You've already forked lazarus-ccr
LazStats: Refactor NormalityUnit (integrate report, add probability chart based on TAChart).
git-svn-id: https://svn.code.sf.net/p/lazarus-ccr/svn@7694 8e941d3f-bd1b-0410-a28a-d453659cc2b4
This commit is contained in:
wp_xxyyzz
@ -1,417 +1,221 @@
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
||||
object Label5: TLabel
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|
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|
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|
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|
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|
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|
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end
|
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object Label6: TLabel
|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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object CloseBtn: TButton
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
||||
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|
||||
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|
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|
||||
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
||||
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
||||
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|
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|
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|
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|
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
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|
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|
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
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|
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|
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|
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|
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|
||||
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|
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|
||||
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|
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|
||||
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|
||||
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|
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|
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|
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
||||
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|
||||
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|
||||
end
|
||||
object TestVarEdit: TEdit
|
||||
AnchorSideLeft.Control = VarOutBtn
|
||||
AnchorSideLeft.Side = asrBottom
|
||||
AnchorSideTop.Control = Label2
|
||||
AnchorSideTop.Side = asrBottom
|
||||
AnchorSideRight.Control = ParamsPanel
|
||||
AnchorSideRight.Side = asrBottom
|
||||
Left = 180
|
||||
Height = 23
|
||||
Top = 45
|
||||
Width = 140
|
||||
Anchors = [akTop, akLeft, akRight]
|
||||
BorderSpacing.Left = 6
|
||||
BorderSpacing.Top = 2
|
||||
TabOrder = 4
|
||||
Text = 'TestVarEdit'
|
||||
end
|
||||
object Label2: TLabel
|
||||
AnchorSideLeft.Control = TestVarEdit
|
||||
AnchorSideBottom.Control = VarInBtn
|
||||
AnchorSideBottom.Side = asrBottom
|
||||
Left = 180
|
||||
Height = 15
|
||||
