Lesson 13
Large-Sample t and F Tests
Big question
Why do large-sample tests look familiar?
Lesson progress
Complete checkpoints as you learn
Learning objectives
- Explain large-sample t and f tests in plain language.
- Use omitted-variable inconsistency correctly in an interpretation.
- Connect the lesson idea to a formula, graph, Python result, or real example.
Simple explanation
Large-sample t tests, confidence intervals, and F tests often use the same workflow as finite-sample inference, but their justification is approximate.
Key terms
- omitted-variable inconsistency
- Large-sample bias caused by leaving out a relevant correlated variable.
- skewness
- A statistic measuring distribution asymmetry.
- chi-square distribution
- The large-sample reference distribution for many joint restriction tests.
Core formula
Use plain-language interpretation before algebra.
Example
401K gives students a real-data setting for large-sample t and f tests. The lesson reports code and diagnostics only after the student runs the live Python lab.
Interactive visual
LargeSampleTTestExplorer
Original Module 5 visual for Large-Sample t and F Tests.
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
Large-Sample t and F Tests Python example
Large-Sample t and F Tests Python example
Stdout
Run Python to see results here.
Status / stderr
Ready to run Python in your browser.
Line-by-line guide
- Line 1Load a Python library needed for data work or regression.
- Line 2Load a Python library needed for data work or regression.
- Line 4Load the dataset into a pandas DataFrame.
- Line 5Keep rows that have the variables required for this model.
- Line 6Add an intercept column to the regression design matrix.
- Line 7Estimate an ordinary least squares regression.
- Line 8Display a result so students can inspect the output.
- Line 9Display a result so students can inspect the output.
Python walkthrough
- 1Load libraries and data or set a simulation seed.
- 2Build the model or simulation that matches the lesson question.
- 3Compute the statistic, graph, or summary table.
- 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.
Related dataset
401K
Estimated time
35 to 55 min
Packages
pandas, numpy, scipy
Expected output
Printed Python results that can be compared with the lesson explanation.
Learning goals
- Load and inspect 401K.
- Run the Python cells connected to Large-Sample t and F Tests.
- Interpret the output using nonnormality and large-sample tests.
Common errors
- File not found: check that 401K.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-5/401K.csv")
df.head()Interactive activity
LargeSampleTTestExplorer
Pick exact, approximate, or robust logic
Decide which inference logic fits the assumptions and sample size.
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 justifies familiar large-sample t and F workflows?
Quick quiz
Which reporting habit is most important in Large-Sample t and F Tests?
Quick quiz
Why is GPA2 a reasonable practice dataset here?
Key takeaway
Large-Sample t and F Tests helps students separate large-sample approximation from valid research design.