VB6 and the Sample Mean

[Code Doc]

I put this small program together and thought I would share it with you. For years I taught college statistics and a concept the students often had trouble with was understanding the behavior of the sample mean and the population mean. As the sample mean grows it approaches the population mean and the sampling error shrinks. However, on occasion even with random sampling, the error could increase temporarily. This program illustrates this behavior rather well:

Dim SampTot As Double, SampSize As Long, Value As Single
Dim MaxValue As Double, MinValue As Double, Power As Integer
Const Range = 200

Private Sub Command1_Click()
Do
    SampSize = SampSize + 1
    Value = Rnd * Range
    SampTot = SampTot + Value
    If SampSize = 1 Then
        MinValue = Value
    ElseIf Value < MinValue Then MinValue = Value
    End If
    If Value > MaxValue Then MaxValue = Value
    If SampSize = 2 ^ (Power + 1) Then
        Power = Power + 1
        With Text1
            .Text = .Text & "Population Mean = " & Range / 2 & vbCrLf
            .Text = .Text & "Sample Size = " & SampSize & vbCrLf
            .Text = .Text & "Sample Mean = " & SampTot / SampSize & vbCrLf
            .Text = .Text & "% error = " & Format$(Abs(Range / 2 - SampTot / SampSize) / (Range / 2), "0.000000%") & vbCrLf
            .Text = .Text & "Minimum Value = " & MinValue & vbCrLf
            .Text = .Text & "Maximum Value = " & MaxValue & vbCrLf & vbCrLf
            .SelStart = Len(.Text)
        End With
        Exit Do
    End If
Loop
End Sub

Private Sub Form_Load()
Randomize
Text1.Text = vbNullString
End Sub

Build a form with a command button and text box with its multiline property set to true. Then use the command button to generate sample values within the range of 0 to 200. We know that the population mean is 100. Watch the sample mean approach it with subsequent command button presses. I welcome comments and discussion.

[RobDog888]

Moved to CodeBank

I moved your thread since it wasnt a question or problem over to our CodeBank for finished tips, tricks and other cool code.

Thanks for the entry

[Code Doc]

OK, RobDog, I wasn't sure if code that was not thoroughly tested was supposed to go to the Codebank thread, but I did run it through several iterations. Anyway, I kind of wish I had something like this to illustrate the principle when I was lecturing in the classroom.

Note that we are sampling essentially from an infinite population, which makes it a bit theoretical compared to actual practice, but there are real world examples of sampling from huge populations. It might also be interesting to count the number of times that the same value is selected at random more than once. However, that would require an array, be rather memory intensive with huge samples, and would definitely slow down the processing.

Another approach would be to first generate a large finite population of values and then extract samples from it without replacement until all are selected.

[RobDog888]

No prob. Most entries are not 100% bug free. Its ok as when members test it out and find a bug they will post it in your thread. Sometimes they have suggestions and improvements so its ok to post replies like that too.