Statistical Analysis

Inference, regression, and probability distributions.

Parameters

Raw Dataset (Comma/Space separated)

Group 1:

Group 2:

Rows

Cols

Data points (x,y per line)

Degree Data (x,y per line)

Distribution

X value for P(X≤x)

See Left Sidebar for test results.

See Left Sidebar for test results.

Statistical Analysis & Inference Handbook

Mathematical Principles & Theorems

Comprehensive descriptive and inferential statistics: Mean \(\bar{x} = \frac{1}{n}\sum x_i\), Sample Variance \(s^2 = \frac{1}{n-1}\sum (x_i - \bar{x})^2\), Standard Deviation \(s\), Standard Error \(SE = s/\sqrt{n}\). Five-number summary: Min, \(Q_1\), Median \(Q_2\), \(Q_3\), Max with Interquartile Range \(IQR = Q_3 - Q_1\). Ordinary Least Squares (OLS) Linear Regression \(y = \beta_0 + \beta_1 x\) with slope \(\beta_1 = \frac{\text{Cov}(x,y)}{\text{Var}(x)}\) and Pearson correlation coefficient \(r = \frac{\text{Cov}(x,y)}{s_x s_y}\).

Operating Instructions

Enter numerical datasets (1D series or paired 2D coordinates) into the data textarea.
Click Analyze to compute complete descriptive statistics (Mean, Median, Std Dev, Skewness, Kurtosis).
Inspect the interactive histogram, box-and-whisker plot, and normal probability overlay.
For paired data: View the scatter plot with fitted OLS regression line and coefficient of determination \(R^2\).