Box Plot Analysis in Minitab – Tabtrainer® for Quality Teams

This training unit focuses on Box Plot Analysis to identify trends and differences in categorical data groups. The central quality management department of the Smartboard Company aims to optimize the scrap rate in skateboard production by analyzing the daily scrap rate from a cleaned and validated dataset ("Scrap Rate 2017-2019"), covering only actual working days (Monday to Friday, single-shift operations). The analysis will compare the scrap rates across five production days to identify patterns or anomalies, such as higher or lower scrap rates on specific days, providing insights for process optimization.

This section provides an overview of preparing and analyzing a dataset for Box Plot Analysis to identify trends in production scrap rates. The dataset contains 750 rows and 3 columns:

1. Date (D) – Indexed with dates for production days.

2. Scrap Rate – Numeric values, representing accumulated scrap on production days.

3. Weekdays (T) – Text information indicating the production day (Monday to Friday).

Key Steps Covered:

• Objective: Examine whether scrap rates vary significantly between weekdays using box plots.

• Advantages of Box Plots: Visualize central tendency (e.g., median, mean) and variability (e.g., min/max) across data groups.

• Basics of Box Plots:

  • Introduced using smaller sample sizes for simplicity:

    • Data Set 1: 11 rows (odd sample size, stored in column C4).

    • Data Set 2: 10 rows (even sample size, stored in column C5).

  • Labels added: n=11 and n=10.

Box Plot Creation Process in Minitab:

• Navigate to the Graph tab (as of version 18).

• Select "Box Plot" → Choose type "One Y, Simple" for the initial dataset.

• The response variable (Y) is the scrap rate.

This section emphasizes the transition from data preparation to practical box plot application, highlighting the clarity and statistical insights box plots provide for analyzing production scrap rates.

This section provides a detailed walkthrough of creating and interpreting a Box Plot using an odd sample dataset (n=11).

Steps to Derive the Box Plot:

1. Order the Data: Arrange the 11 values in ascending order.

   • Median (Q2): Central value (6th position), representing the 50% cutoff (value = 95).

   • Minimum: Smallest value (65).

   • Maximum: Largest value (191).

2. Define Quartiles:

   • Q1 (Lower Quartile): 25% cutoff, calculated at the 3rd position (value = 74).

   • Q3 (Upper Quartile): 75% cutoff, calculated at the 9th position (value = 159).

   • Q4: Maximum value (191).

3. Box Plot Construction:

   • The box spans Q1 to Q3, containing 50% of the dataset values.

   • Whiskers extend from Q1 to the minimum and from Q3 to the maximum.

   • Outliers (values >1.5 times the box length) are marked with asterisks.

4. Statistical Insight:

   • The box plot provides a compact visual representation of key parameters: median, range, quartiles, and outliers.

5. Validation: Compare manually derived values with computer-generated box plots for accuracy.

Didactic Focus:

• Step-by-step explanation helps participants understand quartile calculations and whisker definitions.

• Emphasizes the utility of box plots for visualizing central tendency and variability in a dataset.

Key Concepts and Steps:

1. Odd vs. Even Sample Sizes:

   • Odd Sample Size (n=11): Quartiles (Q1, Q2, Q3) correspond directly to ordered data values.

   • Even Sample Size (n=10): Quartiles and median are calculated using interpolation or the mean of middle values (e.g., Median = (95+78)/2 = 86.5).

2. Data Group Comparisons:

   • To compare scrap rates across weekdays (Monday to Friday), the Box Plot type One Y, with Groups is used.

   • C2 (scrap rates) serves as the numeric data column, and C3 (weekdays) as the categorical column.

3. Customizing Display:

   • Weekdays initially appear in alphabetical order; corrected to chronological order (Monday–Friday) via column property adjustments.

   • Arithmetic means and trend lines can be added to enhance interpretability of data trends.

4. Box Plot Insights:

   • Box represents the interquartile range (IQR: Q1–Q3), with the median (Q2) as a central line.

   • Whiskers extend to a maximum of 1.5x the IQR. Outliers beyond this range are marked with asterisks.

   • Box plots provide a visual outlier test, though less rigorous than formal statistical tests.

5. Graphical Benchmarking:

   • Five box plots (one for each weekday) are displayed side-by-side, highlighting daily variations in scrap rates for benchmarking.

   • Trends become apparent through mean values and connected lines across box plots.

Practical Insights:
Participants gain the ability to construct, customize, and interpret box plots for both simple and grouped datasets, leveraging them to identify trends, outliers, and variability in production metrics like scrap rates.

Key Concepts and Steps:

1. Outlier Test Using Grubbs’ Test:

   • Navigate to Statistics > Basic Statistics > Outlier Test.

   • Null Hypothesis: Data follows normal distribution; no outliers.

   • Alternative Hypothesis: Outliers exist due to deviation from normal distribution.

   • Results:

     • Monday–Thursday: p-values > 0.05 → No significant outliers.

     • Friday: p-value = 0.028 → At least one outlier (scrap rate = 587 in row 383).

   • Practical Insight: Outliers should be investigated for data entry errors or unusual production events.

2. Visualization: Individual Value Plot:

   • Created via Graph > Individual Value Plot > One Y, with Groups.

