Statistical Analysis Toolkit

Overview: Srikar's Toolkit is an all-in-one, browser-based statistical analysis platform. It enables seamless transition from raw CSV/Excel data to publication-ready insights using 13 distinct analysis, visualization, and reporting modules.

Phase 1: Data Ingestion & Preprocessing

Module 01: Dataset Upload

The entry point for the toolkit. This module handles file parsing and provides an immediate macroscopic view of the uploaded data.

• Uploading Data: Click the drop-zone to browse for a CSV file or drag and drop a file directly into the outlined area.
• Demo Dataset: If you are testing the platform, click Load Demo Dataset to instantly populate the toolkit with a pre-configured sample dataset.
• Dataset Overview: Upon upload, the module instantly calculates total rows, total columns, missing values, and duplicate rows.
• Column Info: Review a breakdown of each column, including its inferred data type, unique value counts, and data previews.

Module 02: Data Cleaning

Transform raw, messy data into a structured format suitable for rigorous statistical testing.

• Deduplication: Click Remove Duplicates to instantly strip out identical rows.
• Missing Value Handling: Choose to impute missing numeric values using the Mean, Median, or Mode, or opt to strictly drop rows containing missing values entirely.
• Data Transformation: Select specific columns to apply mathematical transformations:
  • Standardize (Z-score): Rescales data to have a mean of 0 and a standard deviation of 1.
  • Normalize (Min-Max): Rescales data strictly between the bounds of 0 and 1.
• Categorical Encoding: Converts string-based category labels (e.g., "A", "B") into numeric equivalents (0, 1) for modeling.
• Reset: A safe Reset to Original button reverts all cleaning operations.

Module 03: Outlier Detection

Identify anomalous data points that may heavily skew your parametric analyses.

• Select Method: Choose from three robust detection algorithms:
  • Z-Score: Flags data points greater than 3 standard deviations from the mean.
  • IQR Method: Flags data points outside 1.5 x the Interquartile Range.
  • Robust MAD: Uses Median Absolute Deviation (threshold 3) to resist skewing from the outliers themselves.
• Visualization: View the flagged outliers dynamically across generated Box Plots, Scatter Plots, and Histograms.
• Action: Use the Remove Detected Outliers button to purge anomalies from your working dataset.

Phase 2: Exploratory Data Analysis (EDA)

Module 04: Descriptive Statistics

Generate summary statistics for any numeric column to understand the central tendency and dispersion of your data.

• Metrics Generated: Mean, Median, Mode, Standard Deviation, Variance, Min, Max, Range, Skewness, Kurtosis, Q1, and Q3.
• Interpretations: The results table automatically provides textual interpretations.
• Export: Click the PDF Report button to download a dedicated, standalone descriptive summary.

Module 05: Data Visualization

Leverage the integrated Plotly engine to render publication-ready, interactive charts. Rendered plots can be exported directly as PNG images or embedded into PDF format.

• Univariate: Histogram, Density Plot (KDE), Box Plot, Violin Plot.
• Bivariate: Scatter Plot, Line Plot, Bar Plot (requires selecting both X and Y axes).
• Multivariate: Correlation Heatmap, Pair Plot.

Phase 3: Theoretical Probability & Distributions

Module 06 & 07: Distributions & Normal Curve

These modules act as an educational suite and calculator for standard probability distributions.

• Distribution Explorer: Select between Discrete (Bernoulli, Binomial, Poisson) and Continuous (Uniform, Exponential, Normal) distributions. Adjust parameters via sliders to dynamically update PMF/PDF and CDF.
• Normal Distribution Center: Input custom Mean (μ) and Standard Deviation (σ) to visualize the Bell Curve and Empirical Rule (68-95-99.7%).

Module 08: Central Limit Theorem (CLT)

A real-time simulator demonstrating that the sampling distribution of the sample means approaches a normal distribution as the sample size gets larger.

• Select a base population column, set the Sample Size (n), and Number of Samples.
• Use the Animate function to watch the histogram visually build and converge into a normal bell curve in real-time.

Module 09: Z-Score Calculator

Compute standardized scores to find the exact percentile rank of a specific data point. The result is plotted dynamically on a standard normal curve for visual confirmation.

Phase 4: Advanced Statistical Testing

Module 10: Normality Testing

Determine if your data follows a normal distribution—a crucial prerequisite for parametric hypothesis testing.

• The module runs the Shapiro-Wilk, Kolmogorov-Smirnov, and Anderson-Darling tests simultaneously.
• Evaluates against an alpha of 0.05, providing a clear "Reject H₀" or "Fail to Reject" decision.
• Generates visual diagnostics: Q-Q Plots, Histograms overlaid with Normal Fits, and Density Comparisons.

Module 11: Hypothesis Testing (Parametric)

Test Type	Use Case in Toolkit
T-Test	Supports One-Sample, Independent Two-Sample, and Paired setups. Outputs T-statistic and P-value.
Z-Test	Used for One-Sample testing when the population variance is known.
One-Way ANOVA	Compare means across 3 independent groups simultaneously.
Chi-Square	Test goodness-of-fit or independence between observed and expected categorical frequencies.
Levene's Test	Assess the equality of variances across two groups (homoscedasticity).

Module 12: Non-Parametric Testing

For ordinal data or continuous data that failed the normality tests.

• Mann-Whitney U: Non-parametric equivalent to the independent T-test.
• Wilcoxon Signed-Rank: Alternative to the paired T-test.
• Kruskal-Wallis: Non-parametric alternative to One-Way ANOVA.
• Friedman Test: Alternative to repeated-measures ANOVA.

Phase 5: Final Output

Module 13: Report Generator

The culmination of the toolkit. Compiles all analyses into a single, cohesive document.

• Configuration: Provide a custom Report Title and Author name.
• Contents: Automatically pulls Dataset Summaries, Descriptive Statistics, Data Cleaning logs, Normality Analysis results, and Outlier summaries.
• Export: Click Download PDF to generate a cleanly formatted, standalone PDF report representing your entire session's work.