual sample/animal and columns are the technical replicates. Selecting a block of 5 rows $\times$ 3 columns yields $n=5$ biological samples, with each value being the mean of its 3 technical readings.
- Samples in columns (replicates across rows): For transposed layouts where columns represent samples and rows represent replicates.
Live-$n$ display: The group list and bottom status bar immediately show the true sample size (e.g., WT (n=5) and (3 reps)).
Safety check: Attempting to apply a group with $n < 2$ displays a clear warning, preventing accidental analysis of single-sample groups.
Reporting & Provenance: The technical replicate summary (e.g., "Values averaged from 3 technical replicates per sample") is carried through to the HTML report's Data quality check (pre-analysis) table and saved in the report metadata.

3. Smart Mapping

The center panel provides six mapping buckets. Drag column cards from the Columns list into the appropriate bucket. The application auto-detects an initial mapping, which you can override.

Each bucket carries an ⓘ info button describing what belongs there.

Dependent Variable: The numeric outcome to be analysed: gene expression, cell count, weight, or any continuous measurement. Single analysis mode accepts one column; Multi-Dataset mode accepts several.
Factor 1: The primary predictor. Categorical input (e.g. Group with levels WT, KO) triggers t-Test or ANOVA. Continuous input (e.g. Pump time) triggers Correlation or Regression. Only one column allowed here.
Factor 2 (optional): A second grouping variable. Without Subject ID → Two-Way ANOVA. With Subject ID → Mixed ANOVA.
Subject ID (optional): The individual-level identifier for paired or repeated-measures designs. Assign this only when the same participant or experimental unit contributes more than one row.
Covariates (optional): Continuous confounders to control for (e.g. Age, BMI, Baseline). Categorical Factor 1 + Covariates → ANCOVA. Continuous Factor 1 + Covariates → Multiple Regression.
Filter (optional): Restricts the analysis to a subset of rows before any assumption checks or model fitting. See Section 15.

Factor 1 vs. Subject ID: where most mistakes happen

A grouping variable and a subject identifier look identical in the data (both contain labels), but play opposite roles. Group with values WT and KO defines what you are comparing. PatientID with values P001, P002 identifies who was measured. Getting this wrong produces an unpaired test where a paired design was intended, which inflates the error variance and reduces power.

Mapping-to-design reference

Design	Dep. Var.	Factor 1	Factor 2	Subject ID
Independent t-Test	Value	Group (WT / KO)	—	—
Paired t-Test	Value	Timepoint (Pre / Post)	—	SubjectID
One-Way ANOVA	Value	Group (≥ 3 levels)	—	—
Repeated Measures ANOVA	Value	Timepoint (≥ 3)	—	SubjectID
Two-Way ANOVA	Value	Group	Treatment	—
Mixed ANOVA	Value	Timepoint	Group	SubjectID
ANCOVA	Value	Group (categorical)	—	—
Correlation	Outcome	Predictor (continuous)	—	—
Linear Regression	Outcome	Predictor (continuous)	—	—

The mapping status line below the buckets updates in real time and confirms which test will run. The messages are literal; the most common are (the app shows further messages for other incomplete states, e.g. a missing measurement column or too many subject-ID columns):

"Load a file to activate the mapping workflow." — no file loaded yet.
"Assign at least one factor column." — Dependent Variable is filled but Factor 1 is not.
"Auto-pilot currently supports at most two factor columns." — too many factor columns mapped; reduce to one or two.
"Mapping looks valid. Start the analysis when you are ready." — all required buckets are filled.
"Auto-pilot is analyzing the mapped design." — analysis is running and the interface is locked.

After assigning Factor 1, use Select Groups For Analysis to restrict the analysis to a subset of factor levels. Leaving this empty runs all available groups.

4. Single vs. Multi-Dataset Analysis

Switch between modes with the radio buttons above the table preview.

Single Analysis runs one measurement column through the full pipeline. Use this for any single readout: one gene, one clinical parameter.

Multi-Dataset Analysis runs two or more measurement columns through the same factor mapping in sequence. The HTML report presents a summary card per column, with Benjamini–Hochberg FDR correction applied across all $m$ p-values. Restricted to ANOVA-capable designs.

