The previous article, “Master Basic Statistical Concepts in 3 Minutes with AI-Generated Charts,” introduced important statistical concepts, distributions, and ANOVA test methods.

Today, we will complete a practical data visualization example using the Bayeslab (AI-gen data analysis tool), where AI can generate Python code for one-way ANOVA and post-hoc analysis based on natural language descriptions.

Case Overview:

The study examined the effect of soybeans on iron-deficiency anemia.

Thirty-six mice with established anemia models were randomly divided into three groups, each with 12 mice, and fed the following three types of feed:

Regular feed without soybeans

Feed containing 10% soybeans

Feed containing 15% soybeans

A week later, the red blood cell count in the mice’s blood (x10⁶) was measured.

The results are stored in the “Soybean Feed vs. Iron-Deficiency Anemia.xlsx” spreadsheet, a typical Column Table. With only one variable group, the different soybean feed proportions, this is a one-way ANOVA experiment design, hence the results are stored in a Column Table.

If another variable, such as daily exercise of the mice (0.5 hours/day, 1 hour/day, 2 hours/day, 3 hours/day), were added, it would require a Grouped Table for two-way ANOVA.

We can compare the differences between these two table designs:

This is a brief introduction to one-way and two-way ANOVA.

Don’t worry about using the AI Agent-driven Bayeslab, all you need is natural language to get the data analysis result.

All content will be explained in the most comprehensible natural language descriptions to help you get started with data analysis from scratch.

We’ll start with a data table featuring three columns: “Regular feed,” “10% soybean feed,” and “15% soybean feed.”

This chart will help visualize the differences in red blood cell counts among these feed groups.

We’ll delve into how these prompts influence the final charts and uncover techniques for effective data visualization.

In just 2 minutes, you’ll learn to harness ANOVA for impactful data insights.

Using different prompt inputs, we’ll demonstrate how AI generates detailed statistical analyses and visualizations, our steps will include:

Step 1: Normality Test

Step 2: One-Way ANOVA

Step 3: Post-Hoc Comparison

Step 4: Draw Histogram (With SD)

Step 1 — Normality Test

Conduct a normality test for each column to verify data distribution prerequisites for ANOVA.

The Prompt is :

Once the above prompt is written, click ‘Run’ to view the normality test results for each column.

Step 2 -One-Way ANOVA

Perform one-way ANOVA to detect any statistically significant differences in red blood cell counts across feed types.

The Prompt is :

Once the above prompt is written, click ‘Run’ to obtain a summary of the ANOVA results.

Step 3 -Post-Hoc Comparison

Conduct post-hoc comparisons to identify which specific group pairs differ significantly.

Due to the output of one-way ANOVA Significant diff. among means (P < 0.05): Yes, we need to perform post hoc comparisons.

For this, use:

- For pairwise comparisons, generally use Tukey.

- For multiple comparisons, generally use Dunnett.

The Prompt is :

Once the above prompt is written, click ‘Run’ to produce pairwise comparison results.

Step 4 -Draw Histogram (With SD)

Draw a histogram with mean values and standard deviations for visual comparison of the different feed groups.

The Prompt is :

Once the above prompt is written, click ‘Run’ to generate the histogram chart portraying group statistics.

Thank you for reading this installment of the AI and Statistics series!

We showed how to apply one-way ANOVA for determining the effects of different soybean feed concentrations on anemia, enhancing your data insights.

Stay tuned for our upcoming demonstrations to explore more fascinating data visualization.

Using AI Agent and Bayeslab, anyone can organize, analyze, plot data charts, and make business data predictions like a professional data analyst based on previous data.

Supplement: Advanced ANOVA Alternatives for Unequal Variances

In addition to the classic ANOVA, we can also use the following tests when the sample groups have unequal variances during variance analysis:

→ the Brown-Forsythe and Welch ANOVA tests.

Both the Brown-Forsythe and Welch ANOVA tests are statistical methods used to analyze whether the means of multiple groups are equal, particularly in the case of unequal variances among the groups.

They are variants of the classic ANOVA, providing more robust analysis for data that does not meet the homogeneity of variance assumption.

▶︎ Welch ANOVA

(1) Purpose: Used to compare the means of multiple groups even when variances are unequal (violating the assumption of homogeneity of variances).

(2) Features:

- Does not assume homogeneity of variances; suitable for cases with unequal variances.

- Performs well when sample sizes are unequal across groups.

(3) Implementation: Uses a weighted average approach to adjust for the impact of unequal variances on the test results.

▶︎ Brown-Forsythe Test

(1) Purpose: Used to assess the homogeneity of variances across multiple groups to determine if there are significant differences in variances among the groups.

(2) Features:

- Often used as a robust alternative to Levene’s Test, especially when samples exhibit skewed distributions.

- Based on medians rather than means, reducing sensitivity to non-normal data.

(3) Implementation: Evaluates homogeneity of variances by comparing the Median Absolute Deviation (MAD) of each group.

Main Differences

- Welch ANOVA: Primarily addresses the issue of unequal variances, focusing on comparing means; suitable for mean comparison hypotheses.

- Brown-Forsythe: Primarily detects variance homogeneity; suitable for variance comparison hypotheses.

However, both are used to address problems of unequal variances. Therefore, they are sometimes used in similar situations.

In Practical Application

Combined Use: Sometimes, when dealing with uncertain variances, these two methods are discussed or used together to comprehensively assess group differences. Thus, they complement each other in statistical analysis.

About Bayeslab

Bayeslab: Website

The AI First Data Workbench

X: @BayeslabAI

Documents: https://bayeslab.gitbook.io/docs

Blogs:https://bayeslab.ai/blog

Bayeslab is a powerful web-based AI code editor and data analysis assistant designed to cater to a diverse group of users, including :

👥 data analysts ，🧑🏼‍🔬experimental scientists, 📊statisticians, 👨🏿‍💻 business analysts, 👩‍🎓university students, 🖍️academic writers, 👩🏽‍🏫scholars, and ⌨️ Python learners.