What the Application Does

For selected numeric variables, the application supports CSV import, automatic numeric-variable detection, descriptive statistics, missing-value identification, iterative univariate outlier screening, standalone and sequential Mahalanobis-distance analysis, graphical diagnostics, normality procedures, optional single imputation, and export of screened or imputed datasets.

• Sample size, missing-data frequency, mean, sample standard deviation, minimum, maximum, quartiles, and median.
• Skewness, excess kurtosis, standardized scores, interquartile-range limits, squared Mahalanobis distances, and Pearson correlations with a high-correlation screening caution at |r| ≥ .85.
• Histograms with fitted normal curves, boxplots, univariate normal Q-Q plots, and multivariate chi-square Q-Q plots.
• Shapiro-Wilk diagnostics using a Royston-style p-value approximation, Kolmogorov-Smirnov normal-fit diagnostics, Mardia's multivariate skewness and kurtosis, and simulation-based Henze-Zirkler-type diagnostics.
• Data-screening summaries, corrective-method suggestions, case review lists, and exportable assessment reports.

Computational Engine

PurifyData Pro runs as a client-side web application. The statistical calculations, table generation, plots, imputation procedures, screening notes, and CSV exports are executed in the user's web browser using JavaScript.

Why Browser-based JavaScript is Used

The browser-based design was chosen so users can screen data immediately without installing R, Python, SPSS, SAS, Stata, or additional statistical packages. It also supports privacy by keeping uploaded CSV data in local browser memory during analysis, while making the app easier to access across common operating systems.

• The app does not run R, Python, SPSS, SAS, Stata, or a server-side statistical engine behind the interface.
• Supabase is used for authentication, profile records, account management, marketing preferences, and feedback responses.
• Uploaded CSV datasets are analysed in browser memory and are not intentionally sent to Supabase for statistical processing.
• When enabled, the optional AI assistant uses Llama through a separate Cloudflare Workers AI endpoint. It receives only the user's typed question and minimal app context unless the user explicitly reviews and approves a compact aggregate results summary. Uploaded CSV values, rows, variable names, case IDs, charts, and exports are not sent automatically.
• Because calculations are browser-based, very large datasets may be affected by the user's device, browser, memory, and processing capacity.
• When exact replication is required, users are encouraged to cross-check important outputs with R, Python, SPSS, SAS, Stata, or another validated statistical engine using the same screened dataset and the same assumptions.

Formula Cross-checking

Core deterministic formulas used by the app have been cross-checked locally against independent Python, NumPy, and pandas reference calculations. The checked items include mean, sample standard deviation, linear quartiles, z-scores, covariance, Pearson correlation, squared Mahalanobis-distance behaviour, and the app's unadjusted moment-based skewness and excess kurtosis formulas.

This cross-check does not mean that every output has been directly replicated in R, SPSS, SAS, Stata, or every server-side statistical engine. Some software packages use different defaults, corrections, or finite-sample adjustments, especially for skewness, kurtosis, normality tests, p-values, quantile definitions, and missing-data handling. Users should therefore cross-check key outputs in their preferred validated software when exact software-to-software agreement is required.

Confidence for Use

PurifyData Pro's main functions, namely univariate outlier detection and deletion, multivariate Mahalanobis-distance outlier detection and deletion, and documented single-imputation workflows, are regarded as high-confidence tools for general and academic preliminary data preparation when users apply appropriate cut-off values, inspect flagged cases, justify deletion or imputation decisions, and report the chosen settings transparently.

For normality assessment, confidence depends on the selected assessment and coverage. The Univar. Outliers univariate formal tests are regarded as higher-confidence when users select Full available cases, because Shapiro-Wilk and Kolmogorov-Smirnov are then computed using all finite values remaining after Univar. Outliers. Standalone multivariate normality is regarded as higher-confidence when all selected variables and complete standalone Multivar. Outliers cases are included. Combined normality is reported separately using the final data after Univar. Outliers followed by stage 2 Multivar. Outliers. If the app reports a variable cap or case subset, the result should be treated as preliminary screening evidence and cross-checked in validated statistical software when required by a thesis committee, journal, institution, regulator, or research protocol.

Intended Use

PurifyData Pro is intended for preliminary screening and educational use. Results should be interpreted as diagnostic evidence rather than definitive proof that a dataset is normal, non-normal, valid, invalid, suitable, or unsuitable for a particular analysis.

• A flagged observation is not automatically an error.
• Flagged cases may reflect data-entry problems, measurement issues, valid extreme observations, distinct subgroups, or substantively important cases.
• Users should examine every flagged observation and document why the selected automated screening action is appropriate.
• Normality should be judged using several sources of evidence, including plots, skewness and kurtosis, formal tests, sample size, outliers, measurement features, and the assumptions of the intended model.

Independent Use and Intellectual Property

PurifyData Pro is an independent browser application developed by ADV Research and Consultancy. It is not affiliated with, endorsed by, sponsored by, or approved by IBM, SPSS, SAS, Stata, R, Python, or their respective owners.

• References to third-party software identify tools that users may choose for independent cross-checking only.
• The PurifyData Pro name, logos, original interface, code, documentation, and app-generated materials are protected by applicable intellectual-property law.
• See Third-Party Notices and Source Record for the current dependency and asset record.

Data-Screening Methods

Missing Values

Blank cells, whitespace-only entries, null, undefined, and NA are treated as missing values. Other missing-value codes such as N/A, -99, ., or MISSING should be recoded before import.

Univariate Outliers

Univariate outliers can be screened using absolute standardized scores, interquartile-range limits, or both. Screening is iterative: after flagged cases are removed, the app recalculates the descriptive statistics and screening limits until no additional cases are identified.

