OneWayANOVA — Analysis Tool Box

Introduction

With only two groups, a t-test settles the question of whether their means differ. With three or more — regions, dosages, product tiers — running pairwise t-tests inflates your false-positive rate, which is exactly the problem ANOVA solves. OneWayANOVA tests whether at least one group mean differs from the rest, and then automatically runs Tukey's HSD post-hoc test so you know which specific pairs of groups are actually different, not just that some difference exists somewhere.

Teaching Note

One-way ANOVA is essential for:

Comparing sales performance across different retail regions
Testing the efficacy of multiple drug treatments relative to a control
Analyzing variations in machinery output under different operating temperatures
Evaluating differences in customer satisfaction scores across product tiers
Assessing the impact of various educational methods on student scores
Comparing investment returns across different asset classes
Validating whether different marketing campaigns result in distinct conversion rates

Parameters

Parameter	Default	Description
`dataframe`required	—	The pandas DataFrame containing the experimental data.
`outcome_column`required	—	Name of the column containing the continuous outcome variable (dependent variable).
`grouping_column`required	—	Name of the column containing the categorical grouping labels (independent variable).
`signficance_level`	`0.05`	The alpha level used to determine statistical significance. Defaults to 0.05.
`homogeneity_of_variance`	`True`	If True, assumes equality of variance between groups. If False, adjusts calculations for unequal variances. Defaults to True.
`use_welch_correction`	`False`	If True, applies Welch's correction to the ANOVA calculation, which is recommended when group variances or sample sizes are unequal. Defaults to False.
`plot_sample_distributions`	`True`	If True, displays a kernel density estimate of simulated sample means for each group to visualize differences. Defaults to True.
`color_palette`	`'Set2'`	Seaborn color palette name used for the lines and fills in the plot. Defaults to 'Set2'.
`title_for_plot`	`'One-Way ANOVA'`	Main title text to display at the top of the plot. Defaults to 'One-Way ANOVA'.
`subtitle_for_plot`	`'Shows the distribution of the sample means for each group.'`	Subtitle text to display below the main title.
`caption_for_plot`	`None`	Caption text displayed at the bottom of the plot. Defaults to None.
`data_source_for_plot`	`None`	Optional text identifying the data source, displayed in the caption area. Defaults to None.
`show_y_axis`	`False`	If True, displays the y-axis (density scale) on the distribution plot. Defaults to False.
`title_y_indent`	`1.1`	Vertical position for the main title relative to the axes. Defaults to 1.1.
`subtitle_y_indent`	`1.05`	Vertical position for the subtitle relative to the axes. Defaults to 1.05.
`caption_y_indent`	`-0.15`	Vertical position for the caption relative to the axes. Defaults to -0.15.
`figure_size`	`(8, 6)`	Tuple specifying the (width, height) of the figure in inches. Defaults to (8, 6).

Returns

A statsmodels Summary object containing the results of Tukey's Honestly Significant Difference (HSD) post-hoc test, including pairwise group differences, confidence intervals, and rejection decisions.

Example

python

from analysistoolbox.hypothesis_testing import OneWayANOVA
import pandas as pd
import numpy as np

# Compare average sales across three different regions
sales_df = pd.DataFrame({
    'sales': np.random.normal(500, 50, 60),
    'region': ['East', 'West', 'South'] * 20
})
tukey_results = OneWayANOVA(
    dataframe=sales_df,
    outcome_column='sales',
    grouping_column='region'
)
print(tukey_results)