A column that cannot be analysed does not silently drop out of the overview. The report states how many columns were summarized and how many failed, and lists each failed column with the reason under Not Analysed, so the summary cards are read against the full selection rather than only its survivors. The overview is written even when no column could be analysed at all. Note that the FDR family covers the columns that produced a p-value: with fewer than two survivors no correction is applied, and the report then carries no FDR note.

5. Starting the Analysis

Click Start Auto Analysis. The pipeline executes in this order:

Apply the active data scope (Filter + group selection).
Normality check (Shapiro–Wilk on model residuals; bypassed if $N \ge 30$ per the Central Limit Theorem).
Variance homogeneity check (Levene's test).
Test selection (parametric, Welch, or nonparametric).
Main test.
Post-hoc comparisons (when $p < \alpha$ and $\geq 3$ groups).
Plot and HTML report generation.

Two interactive prompts may appear: transformation choice (Section 7) and post-hoc method selection (Section 8).

6. Export Settings

When you click Start Auto Analysis, a Save Analysis Report dialog opens first. Choose the folder and file name there: the location you pick becomes the output directory, and the base name is reused for all exports from that run (Excel file, HTML report, and plot image). The dialog suggests a name derived from your data file and measurement column; cancelling it aborts the run. There is no separate file-name field on the main window — the save dialog is where the output location is set.

7. Assumption Checks and Data Transformations

Shapiro–Wilk tests normality of model residuals (normality is assumed if $N \ge 30$ per the Central Limit Theorem); Levene's test checks variance homogeneity. When assumptions fail, the application prompts for a transformation.

Transformation	Use case
Log₁₀	Right-skewed data; requires strictly positive values
Box–Cox	Automatic power transformation; $\lambda$ optimised by maximum likelihood
Arcsin $\sqrt{x}$	Proportion or percentage data; the scale is declared explicitly (see below)

Skipping the transformation is always valid. The application takes the nonparametric route (Mann–Whitney U, Kruskal–Wallis, Friedman) without further prompting.

Arcsin-square-root and the data domain. Because arcsin($\sqrt{x}$) stabilises variance only for genuine proportion data, selecting it opens a prompt to declare the scale: Proportion (0 – 1) or Percent (0 – 100). Values outside the declared range are rejected: the transformation is not applied and there is no silent fallback, so a percentage column mistakenly declared as a proportion stops with an error instead of corrupting the data. Cancelling the prompt (declaring no domain) skips arcsin and routes the analysis to the nonparametric test. The transform rescales against the global data range, not per group.

On very skewed data the Box–Cox $\lambda$ search can run away to a value so large it inflates the variance instead of taming it. The app guards against this: it checks the optimised $\lambda$ against the range $[-3, 3]$, and if $\lambda$ falls outside, it discards the estimate and uses a plain log transformation ($\lambda = 0$) instead. The report adds a note when this fallback happens.

8. Post-Hoc Comparisons

A significant main test with $\geq 3$ groups triggers a post-hoc selection prompt.

Parametric options:

Test	When to use
Tukey HSD	All pairwise comparisons. Available for one-way designs and Two-Way ANOVA. Repeated-Measures and Mixed ANOVA do not offer Tukey; they use the Holm-Šidák pairwise option below, which stays coherent with the sphericity-corrected omnibus.
Games-Howell	All pairwise comparisons; does not assume equal variances. Default for One-Way Welch-ANOVA.
Dunnett	Each treatment group vs. one control; more power than Tukey when a reference group exists
Holm-\u0160id\u00e1k corrected pairwise t-tests	User-selected pairs; sequential \u0160id\u00e1k correction
FDR-corrected pairwise t-tests	User-selected pairs; Benjamini-Hochberg FDR (Available for Advanced ANOVAs)

Nonparametric path:

After Kruskal–Wallis, a prompt offers Dunn's test (all pairs, Holm-Šidák correction; the default) or pairwise Mann–Whitney U on pairs you pick.
After Friedman, the app applies the Conover-Iman post-hoc (all pairs, Holm-corrected) directly, without a prompt; pairwise Wilcoxon signed-rank is used only as a fallback if the Conover-Iman routine is unavailable. The advanced nonparametric fallbacks (e.g. after Brunner–Langer) apply pairwise Wilcoxon/Mann–Whitney with Holm correction.

Cancelling a post-hoc prompt is a valid choice: the analysis keeps the main-test result and reports no pairwise comparisons. Pick it when only the overall effect matters.

The group-selection dialog and the pairwise-comparison dialog both provide Select All and Deselect All buttons to check or clear the whole list at once rather than ticking boxes individually.

