Statistical Testing :: Using Pen, Paper, Python and Excel

This repository is created for storing the components of Statistical Tests carried out on One, Two and Three or more populations using Python. Here, I have also worked on some of the real-life datasets to perform Statistical or Hypothesis Testing.

Also, shared the hand-written notes & python implementations which I created to attain better knowledge around these tests.

Below are the tasks carried out in this project:

1. Python implementation of statistical tests

2. Solved One Population problems

   1. T Test or STUDENT-T or STUDENT Test
   2. Z Test
   3. Population Proportion
   4. Chi-Square Test

3. Solved Two Populations problems

   1. Large Independent Samples
      1. Pooled Large Independent Samples
      2. Not-Pooled Large Independent Samples
   2. Small Independent Samples
      1. Pooled Small Independent Samples
      2. Not Pooled Small Independent Samples
   3. Population Proportions
      1. Large Independent Proportions -- Z Test
   4. Dependent Samples
      1. Small Dependent Samples -- T Test
   5. F-Distribution (2 variances or standard deviations)

4. ANOVA

   1. Solved One-factor problems

      1. Post-Hoc Analysis
      2. Normality Test
      3. Homogenity Test

   2. Solved Two-factors W/O Repetition problems

      1. Running 1-Way ANOVA
      2. Running 2-Way ANOVA
      3. Post-Hoc Analysis
      4. Normality Test
      5. Homogenity Test

   3. Solved Two-factors With Repetition problems

      1. Running 1-Way ANOVA
         1. 1-Way ANOVA Post-Hoc
      2. Running 2-Way ANOVA
         1. Post-Hoc Analysis
         2. Normality Test
         3. Homogenity Test

5. Bootstrapping and its usecases

6. How to use Multi-variate ANOVA, ANCOVA & MANCOVA & interpret their results?

7. Let's use Excel for ANOVA

8. Understand various Distribution Functions graphically

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🤿 Fun-Fact :: Why I wrote some of these statistical tests from scratch? 🤷‍♂️

• It was not only my eagerness to gain a full understanding but python statistical packages (like statsmodels and others) were following slightly different mathematical formulations for these tests.
• So, I was getting a noticeable difference while comparing my on-paper calculated p-values with python-generated p-values. That motivated me to look into the statsmodels implementations and find such differences. 😇

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📙 Textbook referred :: Biostatistics: A Foundation for Analysis in the Health Sciences, 10th Edition

✅ Datasets used in Textbook :: Download 👈