Top = 28
|
||||
Width = 93
|
||||
Anchors = [akLeft, akBottom]
|
||||
BorderSpacing.Bottom = 2
|
||||
Caption = 'Test Normality of:'
|
||||
ParentColor = False
|
||||
end
|
||||
end
|
||||
object Bevel1: TBevel
|
||||
AnchorSideLeft.Control = Owner
|
||||
AnchorSideRight.Control = Owner
|
||||
AnchorSideRight.Side = asrBottom
|
||||
AnchorSideBottom.Control = Panel1
|
||||
Left = 0
|
||||
Height = 8
|
||||
Top = 346
|
||||
Width = 402
|
||||
Anchors = [akLeft, akRight, akBottom]
|
||||
Shape = bsBottomLine
|
||||
object ParamsSplitter: TSplitter
|
||||
Left = 332
|
||||
Height = 516
|
||||
Top = 0
|
||||
Width = 5
|
||||
ResizeStyle = rsPattern
|
||||
end
|
||||
object PageControl: TPageControl
|
||||
Left = 341
|
||||
Height = 500
|
||||
Top = 8
|
||||
Width = 649
|
||||
ActivePage = ChartPage
|
||||
Align = alClient
|
||||
BorderSpacing.Left = 4
|
||||
BorderSpacing.Top = 8
|
||||
BorderSpacing.Right = 8
|
||||
BorderSpacing.Bottom = 8
|
||||
TabIndex = 1
|
||||
TabOrder = 2
|
||||
object ReportPage: TTabSheet
|
||||
Caption = 'Report'
|
||||
end
|
||||
object ChartPage: TTabSheet
|
||||
Caption = 'Chart'
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
@ -7,9 +7,9 @@ unit NormalityUnit;
|
||||
interface
|
||||
|
||||
uses
|
||||
Classes, SysUtils, FileUtil, LResources, Forms, Controls, Graphics, Dialogs,
|
||||
StdCtrls, Buttons, ExtCtrls,
|
||||
MainUnit, Globals, FunctionsLib, DataProcs, OutputUnit;
|
||||
Classes, SysUtils, FileUtil, Forms, Controls, Graphics, Dialogs,
|
||||
StdCtrls, Buttons, ExtCtrls, ComCtrls,
|
||||
MainUnit, Globals, FunctionsLib, DataProcs, ReportFrameUnit, ChartFrameUnit;
|
||||
|
||||
|
||||
type
|
||||
@ -18,48 +18,45 @@ type
|
||||
|
||||
TNormalityFrm = class(TForm)
|
||||
Bevel1: TBevel;
|
||||
PageControl: TPageControl;
|
||||
ParamsPanel: TPanel;
|
||||
ResetBtn: TButton;
|
||||
PrintBtn: TButton;
|
||||
ApplyBtn: TButton;
|
||||
ComputeBtn: TButton;
|
||||
CloseBtn: TButton;
|
||||
ConclusionEdit: TEdit;
|
||||
Label8: TLabel;
|
||||
Panel1: TPanel;
|
||||
StatEdit: TEdit;
|
||||
KurtosisEdit: TEdit;
|
||||
SkewEdit: TEdit;
|
||||
GroupBox2: TGroupBox;
|
||||
Label5: TLabel;
|
||||
Label6: TLabel;
|
||||
Label7: TLabel;
|
||||
ProbEdit: TEdit;
|
||||
Label4: TLabel;
|
||||
WEdit: TEdit;
|
||||
GroupBox1: TGroupBox;
|
||||
Label3: TLabel;
|
||||
ParamsSplitter: TSplitter;
|
||||
ReportPage: TTabSheet;
|
||||
ChartPage: TTabSheet;
|
||||
TestVarEdit: TEdit;
|
||||
Label2: TLabel;
|
||||
VarInBtn: TBitBtn;
|
||||
VarOutBtn: TBitBtn;
|
||||
Label1: TLabel;
|
||||
VarList: TListBox;
|
||||
procedure ApplyBtnClick(Sender: TObject);
|
||||
procedure ComputeBtnClick(Sender: TObject);
|
||||
procedure FormActivate(Sender: TObject);
|
||||
procedure FormCreate(Sender: TObject);
|
||||
procedure FormShow(Sender: TObject);
|
||||
procedure PrintBtnClick(Sender: TObject);
|
||||
procedure ResetBtnClick(Sender: TObject);
|
||||
procedure VarInBtnClick(Sender: TObject);
|
||||
procedure VarListDblClick(Sender: TObject);
|
||||
procedure VarListSelectionChange(Sender: TObject; User: boolean);
|
||||
procedure VarOutBtnClick(Sender: TObject);
|
||||
private
|
||||
{ private declarations }
|
||||
FReportFrame: TReportFrame;
|
||||
FChartFrame: TChartFrame;
|
||||
FAutoSized: boolean;
|
||||
function Norm(z : double) : double;
|
||||
function Calc_ShapiroWilks(const AData: DblDyneVec; out W, Prob: Double): Boolean;