Results appear on the plot as either significance brackets with stars or a compact letter display (see §9), and as a comparison table in the HTML report.

9. Plot Customisation

The HTML report includes an interactive Plot Designer section that rebuilds the plot in real time. Adjust settings and download publication-ready figures without re-running the analysis.

The Plot Designer has five tabs:

Plot: chart type (Bar, Box, Violin, Raincloud, Forest, or Estimation), data point overlay (Jitter or Beeswarm), error bars (SD, SEM, 95% CI, IQR, or Range), central measure (mean or median), and a Connect subjects overlay. The overlay draws one line per subject across the levels — what a paired test actually analyses, and the only way to tell apart two datasets with identical boxes where one has every subject moving the same way and the other does not. It stays available only when the result carries subject identities, the level order is given by the data rather than guessed alphabetically, and no more than 30 subjects would be drawn; otherwise the checkbox is greyed out and says which condition failed. Raincloud places each group on its own row, so it is excluded there. Box plots show the median and interquartile range only; a mean ± error overlay is not drawn on a box (use the bar or violin plot for mean-based error bars).
Axes: X/Y axis labels, Y-axis range and format, grid style, tick direction, legend position and orientation, and optional reference lines (y = 0 baseline, y = 1 fold-change, threshold lines from payload).
Style: plot title, axis labels, font family and size, per-group colours (six curated palettes: Nature, Okabe-Ito, Grayscale HC, Muted Pastel, Deep, and Turbo, with Nature the default), bar fill patterns, and data point symbols.
Stats: the Significance display selector (None, Brackets + stars, or Letters), line width, spacing, label size and offset, plus a checkbox per comparison. The selector opens on whichever form suits the result: letters when the post-hoc compared every pair and four or more groups are shown, brackets otherwise. Only significant pairs are drawn.
- Brackets + stars annotate each comparison individually. Their checkboxes hide single brackets to declutter a crowded plot; the ones left standing each remain true on their own.
- Letters label every group instead: groups sharing a letter are not significantly different. This stays available only when the post-hoc compared all pairs, because a comparison that was never run cannot honestly be shown as “not different” — with Dunnett or another control-referenced post-hoc the option is greyed out and the panel explains why. Letters are computed from the complete set of comparisons, so the per-pair checkboxes are disabled in this mode: dropping one comparison would merge two groups that do differ onto a shared letter and make the plot state the opposite of the result.
Export: figure dimensions in inches, PNG scale (1x to 4x, up to ~400 DPI), SVG download, and PNG download.

10. Statistical Analyses: full reference

Test	Triggered when
Independent t-Test (Welch's by default)	Factor 1 categorical, 2 groups, no Subject ID
Paired t-Test	Factor 1 categorical, 2 groups, Subject ID assigned
Mann–Whitney U	t-Test conditions; normality violated
Wilcoxon signed-rank	Paired t-Test conditions; normality violated
Welch's ANOVA	Factor 1 categorical, $\geq 3$ groups, no Subject ID. Default parametric One-Way ANOVA (robust to unequal variances)
Kruskal–Wallis	ANOVA conditions; normality violated
Repeated Measures ANOVA	Factor 1 categorical, Subject ID assigned, $\geq 3$ levels
Friedman test	RM-ANOVA conditions; normality violated
Two-Way ANOVA	Factor 1 + Factor 2 categorical, no Subject ID
Freedman–Lane permutation	Two-Way ANOVA conditions; normality violated
Mixed ANOVA	Factor 1 + Factor 2 + Subject ID assigned
Brunner–Langer ATS	Mixed ANOVA conditions; normality violated
ANCOVA	Factor 1 categorical + Covariates present
Correlation (Pearson/Spearman)	Factor 1 continuous, no Covariates, no Subject ID
Simple/Multiple Regression (OLS)	Factor 1 continuous + Covariates; or Regression toggle active
Linear Mixed Model	Factor 1 continuous + Subject ID
Logistic Regression	Dependent Variable contains exactly 2 distinct values

Effect sizes reported per test family:

Test family	Effect size
t-Test (independent)	Cohen's $d = \frac{\bar{x}_1 - \bar{x}_2}{s_p}$
t-Test (Welch)	Hedges' $g$
Wilcoxon / Mann–Whitney	Rank-biserial $r$
ANOVA family	Partial $\eta^2_p$
Correlation	Pearson $r$ or Spearman $\rho$
Regression	$R^2$, adjusted $R^2$
LMM	ICC $= \frac{\sigma^2_u}{\sigma^2_u + \sigma^2_\varepsilon}$
Logistic Regression	AUC, McFadden $R^2$

11. Decision Tree Visualisation

The HTML report contains an interactive decision tree. The path actually taken is highlighted with animated arrows that replay in sequence. The initial view centres on the active path. Zoom, pan, and reset are available.

