One-Way Anova in C# QuickStart Sample

Illustrates how to use the OneWayAnovaModel class to perform a one-way analysis of variance in C#.

This sample is also available in: Visual Basic, F#, IronPython.

Overview

This QuickStart sample demonstrates how to perform a one-way analysis of variance (ANOVA) using the OneWayAnovaModel class in Numerics.NET.

The sample analyzes a marketing dataset examining the effect of package color on product sales across 12 stores. The data includes sales figures for packages in three colors (red, blue, and green). Using one-way ANOVA, the sample shows how to:

• Create a DataFrame from a collection of anonymous objects containing the sales data
• Construct and fit a OneWayAnovaModel using both direct variable specification and formula syntax
• Verify the balance of the experimental design
• Generate and display a classic ANOVA table
• Access group means and other statistics for each color group (treatment level)
• Calculate overall summary statistics like the grand mean

The code demonstrates proper model construction, checking model assumptions, and extracting both detailed and summary statistics from the analysis. This example is particularly relevant for researchers and analysts conducting experiments with a single categorical factor.

The code

using System;

using Numerics.NET.DataAnalysis;
using Numerics.NET.Statistics;

// Illustrates the use of the OneWayAnovaModel class for performing
// a one-way analysis of variance.

// The license is verified at runtime. We're using
// a 30 day trial key here. For more information, see
//     https://numerics.net/trial-key
Numerics.NET.License.Verify("your-trial-key-here");

// This QuickStart Sample investigates the effect of the color of packages
// on the sales of the product. The data comes from 12 stores.
// Packages can be either red, green or blue.

// Set up the data as anonymous records:
var values = new[] {
    new { Store = 1, Color = "Blue", Shape = "Square", Sales = 6 },
    new { Store = 2, Color = "Blue", Shape = "Square", Sales = 14 },
    new { Store = 3, Color = "Blue", Shape = "Rectangle", Sales = 19 },
    new { Store = 4, Color = "Blue", Shape = "Rectangle", Sales = 17 },

    new { Store = 5, Color = "Red", Shape = "Square", Sales = 18 },
    new { Store = 6, Color = "Red", Shape = "Square", Sales = 11 },
    new { Store = 7, Color = "Red", Shape = "Rectangle", Sales = 20 },
    new { Store = 8, Color = "Red", Shape = "Rectangle", Sales = 23 },

    new { Store = 9, Color = "Green", Shape = "Square", Sales = 7 },
    new { Store = 10, Color = "Green", Shape = "Square", Sales = 11 },
    new { Store = 11, Color = "Green", Shape = "Rectangle", Sales = 18 },
    new { Store = 12, Color = "Green", Shape = "Rectangle", Sales = 10 },
};
var dataFrame = DataFrame.FromObjects(values);

// Construct the OneWayAnovaModel object.
var anova = new OneWayAnovaModel(dataFrame, "Sales", "Color");
// Alternatively, you can use a formula to specify the variables:
anova = new OneWayAnovaModel(dataFrame, "Sales ~ Color");
// Perform the calculation.
anova.Fit();

// Verify that the design is balanced:
if (!anova.IsBalanced)
    Console.WriteLine("The design is not balanced.");

// The AnovaTable property gives us a classic ANOVA table.
// We can write the table directly to the console:
Console.WriteLine(anova.AnovaTable.ToString());
Console.WriteLine();

// A Cell object represents the data in a cell of the model,
// i.e. the data related to one level of the factor.
// We can use it to access the group means of our color groups.

// First we get the index so we can easily iterate
// through the levels:
var colorFactor = anova.GetFactor<string>(0);
foreach(string level in colorFactor)
    Console.WriteLine("Mean for group '{0}': {1:F4}",
        level, anova.Cells.Get(level).Mean);

// We could have accessed the cells directly as well:
Console.WriteLine("Variance for blue packages: {0}",
    anova.Cells.Get("Blue").Variance);
Console.WriteLine();

// We can get the summary data for the entire model
// from the TotalCell property:
Cell totalSummary = anova.TotalCell;
Console.WriteLine("Summary data:");
Console.WriteLine($"# observations: {totalSummary.Count}");
Console.WriteLine($"Grand mean:     {totalSummary.Mean:F4}");

Console.Write("Press any key to exit.");
Console.ReadLine();