Data Analysis Mathematics Linear Algebra Statistics
New Version 7.0!  QuickStart Samples

# Two-Way Anova QuickStart Sample (Visual Basic)

Illustrates how to use the TwoWayAnovaModel class to perform a two-way analysis of variance in Visual Basic.

```Option Infer On

Imports Extreme.DataAnalysis
Imports Extreme.Statistics

Namespace Extreme.Numerics.QuickStart.VB
' Illustrates the use of the TwoWayAnovaModel class for performing
' a two-way analysis of variance.
Module AnovaTwoWay

Sub Main()
' 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
Dim data = {
New With {.Store = 1, .Color = "Blue", .Shape = "Square", .Sales = 6},
New With {.Store = 2, .Color = "Blue", .Shape = "Square", .Sales = 14},
New With {.Store = 3, .Color = "Blue", .Shape = "Rectangle", .Sales = 19},
New With {.Store = 4, .Color = "Blue", .Shape = "Rectangle", .Sales = 17},
New With {.Store = 5, .Color = "Red", .Shape = "Square", .Sales = 18},
New With {.Store = 6, .Color = "Red", .Shape = "Square", .Sales = 11},
New With {.Store = 7, .Color = "Red", .Shape = "Rectangle", .Sales = 20},
New With {.Store = 8, .Color = "Red", .Shape = "Rectangle", .Sales = 23},
New With {.Store = 9, .Color = "Green", .Shape = "Square", .Sales = 7},
New With {.Store = 10, .Color = "Green", .Shape = "Square", .Sales = 11},
New With {.Store = 11, .Color = "Green", .Shape = "Rectangle", .Sales = 18},
New With {.Store = 12, .Color = "Green", .Shape = "Rectangle", .Sales = 10}}
Dim frame = DataFrame.FromObjects(data)

' Construct the OneWayAnova object.
Dim anova As New TwoWayAnovaModel(frame, "Sales", "Color", "Shape")
' Alternatively, you can use a formula to specify the variables
anova = New TwoWayAnovaModel(frame, "Sales ~ Color + Shape")

' Perform the calculation.
anova.Compute()

' Verify that the design is balanced:
If (Not anova.IsBalanced) Then
Console.WriteLine("The design is not balanced.")
End If

' 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 IIndex object so we can easily iterate
' through the levels:
Dim colorFactor = anova.GetFactor(Of String)(0)
For Each level In colorFactor
Console.WriteLine("Mean for square boxes group '{0}': {1:F4}",
level, anova.Cells.Get(level, "Square").Mean)
Next

' 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
Dim shapeFactor = anova.GetFactor(Of String)(1)
For Each level In shapeFactor
Console.WriteLine("Mean for group '{0}': {1:F4}",
level, anova.ColumnTotals.Get(level).Mean)
Next
Console.WriteLine()

' We can get the summary data for the entire model
' by using the TotalCell property:
Dim totalSummary As Cell = anova.TotalCell
Console.WriteLine("Summary data:")
Console.WriteLine("# observations: {0}", totalSummary.Count)
Console.WriteLine("Grand mean:     {0:F4}", totalSummary.Mean)

Console.WriteLine("Press Enter key to continue.")