The decision-tree panel in the results area also has a Maximize button that opens the tree in a full-window overlay — useful on complex designs where the default panel size clips branches.

12. Reviewing Results: HTML Report

Analysis produces a single self-contained .html file that opens in your browser.

The report contains:

Header: test name, $p$-value, significance label, effect size with magnitude badge (Small / Medium / Large by Cohen's conventions)
Statistical results: statistic, degrees of freedom, $p$-value, effect size, 95% CI, power ($1 - \hat{\beta}$)
Assumption results: normality, variance, and applied corrections
Data quality checks (pre-analysis): a warning table flagging any rows or values dropped during import (non-numeric cells, missing group labels), shown when the import found problems
Descriptive statistics: $\bar{x}$, SD, SEM, median, $n$ per group
Pairwise comparison table: post-hoc results with corrected $p$-values
Interactive decision tree: full path with zoom and replay
Interactive plot: main chart with optional plot designer
Raw data: the filtered, analysis-ready dataset
Methods text: a plain-language description of the pipeline, formatted for direct inclusion in a Methods section

13. Outlier Detection

Analysis → Detect Outliers offers:

Grubbs' test (single or iterative). The default; holds its nominal false-positive rate down to small samples.
Modified Z-Score (threshold at $|M_i| > 3.5$, where $M_i = \frac{0.6745(x_i - \tilde{x})}{MAD}$). Not the default: its median/MAD scale is unstable on small groups and flags a normal point as an outlier in about 29% of clean $n = 3$ samples, so the dialog shows a caution when it is selected on groups below $n = 8$.

Review flagged observations before proceeding. Removing outliers changes the analysis. Document this decision in your methods.

14. Quick-Reference Workflow

Launch the application.
Load file; select worksheet.
Assign: Dependent Variable, Factor 1, and (if needed) Factor 2, Subject ID, Covariates.
Choose Single or Multi-Dataset mode.
Optionally restrict the analysis to a subset of levels with Select Groups For Analysis.
Click Start Auto Analysis, then set the output folder and file name in the save dialog.
Respond to transformation and post-hoc prompts if they appear.
Open the HTML report from the output directory.

Tips

Group labels (WT, KO, Control) belong in Factor 1: they define experimental conditions, not individuals.
Subject ID is needed only when one individual contributes more than one row.
In paired designs, every subject must appear exactly once per condition. Imbalanced data triggers a warning.
Copy the Methods text section from the HTML report directly into your manuscript draft.
For skewed data, the Log₁₀ transformation is the safe first choice. Box–Cox is more aggressive and less interpretable after back-transformation.

15. Filter Bucket — Subgroup Analysis

The Filter bucket restricts the dataset before assumption checks and model fitting — the correct approach for a subgroup analysis, rather than filtering results after the fact.

How to use:

Drag a categorical column (e.g. OP_Group, Sex) into the Filter bucket.
Select the value to keep from its dropdown.
Click Start Auto Analysis — the whole pipeline runs on the restricted subset.

If the chosen subset leaves too few observations for the design, the analysis stops with a "Too few observations after filter" message rather than running on unstable data.

The ⓘ button on the bucket title explains its purpose at any time.

16. Correlation Analysis

Trigger conditions: Factor 1 continuous (> 10 unique numeric values), no Covariates, no Subject ID.

Configuration

Bucket	Assign
Dependent Variable	Numeric outcome
Factor 1	Continuous predictor
Covariates	Leave empty: any entry here switches to Regression
Subject ID	Leave empty: any entry here switches to LMM
Filter	Optional subgroup restriction

Pearson vs. Spearman: the decision rule

The choice is driven by sample size and distribution shape (skewness and excess kurtosis), not by a Shapiro–Wilk significance gate. A normality pre-test has too little power at the small $n$ typical of biomedical correlation and rejects trivial departures at large $n$; the app selects on shape tiers instead (the same reasoning behind the Welch-only $t$-test default). Shapiro–Wilk is still computed and shown in the report, but it does not decide the method.

