Two-Way Anova in C# QuickStart Sample

Illustrates how to use the TwoWayAnovaModel class to perform a two-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 two-way analysis of variance (ANOVA) using the TwoWayAnovaModel class in Numerics.NET.

The example analyzes a marketing study investigating how package color and shape affect product sales. The data comes from 12 stores where packages varied in:

• Color (blue, red, or green)
• Shape (square or rectangular)

The sample shows how to:

• Create a data frame from anonymous records containing the experimental data
• Construct and fit a two-way ANOVA model using both direct parameters and formula syntax
• Check if the design is balanced
• Display the ANOVA table with significance tests
• Access cell-level statistics like means and variances for specific factor combinations
• Calculate marginal means using row and column totals
• Obtain overall summary statistics for the complete dataset

The code demonstrates key TwoWayAnovaModel features including factor access, cell statistics, and data summarization capabilities for analyzing multifactor experimental designs.

The code

using System;

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

// Illustrates the use of the TwoWayAnovaModel class for performing
// a two-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 example investigates the effect of the color and shape
// of packages on the sales of the product. The data comes from
// 12 stores. Packages can be either red, green or blue in color.
// The shape can be either square or rectangular.

// 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 OneWayAnova object.
var anova = new TwoWayAnovaModel(dataFrame, "Sales", "Color", "Shape");
// Alternatively, we could have used a formula to define the model:
anova = new TwoWayAnovaModel(dataFrame, "Sales ~ Color + Shape");

// 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 combination of levels of each 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(0);
foreach(string level in colorFactor)
    Console.WriteLine("Mean for square boxes group '{0}': {1:F4}",
        level, anova.Cells.Get(level, "Square").Mean);

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

// The RowTotals and ColumnTotals properties permits us to
// summarize the data over all levels of a factor. For example,
// to get the means of the shape groups, we use:
var shapeFactor = anova.GetFactor(1);
foreach(string level in shapeFactor)
    Console.WriteLine("Mean for group '{0}': {1:F4}",
        level, anova.ColumnTotals.Get(level).Mean);
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();