|
||||
procedure Calc_Lilliefors(const AData: DblDyneVec;
|
||||
out ASkew, AKurtosis, AStat: Double; out AConclusion: String);
|
||||
function Norm(z : double): double;
|
||||
procedure PlotData(AData: DblDyneVec);
|
||||
function PrepareData(const VarName: String): DblDyneVec;
|
||||
procedure UpdateBtnStates;
|
||||
|
||||
public
|
||||
{ public declarations }
|
||||
procedure Reset;
|
||||
end;
|
||||
|
||||
var
|
||||
@ -67,50 +64,16 @@ var
|
||||
|
||||
implementation
|
||||
|
||||
{$R *.lfm}
|
||||
|
||||
uses
|
||||
Math;
|
||||
Math,
|
||||
TAChartUtils, TATextElements, TACustomSeries, TATransformations,
|
||||
TACustomSource, TASources,
|
||||
Utils;
|
||||
|
||||
{ TNormalityFrm }
|
||||
|
||||
procedure TNormalityFrm.PrintBtnClick(Sender: TObject);
|
||||
var
|
||||
lReport: TStrings;
|
||||
begin
|
||||
lReport := TStringList.Create;
|
||||
try
|
||||
lReport.Add('NORMALITY TESTS FOR '+ TestVarEdit.Text);
|
||||
lReport.Add('');
|
||||
lReport.Add('Shapiro-Wilkes W = ' + WEdit.Text);
|
||||
lReport.Add('Shapiro-Wilkes Prob. = ' + ProbEdit.Text);
|
||||
lReport.Add('');
|
||||
lReport.Add('Skew = ' + SkewEdit.Text);
|
||||
lReport.Add('Kurtosis = ' + KurtosisEdit.Text);
|
||||
lReport.Add('Lilliefors Test Statistic = ' + StatEdit.Text);
|
||||
lReport.Add('Conclusion: ' + ConclusionEdit.Text);
|
||||
|
||||
DisplayReport(lReport);
|
||||
finally
|
||||
lReport.Free;
|
||||
end;
|
||||
end;
|
||||
|
||||
procedure TNormalityFrm.ResetBtnClick(Sender: TObject);
|
||||
var
|
||||
i: integer;
|
||||
begin
|
||||
TestVarEdit.Text := '';
|
||||
WEdit.Text := '';
|
||||
ProbEdit.Text := '';
|
||||
ConclusionEdit.Text := '';
|
||||
SkewEdit.Text := '';
|
||||
KurtosisEdit.Text := '';
|
||||
StatEdit.Text := '';
|
||||
VarList.Items.Clear;
|
||||
for i := 1 to NoVariables do
|
||||
VarList.Items.Add(OS3MainFrm.DataGrid.Cells[i,0]);
|
||||
UpdateBtnStates;
|
||||
end;
|
||||
|
||||
procedure TNormalityFrm.FormActivate(Sender: TObject);
|
||||
var
|
||||
w: Integer;
|
||||
@ -118,123 +81,285 @@ begin
|
||||
if FAutoSized then
|
||||
exit;
|
||||
|
||||
w := MaxValue([ResetBtn.Width, PrintBtn.Width, ApplyBtn.Width, CloseBtn.Width]);
|
||||
w := MaxValue([ResetBtn.Width, ComputeBtn.Width, CloseBtn.Width]);
|
||||
ResetBtn.Constraints.MinWidth := w;
|
||||
PrintBtn.Constraints.MinWidth := w;
|
||||
ApplyBtn.Constraints.MinWidth := w;
|
||||
ComputeBtn.Constraints.MinWidth := w;
|
||||
CloseBtn.Constraints.MinWidth := w;
|
||||
|
||||
ParamsPanel.Constraints.MinWidth := Max(
|
||||
3*w + 2*CloseBtn.BorderSpacing.Left,
|
||||
Max(Label1.Width, Label2.Width) + VarInBtn.Width + 2*VarList.BorderSpacing.Right);
|
||||
ParamsPanel.Constraints.MinHeight := VarOutBtn.Top + VarOutBtn.Height +
|
||||
VarOutBtn.BorderSpacing.Bottom + Bevel1.Height + Panel1.Height +
|
||||
Panel1.BorderSpacing.Top;
|
||||
|
||||
Constraints.MinWidth := ParamsPanel.Constraints.MinWidth + 300;
|
||||
Constraints.MinHeight := ParamsPanel.Constraints.MinHeight + 2*ParamsPanel.BorderSpacing.Top;
|
||||
|
||||
Position := poDesigned;
|
||||
FAutoSized := True;
|
||||
end;
|
||||
|
||||
procedure TNormalityFrm.FormCreate(Sender: TObject);
|
||||
const
|
||||
MARKS: array[0..23] of double = (0.001, 0.002, 0.005, 0.01, 0.02, 0.03, 0.05, 0.07,
|
||||
0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 0.93, 0.95, 0.98, 0.99,
|
||||