$n < 20$ → Spearman $\rho$ (too few points to judge shape reliably).
$20 \leq n < 100$ → Pearson $r$ if both variables have $|\text{skew}| \leq 1.0$ and $|\text{excess kurtosis}| \leq 2.0$; otherwise Spearman $\rho$.
$n \geq 100$ → Pearson $r$ unless either variable has $|\text{skew}| > 2.0$ or $|\text{excess kurtosis}| > 4.0$ (extreme asymmetry → Spearman).

Correlation→Regression toggle

When Factor 1 is continuous and Covariates is empty, a checkbox appears:

"Analyze as Linear Regression (Y = a + bX)"

Leaving it unchecked runs Correlation. Checking it runs Simple OLS Regression with one predictor: slope coefficient $\hat{\beta}_1$, 95% CI on $\hat{\beta}_1$, and the full residual diagnostic battery (Shapiro–Wilk, Breusch–Pagan, Ramsey RESET).

What is reported (HTML report)

Statistic	Description
$r$ or $\rho$	Correlation coefficient, range $[-1, 1]$
$p$	Two-tailed significance
95% CI	Fisher $z$-transformation interval
$n$	Valid pairs after pairwise deletion
Method	Pearson or Spearman
Interpretation	Strength label (Negligible / Weak / Moderate / Strong / Very strong)

Strength thresholds follow Cohen (1988): $|r| < 0.10$ negligible, $0.10$–$0.29$ weak, $0.30$–$0.49$ moderate, $0.50$–$0.69$ strong, $\geq 0.70$ very strong.

17. Linear Regression (OLS)

Trigger conditions: Factor 1 continuous + at least one Covariate assigned. Or: Regression toggle active (no Covariate needed for simple regression).

The fitted model:

$$Y_i = \beta_0 + \beta_1 X_{1i} + \beta_2 X_{2i} + \ldots + \beta_k X_{ki} + \varepsilon_i, \quad \varepsilon_i \sim \mathcal{N}(0, \sigma^2)$$

Configuration

Bucket	Assign
Dependent Variable	Numeric outcome
Factor 1	Primary continuous predictor
Covariates	Additional predictors to control for
Filter	Optional subgroup restriction

Variable transformations

Available for both X (Factor 1) and Y (Dependent Variable) when Regression mode is active:

Transform	Formula	Use case
log₁₀	$X' = \log_{10}(X)$	Right-skewed positive variables
log₁₀(x+1)	$X' = \log_{10}(X+1)$	Count data with exact zeros
sqrt	$X' = \sqrt{X}$	Count data; moderate skew
Box–Cox	$X' = \frac{X^\lambda - 1}{\lambda}$	Automatic $\lambda$ optimisation

When a transform is applied, the displayed $\hat{\beta}$ operates on the transformed scale. A $\hat{\beta}_1 = 0.3$ with log₁₀-transformed Y means a one-unit increase in X multiplies the original Y by $10^{0.3} \approx 2.0$. The HTML report states this interpretation explicitly.

If both X and Y are log-transformed (Log-Log model), $\beta$ represents an elasticity: a 1% increase in X is associated with a $\beta$% change in Y.

Warning

Transformations should be chosen based on theoretical grounds or to resolve assumption violations (e.g., heteroscedasticity or non-linearity), not purely because raw predictors "look skewed". Normality of predictors (X) is not an assumption of OLS regression. Avoid P-Hacking: Do not iteratively try different transformations just to drive the p-value below 0.05. This invalidates your statistical inference.

What is reported (HTML report)

Model summary: $R^2$, adjusted $R^2 = 1 - \frac{(1-R^2)(n-1)}{n-k-1}$, $F(k, n-k-1)$, $p(F)$, AIC, BIC, $n$.

Coefficient table:

Column	Content
$\hat{\beta}$	Unstandardised regression coefficient
SE	Standard error of $\hat{\beta}$
$t$	$\hat{\beta} / \text{SE}$, evaluated on $t_{n-k-1}$
$p$	Two-tailed
95% CI	$\hat{\beta} \pm t_{0.975, n-k-1} \cdot \text{SE}$

Residual diagnostics: Shapiro–Wilk (normality), Breusch–Pagan (homoscedasticity), Ramsey RESET (linearity). See CORRELATION_REGRESSION_GUIDE.md for interpretation.