Multivariate Outliers

Multivariate outliers are assessed using squared Mahalanobis distance compared with a high-accuracy numerical chi-square cut-off based on the number of selected variables and the user-selected percentile. The calculation follows the same distributional method used by standard R and Python statistics libraries. The Mahalanobis procedure is iterative and uses all selected numeric variables without an arbitrary variable-count cap.

Mahalanobis screening requires complete numerical observations for the selected variables. If the ordinary covariance matrix is singular or high-dimensional, the app uses a small ridge-regularized covariance inverse and reports this caution in the output.

Combined Outliers

The Combined Outliers workflow runs the univariate procedure first, then recalculates Mahalanobis distances using the cases remaining after the univariate stage. It is useful when a study needs both single-variable and multivariable-pattern screening in a documented sequence.

Normality Assessment

Univariate Normality

The app examines skewness and excess kurtosis, Shapiro-Wilk diagnostics, Kolmogorov-Smirnov normal-fit diagnostics, histograms, normal Q-Q plots, boxplots, and the relationship between the mean and median.

A variable is classified as approximately normal when at least one active numerical method supports normality. This is a permissive preliminary-screening rule, not a universal statistical definition of normality.

Multivariate Normality

Multivariate normality is assessed using Mardia's multivariate skewness, Mardia's multivariate kurtosis, a simulation-based Henze-Zirkler-type diagnostic, squared Mahalanobis distances, and a chi-square Q-Q plot.

The app combines these findings using graded screening interpretations such as approximately reasonable, mixed evidence, asymmetry, tail-weight departure, mild statistical departure, or clear evidence of non-normality.

The app reports three separate normality assessments. Univar. Outliers normality uses cases remaining after missing-value handling and Univar. Outliers. Standalone Multivar. Outliers normality uses complete cases remaining after missing-value handling and standalone Multivar. Outliers. Combined Outliers normality uses the final cases after Univar. Outliers followed by stage 2 Multivar. Outliers. Each output labels its own data basis so the results are not mixed.

Important Statistical Cautions

• The Shapiro-Wilk procedure uses a Royston-style approximation. In Full available cases mode, the app applies its all-case Shapiro-Wilk path to all finite tested values. For closer comparison with other software, test the same screened CSV.
• The Henze-Zirkler-type diagnostic uses Monte Carlo simulation; p-values are relatively coarse because simulations are limited for browser responsiveness.
• The Kolmogorov-Smirnov procedure estimates the mean and standard deviation from the analysed data. In Full available cases mode, the app applies Kolmogorov-Smirnov with Lilliefors correction; Fast, Balanced, and Detailed modes use subset-based KS normal-fit without Lilliefors correction.
• Chi-square quantiles and some chi-square probabilities are calculated using numerical approximations.
• For theses, dissertations, journal articles, confirmatory analyses, CFA, SEM, clinical research, or other high-stakes work, users should verify important findings using validated statistical software and the full dataset.

Computational Limits

To maintain acceptable browser performance, the app applies limits to additional diagnostic outputs. These are computational limits, not recommended statistical sample-size thresholds.

• Up to 50 selected variables in the univariate normality computation.
• Up to 24 variables in normality plots.
• Up to 80 variables in multivariate normality assessment. Above this, use a model-relevant variable set or verify the full model in dedicated statistical software; outlier screening remains uncapped.
• User-selectable multivariate-normality coverage: Responsive uses up to 120 complete cases; Extended uses up to 500 for modest variable sets, with automatic smaller safeguards for higher-dimensional data.
• User-selectable univariate formal-test case limit: Fast uses up to 250 Shapiro-Wilk values and 500 Kolmogorov-Smirnov values; Balanced uses 500 and 1,000; Detailed uses 1,000 and 2,000; Full available cases uses all finite values, applies all-case Shapiro-Wilk, and applies Kolmogorov-Smirnov with Lilliefors correction. The Normality table reports the number of cases actually tested.
• Limited Monte Carlo simulations for the Henze-Zirkler-type diagnostic.
• Correlation matrices include all selected variables and provide horizontal and vertical scrolling. Displayed case tables show up to 1,000 cases.

Imputation

The application provides optional single-imputation methods: mean imputation, median imputation, random hot-deck imputation, and correlation-weighted regression-style imputation.

• Hot-deck imputation uses a user-specified random seed so identical data and settings produce reproducible donor selections.
• The correlation-weighted method combines predictions from available variables according to their absolute correlations with the target variable. It is not a fitted multiple-regression model and should not be described as multiple imputation.
• All available methods are single-imputation procedures and do not represent uncertainty caused by missing data.
• For confirmatory research or substantial missingness, users should consider validated multiple-imputation or full-information methods.

Data Privacy and Reproducibility

In the local-processing version, uploaded data are processed within the user's browser. The application does not intentionally transmit or permanently store uploaded datasets on an external server.

Researchers should retain exported reports and record the application version, selected variables, missing-value settings, standardized-score cut-off, IQR multiplier, skewness and kurtosis cut-offs, selected Mahalanobis percentile, outlier-exclusion settings, imputation method, and random seed.

Developer

Ady Hameme Bin Nor Azman

Co-founder, Managing Director, and Principal Specialist
ADV Research and Consultancy

ORCID: https://orcid.org/0009-0001-1520-2591

Email: ady@myadvrc.com

Website: www.myadvrc.com

Disclaimer

PurifyData Pro is provided as an educational and research-support tool. Although reasonable efforts have been made to ensure computational accuracy, the developer does not guarantee that the application is free from defects or suitable for every dataset, discipline, research design, statistical model, or analytical purpose.

Users are responsible for checking imported data, confirming variable classifications, selecting defensible screening criteria, reviewing flagged observations, documenting data exclusions or modifications, confirming assumptions of the intended analysis, verifying approximate results where necessary, and making the final methodological decisions.