Category: Statistics

Boxplot analysis can visually summarize data’s spread, symmetry, and outliers. 1. Key Terms to Know Interquartile Range (IQR): IQR = Q3 – Q1. This is the “box” itself. It represents the middle 50% of the data. Outliers: Data points that...

Skewness is a measure of the asymmetry of a probability distribution. In a perfectly symmetrical distribution (like the Normal distribution), the left and right sides are mirror images of each other. However, real-world data is often “skewed” toward one side....

Start with your data matrix \(X =\begin{bmatrix}2 & 0 \\0 & 2 \\3 & 3 \\\end{bmatrix} \) Step 1: Centering (standard for PCA): \( X_{centered} =X – \bar{X} \) Sometimes you also scale (normalize) each feature to have unit variance...

1. Definition A Z-score, also known as a standard score, measures how many standard deviations a data point is from the mean of a dataset. It is used in statistics to standardize data, compare different distributions, and detect outliers. A...

Chi-Square Critical Value Table (Distribution Table) df p = 0.995 p = 0.99 p = 0.975 p = 0.95 p = 0.9 p = 0.75 p = 0.5 p = 0.25 p = 0.1 p = 0.05 p = 0.025...

T-Distribution Table Student’s T-Distribution Table This table shows critical values of the t-distribution for both one-tailed and two-tailed tests. df α = 0.1 α = 0.05 α = 0.01 One-Tail Two-Tail One-Tail Two-Tail One-Tail Two-Tail 1 3.0777 6.3138 6.3138 12.7062...

Central Limit Theorem (CLT) states that when you take a sufficiently large number of independent random samples from a population (regardless of the population’s original distribution), the sampling distribution of the sample mean will approach a normal distribution. This tutorial...

Two-tail Standard Normal Z-table Two-tail Standard Normal Z-Table |Z| 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 1.0000 0.9920 0.9840 0.9761 0.9681 0.9601 0.9522 0.9442 0.9362 0.9283 0.1 0.9203 0.9124 0.9045 0.8966 0.8887 0.8808 0.8729 0.8650 0.8572...

The following is the F Distribution Critical Value Table. The numbers in the table are critical values for F distribution with probably p in right tail of the distribution (see the figure illustration below). F Distribution Critical Values df2 p-value...

This tutorial shows how you can calcuate sample size for one variable chi-square test here. The example in this tutorial is that a marketing agency tests two versions of packaging (A version vs. B Version). The null hypothesis is that...