18. Exploratory Correlation Matrix

Analysis → Exploratory Correlation Matrix computes all pairwise correlations across selected numeric variables and corrects for multiple testing.

Option	Description
Variable selection	Check/uncheck numeric columns
Method	Auto (Shapiro–Wilk per pair), Spearman, or Pearson
Missing data	Pairwise deletion ($n$ varies per pair) or Listwise (complete cases only)
Correction	FDR (Benjamini–Hochberg), Bonferroni, or None
Stratify by	Run the matrix separately per level of a categorical column

For $m$ variables, the matrix contains $\binom{m}{2}$ tests. With $m = 20$, that is 190 simultaneous tests. Uncorrected p-values guarantee false positives. Use FDR or Bonferroni.

HTML report output:

Matrix of $r$ / $\rho$ values
Matrix of corrected $p$-values
Matrix of $n$ per pair (essential when missing data is present)

19. ANCOVA / Two-Way ANCOVA

ANCOVA tests group mean differences while partitioning out the linear effect of one or more continuous covariates. The adjusted group mean for group $j$ estimates:

$$\hat{\mu}_j^* = \hat{\mu}_j - \hat{\beta}_{cov}(\bar{x}_{j,cov} - \bar{x}_{cov})$$

Trigger conditions: Factor 1 categorical + at least one Covariate assigned. Two-Way ANCOVA: Factor 1 + Factor 2 (both categorical) + Covariates.

Configuration

Bucket	Assign
Dependent Variable	Numeric outcome
Factor 1	Categorical grouping factor
Factor 2	Optional second categorical factor → Two-Way ANCOVA
Covariates	Continuous confounders
Filter	Optional subgroup restriction

What is reported (HTML report)

ANOVA table (Type II SS): $F$, $df$, $p$, $\eta^2$ per source
Covariate effects: $\hat{\beta}$, SE, $t$, $p$, 95% CI per covariate
Adjusted means: estimated marginal means at the grand mean of each covariate
Regression slope homogeneity: tests whether the covariate–outcome slope is equal across groups (the core ANCOVA assumption)
Simple Slopes and Johnson–Neyman interval: reported when slopes are heterogeneous ($p < 0.05$ for the Factor × Covariate interaction)
Model fit: $R^2$, adjusted $R^2$, AIC, $n$

The slope homogeneity assumption

ANCOVA assumes parallel regression slopes. When this assumption fails, the adjusted means are misleading. The Johnson–Neyman (J-N) technique identifies the range of covariate values where the group difference is and is not statistically significant, which is more informative than simply flagging an assumption violation.

20. Linear Mixed Model (LMM)

LMM is the appropriate tool for longitudinal data where the same subjects are measured at multiple levels of a continuous factor (e.g. repeated timepoints, varying pump durations). Unlike simple regression, LMM accounts for the within-subject correlation between repeated measurements.

Trigger conditions: Factor 1 continuous + Subject ID assigned.

The model:

$$Y_{ij} = \beta_0 + \beta_1 X_{ij} + u_{0i} + \varepsilon_{ij}$$

where $u_{0i} \sim \mathcal{N}(0, \sigma^2_u)$ is the random intercept for subject $i$ and $\varepsilon_{ij} \sim \mathcal{N}(0, \sigma^2_\varepsilon)$ is the residual.

A random-intercept + random-slope model is also tested:

$$Y_{ij} = (\beta_0 + u_{0i}) + (\beta_1 + u_{1i}) X_{ij} + \varepsilon_{ij}$$

Configuration

Bucket	Assign
Dependent Variable	Numeric outcome
Factor 1	Continuous time or predictor variable
Subject ID	Subject/patient identifier
Covariates	Optional additional predictors
Filter	Optional subgroup restriction

Model selection: random intercept vs. random slope

The application fits both structures and compares them with a Likelihood Ratio Test:

$$\Lambda = -2\bigl(\ell_{\text{RI}} - \ell_{\text{RI+RS}}\bigr) \sim \chi^2(2)$$

If $\Lambda > \chi^2_{0.05}(2) = 5.99$ (i.e. $p < 0.05$), the random-intercept + slope model is retained. Otherwise the simpler random-intercept model is used. The structure chosen is noted in the HTML report.