0.995, 0.998, 0.999);
|
||||
var
|
||||
T : TChartAxisTransformations;
|
||||
InvNormDistTransform: TAxisTransform;
|
||||
L: TListChartSource;
|
||||
i: Integer;
|
||||
begin
|
||||
Assert(OS3MainFrm <> nil);
|
||||
|
||||
InitForm(self);
|
||||
|
||||
FReportFrame := TReportFrame.Create(self);
|
||||
FReportFrame.Parent := ReportPage;
|
||||
FReportFrame.Align := alClient;
|
||||
|
||||
FChartFrame := TChartFrame.Create(self);
|
||||
FChartFrame.Parent := ChartPage;
|
||||
FChartFrame.Align := alClient;
|
||||
FChartFrame.Chart.BottomAxis.Intervals.MaxLength := 80;
|
||||
FChartFrame.Chart.BottomAxis.Intervals.MinLength := 30;
|
||||
|
||||
T := TChartAxisTransformations.Create(FChartFrame);
|
||||
InvNormDistTransform := TCumulNormDistrAxisTransform.Create(T);
|
||||
InvNormDistTransform.Transformations := T;
|
||||
FChartFrame.Chart.LeftAxis.Transformations := T;
|
||||
|
||||
FChartFrame.Chart.LeftAxis.Intervals.Tolerance := 10;
|
||||
FChartFrame.Chart.LeftAxis.Intervals.Count := 30;
|
||||
FChartFrame.Chart.LeftAxis.Intervals.Options := FChartFrame.Chart.leftAxis.Intervals.options + [aipUseCount]; //aipGraphCoords];
|
||||
FChartFrame.Chart.LeftAxis.Marks.OverlapPolicy := opHideNeighbour;
|
||||
{
|
||||
L := TListChartSource.Create(FChartFrame.Chart);
|
||||
for i := 0 to High(MARKS) do
|
||||
L.Add(MARKS[i], MARKS[i]);
|
||||
FChartFrame.Chart.LeftAxis.Marks.Source := L;
|
||||
FChartFrame.Chart.LeftAxis.Marks.Style := smsLabel;
|
||||
}
|
||||
Reset;
|
||||
end;
|
||||
|
||||
procedure TNormalityFrm.FormShow(Sender: TObject);
|
||||
begin
|
||||
ResetBtnClick(nil);
|
||||
end;
|
||||
|
||||
procedure TNormalityFrm.ApplyBtnClick(Sender: TObject);
|
||||
procedure TNormalityFrm.Calc_Lilliefors(const AData: DblDyneVec;
|
||||
out ASkew, AKurtosis, AStat: Double; out AConclusion: String);
|
||||
var
|
||||
w: Double = 0.0;
|
||||
pw: Double = 0.0;
|
||||
temp: double;
|
||||
skew, kurtosis : double;
|
||||
mean, variance, stddev, deviation, devsqr, M2, M3, M4 : double;
|
||||
i, j, n, n1, n2, ier : integer;
|
||||
selcol : integer;
|
||||
data, a, z, x : DblDyneVec;
|
||||
freq : IntDyneVec;
|
||||
fval, jval, DP : DblDyneVec;
|
||||
F1, DPP, D, A0, C1, D15, D10, D05, D025, t2 : double;
|
||||
init : boolean;
|
||||
msg : string;
|
||||
|
||||
procedure Cleanup;
|
||||
begin
|
||||
DP := nil;
|
||||
jval := nil;
|
||||
fval := nil;
|
||||
data := nil;
|
||||
a := nil;
|
||||
freq := nil;
|
||||
z := nil;
|
||||
x := nil;
|
||||
end;
|
||||
|
||||
i, j, n, n1: Integer;
|
||||
freq: IntDyneVec = nil;
|
||||
x: DblDyneVec = nil;
|
||||
z: DblDyneVec = nil;
|
||||
fval: DblDyneVec = nil;
|
||||
jval: DblDyneVec = nil;
|
||||
DP: DblDyneVec = nil;
|
||||
mean, variance, stddev: Double;
|
||||
deviation, devSqr: Double;
|
||||
M2, M3, M4, F1, DPP, t2: Double;
|
||||
A0, C1, D025, D05, D10, D15: Double;
|
||||
begin
|
||||
selcol := 0;
|
||||
for i := 1 to NoVariables do
|
||||
if OS3MainFrm.DataGrid.Cells[i,0] = TestVarEdit.Text then
|
||||
begin
|
||||
selcol := i;
|
||||
break;
|
||||
end;
|
||||
if selCol = 0 then
|
||||
begin
|
||||
MessageDlg('No variable selected.', mtError, [mbOK], 0);
|
||||
exit;
|
||||
end;
|
||||
// Count of data values
|
||||
n := Length(AData) - 1; // -1 due to ignored element at index 0
|
||||
|
||||
init := false;
|
||||
n := 0;
|
||||
|
||||
// place values into the data array
|
||||
