Data Analysis Mathematics Linear Algebra Statistics
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QuickStart Samples

# Repeated Measures Anova QuickStart Sample (C#)

Illustrates how to use the OneWayRAnovaModel class to perform a one-way analysis of variance with repeated measures in C#.

```using System;
using System.Data;

using Extreme.DataAnalysis;
using Extreme.Statistics;

namespace Extreme.Numerics.QuickStart.CSharp
{
/// <summary>
/// Illustrates the use of the OneWayRAnovaModel class for performing
/// a one-way analysis of variance with repeated measures.
/// </summary>
class AnovaRepeatedMeasures
{
/// <summary>
/// The main entry point for the application.
/// </summary>
static void Main(string[] args)
{
// 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 data = new[] {
new { Person = 1, Drug = 1, Score = 30 },
new { Person = 1, Drug = 2, Score = 28 },
new { Person = 1, Drug = 3, Score = 16 },
new { Person = 1, Drug = 4, Score = 34 },
new { Person = 2, Drug = 1, Score = 14 },
new { Person = 2, Drug = 2, Score = 18 },
new { Person = 2, Drug = 3, Score = 10 },
new { Person = 2, Drug = 4, Score = 22 },
new { Person = 3, Drug = 1, Score = 24 },
new { Person = 3, Drug = 2, Score = 20 },
new { Person = 3, Drug = 3, Score = 18 },
new { Person = 3, Drug = 4, Score = 30 },
new { Person = 4, Drug = 1, Score = 38 },
new { Person = 4, Drug = 2, Score = 34 },
new { Person = 4, Drug = 3, Score = 20 },
new { Person = 4, Drug = 4, Score = 44 },
new { Person = 5, Drug = 1, Score = 26 },
new { Person = 5, Drug = 2, Score = 28 },
new { Person = 5, Drug = 3, Score = 14 },
new { Person = 5, Drug = 4, Score = 30 }
};
var dataFrame = DataFrame.FromObjects(data);

// Construct the OneWayAnova object.
OneWayRAnovaModel anova = new OneWayRAnovaModel(dataFrame, "Score", "Drug", "Person");
// Alternatively, we can use a formula to specify the variables
// in the model:
anova = new OneWayRAnovaModel(dataFrame, "Score ~ Drug + Person");
// Perform the calculation.
anova.Compute();

// 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 for each drug.

// We need two indices here: the second index corresponds
// to the person factor.

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

// We could have accessed the cells directly as well:
Console.WriteLine("Variance for second drug: {0}",
anova.TreatmentTotals.Get(2).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: {0}", totalSummary.Count);
Console.WriteLine("Grand mean:     {0:F4}", totalSummary.Mean);

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