   • Identical to outlier plot, but without marking outliers.

3. Box Plot Analysis: Identifying Trends:

   • Higher scrap rates and greater variability on Mondays and Fridays compared to Tuesday–Thursday.

   • Observations:

     • Tuesday: Most stable production.

     • Variability increases through the week, peaking on Friday.

   • Possible causes:

     • Monday: Staff not fully concentrated after the weekend.

     • Friday: Reduced care before the weekend.

4. Statistical Significance:

   • Mean differences (e.g., Monday vs. Friday) and process variability (box height) should be validated with:

     • t-Test for mean differences.

     • ANOVA for process spread (variability).

   • These will be detailed in subsequent training sessions.

5. Automating Analyses with Macros:

   • Useful for repetitive analyses on updated datasets.

   • Steps:

     • Perform analysis manually while recording commands in the Command Line History (View > Command Line History).

     • Example: Create descriptive statistics via Statistics > Basic Statistics > Display Descriptive Statistics.

     • Save the recorded commands to execute daily with a single click.

6. Creating a Custom Macro Button:

   • Add a button (e.g., "Daily Quality Analysis") to the menu bar for quick execution of predefined macros.

   • Streamlines workflows, particularly in routine business tasks.

Practical Takeaways:

Participants learn how to:

• Detect and investigate outliers using Grubbs’ test.

• Analyze trends and variability across production days with box plots.

• Automate daily statistical analyses for efficiency using macros and custom menu items.

This section outlines the creation and implementation of automated macros in Minitab to streamline daily analyses, such as box plots and outlier tests. It also covers customizing a menu for one-click execution.

Key Steps in Macro Creation:

1. Performing and Recording Analyses:

   • Conduct three manual analyses:

     1. Box plot grouped by weekdays.

     2. Outlier test by weekdays.

     3. Statistical summary of central and dispersion parameters.

   • Record all steps in the Command Line History (accessible via View > Command Line History).

2. Testing the Macro:

   • Copy the commands from the Command Line History into the Command Line window.

   • Run the commands to ensure the sequence executes correctly without errors.

   • Clear the history to avoid duplicate entries.

3. Saving the Macro:

   • Export the tested commands from the history as an executable macro file in Exec format.

   • Example filename: daily quality report scrap rate.

4. Macro Guidelines:

   • Ensure consistent data structure (column names, formats).

   • Keep the macro file in a fixed directory to avoid execution errors.

Creating a Custom Menu:

1. Adding a New Menu:

   • Right-click on the menu bar → Customize → New Menu.

   • Drag the new menu to the main menu bar and name it (e.g., "DAILY QUALITY ANALYSIS").

2. Linking the Macro:

   • Under the Tools tab, add a new command with the macro name (e.g., "daily quality report scrap rate").

   • Link the command to the saved macro file via the three-dot button, ensuring the file format is set to show all files.

3. Finalizing the Menu:

   • Drag the linked command to the new menu.

   • Close the customization window to save changes.

Using the Macro:

1. Execution:

   • Ensure the required dataset is imported into Minitab before clicking the custom button in the "DAILY QUALITY ANALYSIS" menu.

   • Missing or incorrectly formatted data will result in errors.

2. Testing:

   • Save the project (e.g., "Boxplot scrap rate") and restart Minitab.

   • Confirm the macro executes successfully when the dataset is correctly loaded.

Benefits:

• Automates repetitive analyses (e.g., box plots, outlier tests) for efficiency.

• Custom menu enables quick execution with a single click.

• Ensures accuracy and consistency in daily quality assessments.

This approach significantly improves workflow efficiency for recurring analyses in quality management tasks.

Key Learnings Summary:

1. Data and Context:

   • Analysis of a dataset containing 750 individual values grouped by production days.

   • Comparison of scrap rates across weekdays to identify trends and variability.

2. Box Plot Analysis:

   • Explored box plot fundamentals, deriving parameters manually for odd (n=11) and even (n=10) sample sizes.

   • Learned about the four types of box plots, with selection depending on the number of categorical and response variables.

   • Key insights:

     • Middle 50% of data is contained within the box (interquartile range, IQR).

     • Box height reflects variability; increasing heights from Tuesday to Friday indicated process instability.

3. Advanced Features:

   • Added additional elements like arithmetic mean and connecting lines to enhance interpretability.

   • Emphasized a minimum sample size of 20 for robust box plot analysis.

4. Outlier Analysis:

   • Conducted a Grubbs outlier test to identify significant deviations (e.g., Friday’s scrap rate of 587 as an outlier).

   • Discussed practical implications of outlier identification and validation.

5. Individual Value Plot:

   • Introduced individual value plots as an alternative display format for visualizing specific data points.

6. Automation and Efficiency:

   • Created macros using commands from the history window, saved in Exec format for recurring analyses.

   • Customized a menu bar button to execute daily analyses with a single click, ensuring efficiency in routine tasks.

Final Notes:

• Save the project under the name Boxplot scrap analysis to preserve data and results.

• Automation tools and box plot insights provide a foundation for robust, repeatable quality management processes.

• Practical applications include identifying production trends, addressing process instability, and efficiently handling routine statistical tasks.

This training equips participants with tools to streamline their analyses and enhance decision-making in daily operations.