SetLength(data, NoCases+1); // arrays start at 1
|
||||
SetLength(a, NoCases+1);
|
||||
SetLength(freq, NoCases+1);
|
||||
SetLength(z, NoCases+1);
|
||||
SetLength(x, NoCases+1);
|
||||
SetLength(fval, NoCases+1);
|
||||
SetLength(jval, NoCases+1);
|
||||
SetLength(DP, NoCases+1);
|
||||
for i := 1 to NoCases do
|
||||
begin
|
||||
if not ValidValue(i,selcol) then
|
||||
continue;
|
||||
n := n + 1;
|
||||
data[n] := StrToFloat(OS3MainFrm.DataGrid.Cells[selcol,i]);
|
||||
end;
|
||||
n1 := n;
|
||||
n2 := n div 2;
|
||||
|
||||
// sort into ascending order
|
||||
for i := 1 to n - 1 do
|
||||
begin
|
||||
for j := i + 1 to n do
|
||||
begin
|
||||
if data[i] > data[j] then
|
||||
begin
|
||||
temp := data[i];
|
||||
data[i] := data[j];
|
||||
data[j] := temp;
|
||||
end;
|
||||
end;
|
||||
end;
|
||||
|
||||
// call Shapiro-Wilks function
|
||||
swilk(init, data, n, n1, n2, a, w, pw, ier);
|
||||
if ier <> 0 then
|
||||
begin
|
||||
msg := 'Error encountered = ' + IntToStr(ier);
|
||||
MessageDlg(msg, mtError, [mbOK], 0);
|
||||
Cleanup;
|
||||
exit;
|
||||
end;
|
||||
WEdit.Text := Format('%.4f', [w]);
|
||||
ProbEdit.Text := Format('%.4f', [pw]);
|
||||
SetLength(freq, n+1); // +1 to make the array 1-based
|
||||
SetLength(x, n+1);
|
||||
SetLength(z, n+1);
|
||||
SetLength(fval, n+1);
|
||||
Setlength(jval, n+1);
|
||||
SetLength(DP, n+1);
|
||||
|
||||
// Now do Lilliefors
|
||||
// Get unique scores and their frequencies
|
||||
n1 := 1;
|
||||
i := 1;
|
||||
freq[1] := 1;
|
||||
x[1] := AData[1];
|
||||
repeat
|
||||
for j := i + 1 to n do
|
||||
if AData[j] = x[n1] then freq[n1] := freq[n1] + 1;
|
||||
i := i + freq[n1];
|
||||
if i <= n then
|
||||
begin
|
||||
n1 := n1 + 1;
|
||||
x[n1] := AData[i];
|
||||
freq[n1] := 1;
|
||||
end;
|
||||
until i > n;
|
||||
|
||||
// Now get skew and kurtosis of scores
|
||||
mean := 0.0;
|
||||
variance := 0.0;
|
||||
for i := 1 to n do
|
||||
begin
|
||||
mean := mean + AData[i];
|
||||
variance := variance + (AData[i] * AData[i]);
|
||||
end;
|
||||
variance := variance - sqr(mean) / n;
|
||||
variance := variance / (n - 1);
|
||||
stddev := sqrt(variance);
|
||||
mean := mean / n;
|
||||
|
||||
// Obtain skew, kurtosis and z scores
|
||||
M2 := 0.0;
|
||||
M3 := 0.0;
|
||||
M4 := 0.0;
|
||||
for i := 1 to n do
|
||||
begin
|
||||
deviation := AData[i] - mean;
|
||||
devsqr := deviation * deviation;
|
||||
M2 := M2 + devsqr;
|
||||
M3 := M3 + (deviation * devsqr);
|
||||
M4 := M4 + (devsqr * devsqr);
|
||||
z[i] := (AData[i] - mean) / stddev;
|
||||
end;
|
||||
for i := 1 to n1 do
|
||||
x[i] := (x[i] - mean) / stddev;
|
||||
ASkew := (n * M3) / ((n - 1) * (n - 2) * stddev * variance);
|
||||
AKurtosis := (n * (n + 1) * M4) - (3 * M2 * M2 * (n - 1));
|
||||
AKurtosis := AKurtosis /( (n - 1) * (n - 2) * (n - 3) * sqr(variance) );
|
||||
|
||||
// Obtain the test statistic
|
||||
for i := 1 to n1 do
|
||||
begin
|
||||
F1 := Norm(x[i]);
|
||||
if x[i] >= 0 then
|
||||
fval[i] := 1.0 - (F1 / 2.0)
|
||||
else
|
||||
fval[i] := F1 / 2.0;
|
||||
end;
|
||||
|
||||
// Cumulative proportions
|
||||
jval[1] := freq[1] / n;
|
||||
for i := 2 to n1 do jval[i] := jval[i-1] + freq[i] / n;
|
||||
for i := 1 to n1 do DP[i] := abs(jval[i] - fval[i]);
|
||||
|
||||
// Sort DP
|
||||
for i := 1 to n1-1 do
|
||||
for j := i+1 to n1 do
|
||||
if DP[j] < DP[i] then
|
||||
Exchange(DP[i], DP[j]);
