Lesson 12

Skewness and Nonnormality Diagnostics

Big question

How do we measure asymmetry?

Lesson progress

Complete checkpoints as you learn

0% complete0 checkpoint streak
Progress tracking available after sign-in. Sign in to save your work.
Big question
Concept
Activity
Quiz

Learning objectives

  • Explain skewness and nonnormality diagnostics in plain language.
  • Use zero conditional mean correctly in an interpretation.
  • Connect the lesson idea to a formula, graph, Python result, or real example.

Simple explanation

Skewness summarizes whether a distribution has a longer right or left tail. A normal distribution has skewness near zero.

Key terms

zero conditional mean
The expected error is zero for every value of the regressors.
standard-error shrinkage
The tendency of standard errors to fall roughly at one over square-root n.
auxiliary regression
A secondary regression used to compute a diagnostic or test statistic.

Core formula

zi=(yi−ybar)/sy;skewness=n−1sumzi3z_i=(y_i-ybar)/s_y; skewness=n^{-1} sum z_i^3

Use plain-language interpretation before algebra.

Example

401KSUBS gives students a real-data setting for skewness and nonnormality diagnostics. The lesson reports code and diagnostics only after the student runs the live Python lab.

Interactive visual

SkewnessCalculator

Original Module 5 visual for Skewness and Nonnormality Diagnostics.

wage_sample.csv

y variable

wage

The dependent variable. It is the outcome students want to explain.

x variable

education

The explanatory variable. It is used to describe changes in wage.

Live Python

Skewness and Nonnormality Diagnostics Python example

Skewness and Nonnormality Diagnostics Python example

Stdout

Run Python to see results here.

Status / stderr

Ready to run Python in your browser.

Line-by-line guide

  1. Line 1Load a Python library needed for data work or regression.
  2. Line 2Load a Python library needed for data work or regression.
  3. Line 4Run this Python instruction as part of the lesson workflow.
  4. Line 5Keep rows that have the variables required for this model.
  5. Line 6Create or update a Python object used in the analysis.
  6. Line 7Run this Python instruction as part of the lesson workflow.
  7. Line 9Load the dataset into a pandas DataFrame.
  8. Line 10Load the dataset into a pandas DataFrame.
  9. Line 11Create or update a Python object used in the analysis.
  10. Line 12Run this Python instruction as part of the lesson workflow.
  11. Line 13Create a log version of the variable so coefficients can be read approximately as percentages.
  12. Line 14Run this Python instruction as part of the lesson workflow.
  13. Line 15Create a log version of the variable so coefficients can be read approximately as percentages.
  14. Line 16Run this Python instruction as part of the lesson workflow.
  15. Line 17Display a result so students can inspect the output.

Python walkthrough

  1. 1Load libraries and data or set a simulation seed.
  2. 2Build the model or simulation that matches the lesson question.
  3. 3Compute the statistic, graph, or summary table.
  4. 4Interpret the result as large-sample evidence, not automatic causality.

Live notebook

Run this lesson as a notebook

Open an editable notebook cell-by-cell, run Python in the browser, and download the `.ipynb` file for later.

Open live notebookDownload .ipynbDownload .py

Related dataset

WAGE1

Estimated time

25 to 40 min

Packages

pandas, numpy, matplotlib

Expected output

A printed summary plus a chart in the output panel.

Learning goals

  • Load and inspect WAGE1.
  • Run the Python cells connected to Histograms, Normality, and Transformations.
  • Interpret the output using histograms and skewness.

Common errors

  • File not found: check that WAGE1.csv is installed or use the course data folder.
  • Package import error: use the browser notebook first, then download for local Jupyter if your local packages differ.
  • Column name error: compare your variable names with the dataset variables listed for this notebook.

Dataset path helper

import pandas as pd

df = pd.read_csv("/data/module-5/WAGE1.csv")
df.head()

Interactive activity

SkewnessCalculator

Interpret skewness

Change the standardized third moment and classify left, right, or near-zero skew.

401KSUBS + BWGHT2

Inputs

Try it yourself

Write one plain-English sentence explaining the main idea from this lesson.

Common mistakes

Check these before you move on.

A regression coefficient describes a pattern unless the assumptions or research design support a causal interpretation.

Quick quiz

What does sample skewness measure?

Quick quiz

Which reporting habit is most important in Skewness and Nonnormality Diagnostics?

Quick quiz

Why is WAGE1 a reasonable practice dataset here?

Key takeaway

Skewness and Nonnormality Diagnostics helps students separate large-sample approximation from valid research design.

Download dataDownload resultsDownload interpretation