ICC: Intraclass Correlation Coefficient

$$\text{ICC} = \frac{\sigma^2_u}{\sigma^2_u + \sigma^2_\varepsilon}$$

ICC	Interpretation
$< 0.10$	Negligible clustering; standard regression may suffice
$0.10$–$0.30$	Weak clustering
$0.30$–$0.60$	Moderate clustering; LMM recommended
$> 0.60$	Strong clustering; LMM strongly indicated

What is reported (HTML report)

Fixed effects table ($\hat{\beta}$, SE, $df$, $t/z$, $p$, 95% CI), random effects variances ($\sigma^2_u$, $\sigma^2_\varepsilon$), ICC, AIC, BIC, log-likelihood, LRT result, random structure chosen, convergence status.

21. Logistic Regression

Trigger conditions: Dependent Variable contains exactly 2 distinct values, either ${0, 1}$ or two unique string labels. The application encodes non-numeric outcomes as 0/1 internally.

The model:

$$\log\frac{P(Y=1)}{1 - P(Y=1)} = \beta_0 + \sum_{j=1}^{k} \beta_j X_j$$

Configuration

Bucket	Assign
Dependent Variable	Binary outcome (0/1 or two-level label)
Factor 1	Primary predictor
Covariates	Additional predictors
Filter	Optional subgroup restriction

What is reported (HTML report)

Output	Description
Odds Ratio (OR)	$\exp(\hat{\beta}_j)$ with 95% CI: $\exp(\hat{\beta}_j \pm 1.96 \cdot \text{SE}_j)$
$p$-value	Per predictor
McFadden $R^2$	$1 - \ell_{\text{full}} / \ell_{\text{null}}$; values $> 0.20$ indicate good fit
AUC (ROC)	Discrimination; $0.70$–$0.80$ acceptable, $0.80$–$0.90$ good, $> 0.90$ excellent
Brier score	Calibration; lower is better
Calibration slope	Ideal = 1.0; deviation indicates over- or underconfidence
AIC / BIC	Model comparison
$n$	Observations after listwise deletion
Model variant	Standard ML or Firth Penalized Likelihood

Interpreting the Odds Ratio. $\text{OR} > 1$: the predictor increases the probability of the event. $\text{OR} < 1$: it decreases the probability. $\text{OR} = 1$: no effect. An $\text{OR} = 2.5$ means the odds of the event are 2.5 times higher per unit increase in the predictor, holding everything else constant.

Firth correction. Complete separation (when one predictor perfectly predicts the outcome) causes standard maximum likelihood to diverge. The application detects this (large SEs, $> 5$) and switches to Firth Penalized Likelihood regression automatically. The report notes which variant was used.

Under Firth, the Wald confidence interval ($\hat{\beta} \pm 1.96,\text{SE}$) is unreliable, because separation is the one case it cannot handle. The app instead reports penalized profile-likelihood intervals and penalized likelihood-ratio $p$-values, the same inference R's logistf uses. The odds-ratio table names the method it applied.

Happy analysing.

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BioMedStatX User Guide

0. First-Time Orientation

1. Launching the Application

2. Importing Data

Minimum data requirements

Wide-format data

Select Data Ranges

1. Choose your experimental design

2. Biological vs. Technical Replicates (Between-subjects)

3. Smart Mapping

Factor 1 vs. Subject ID: where most mistakes happen

Mapping-to-design reference

4. Single vs. Multi-Dataset Analysis

5. Starting the Analysis

6. Export Settings

7. Assumption Checks and Data Transformations

8. Post-Hoc Comparisons

9. Plot Customisation

10. Statistical Analyses: full reference

11. Decision Tree Visualisation

12. Reviewing Results: HTML Report

13. Outlier Detection

14. Quick-Reference Workflow

Tips

15. Filter Bucket — Subgroup Analysis

16. Correlation Analysis

Configuration

Pearson vs. Spearman: the decision rule

Correlation→Regression toggle

What is reported (HTML report)

17. Linear Regression (OLS)

Configuration

Variable transformations

What is reported (HTML report)

18. Exploratory Correlation Matrix

19. ANCOVA / Two-Way ANCOVA

Configuration

What is reported (HTML report)

The slope homogeneity assumption

20. Linear Mixed Model (LMM)

Configuration

Model selection: random intercept vs. random slope

ICC: Intraclass Correlation Coefficient

What is reported (HTML report)

21. Logistic Regression

Configuration

What is reported (HTML report)