You might want to transfer your website to another hosting provider. After spending 2 days trying to figure it out, I feel it would be not a bad idea to write it down here for 2 purposes: (1) For my personal note in case I need that again in the future; (2) for those are … Read more
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 (standard deviation = 1). This is called standardization. \( X_{scaled} = \frac{X – \bar{X}}{\sigma} \) … Read more
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 positive Z-score means the data point is above the mean, while a negative Z-score indicates … Read more
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 p = 0.01 p = 0.005 1 0.000 0.000 0.001 0.004 0.016 0.102 0.455 1.323 … Read more
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 31.8205 63.6567 2 1.8856 2.9200 2.9200 4.3027 6.9646 9.9248 3 1.6377 2.3534 2.3534 3.1824 4.5407 … Read more
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 uses two examples showing while the original data do not follow normal distribution (e.g., uniform … Read more
1. What is Levene’s Test? Levene’s Test is a statistical test used to assess the equality of variances (homogeneity of variance) across multiple groups. It checks whether different samples have similar variances, which is an important assumption for parametric tests like ANOVA and t-tests. 2. How Levene’s Test Works: 3. Hypotheses: 4. Interpreting the Results: … Read more
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 0.8493 0.2 0.8415 0.8337 0.8259 0.8181 0.8103 0.8026 0.7949 0.7872 0.7795 0.7718 0.3 0.7642 0.7566 … Read more
import numpy as npimport matplotlib.pyplot as pltfrom scipy import statsdef plot_f_distribution(df1, df2, alpha=0.05): # Create x values for the plot x = np.linspace(0, 5, 1000) # Calculate F-distribution values y = stats.f.pdf(x, df1, df2) # Calculate critical F-value f_crit = stats.f.ppf(1 – alpha, df1, df2) # Create the plot plt.figure(figsize=(10, 6)) # Add solid black … Read more
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 df1 (Degrees of freedom in numerator) 1 2 3 4 5 6 7 8 12 … Read more