|
||||
|
||||
DPP := DP[n1];
|
||||
AStat := DPP;
|
||||
//StatEdit.Text := Format('%.3f', [D]);
|
||||
A0 := sqrt(n);
|
||||
C1 := A0 - 0.01 + (0.85 / A0);
|
||||
D15 := 0.775 / C1;
|
||||
D10 := 0.819 / C1;
|
||||
D05 := 0.895 / C1;
|
||||
D025 := 0.995 / C1;
|
||||
t2 := AStat;
|
||||
if t2 > D025 then
|
||||
AConclusion := 'Strong evidence against normality.';
|
||||
if ((t2 <= D025) and (t2 > D05)) then
|
||||
AConclusion := 'Sufficient evidence against normality.';
|
||||
if ((t2 <= D05) and (t2 > D10)) then
|
||||
AConclusion := 'Suggestive evidence against normality.';
|
||||
if ((t2 <= D10) and (t2 > D15)) then
|
||||
AConclusion := 'Little evidence against normality.';
|
||||
if (t2 <= D15) then
|
||||
AConclusion := 'No evidence against normality.';
|
||||
end;
|
||||
|
||||
|
||||
{ Call Shapiro-Wilks function }
|
||||
function TNormalityFrm.Calc_ShapiroWilks(const AData: DblDyneVec;
|
||||
out W, Prob: Double): boolean;
|
||||
var
|
||||
init: Boolean = false;
|
||||
n, n1, n2: Integer;
|
||||
a: DblDyneVec = nil;
|
||||
ier: Integer; // error code
|
||||
begin
|
||||
init := false;
|
||||
n := Length(AData) - 1; // -1 because of unused element at index 0
|
||||
n1 := n;
|
||||
n2 := n div 2;
|
||||
SetLength(a, n + 1); // again: 1-based vector!
|
||||
swilk(init, AData, n, n1, n2, a, W, Prob, ier);
|
||||
Result := (ier = 0);
|
||||
case ier of
|
||||
0: ;
|
||||
1: ErrorMsg('Error encountered: N < 3');
|
||||
2: ErrorMsg('Error encountered: N > 5000');
|
||||
3: ErrorMsg('Error encountered: N2 < N/2');
|
||||
4: ErrorMsg('Error encountered: N1 > N or ((N1 < N) and (N < 20))');
|
||||
5: ErrorMsg('Error encountered: The proportion censored (N - N1) / N > 0.8');
|
||||
6: ErrorMsg('Error encountered: Data have zero range.');
|
||||
7: ErrorMsg('Error encounterde: X values are not sorted in ascending order.');
|
||||
else ErrorMsg('Error no. ' + IntToStr(ier) + ' encountered');
|
||||
end;
|
||||
end;
|
||||
|
||||
|
||||
procedure TNormalityFrm.ComputeBtnClick(Sender: TObject);
|
||||
var
|
||||
w: Double = 0.0;
|
||||
pw: Double = 0.0;
|
||||
skew, kurtosis: double;
|
||||
mean, variance, stddev, deviation, devsqr, M2, M3, M4: double;
|
||||
i, j, n, n1: integer;
|
||||
data: DblDyneVec = nil;
|
||||
//a
|
||||
z, x: DblDyneVec;
|
||||
freq: IntDyneVec;
|
||||
fval, jval, DP: DblDyneVec;
|
||||
F1, DPP, D, A0, C1, D15, D10, D05, D025, t2: double;
|
||||
init : boolean;
|
||||
conclusion: String;
|
||||
lReport: TStrings;
|
||||
begin
|
||||
data := PrepareData(TestVarEdit.Text);
|
||||
if data = nil then
|
||||
exit;
|
||||
|
||||
n := Length(data) - 1; // Subtract 1 because of unused element at index 0
|
||||
(*
|
||||
// SetLength(a, n+1); // +1 because all arrays are considered to begin at 1 here
|
||||
SetLength(freq, n+1);
|
||||
SetLength(z, n+1);
|
||||
SetLength(x, n+1);
|
||||
SetLength(fval, n+1);
|
||||
SetLength(jval, n+1);
|
||||
SetLength(DP, n+1);
|
||||
*)
|
||||
// Sort into ascending order
|
||||
for i := 1 to n - 1 do
|
||||
for j := i + 1 to n do
|
||||
if data[i] > data[j] then
|
||||
Exchange(data[i], data[j]);
|
||||
|
||||
if not Calc_ShapiroWilks(data, w, pw) then
|
||||
exit;
|
||||
(*
|
||||
// Call Shapiro-Wilks function
|
||||
init := false;
|
||||
swilk(init, data, n, n1, n2, a, w, pw, ier);
|
||||
if ier <> 0 then
|
||||
begin
|
||||
ErrorMsg('Error encountered: ' + IntToStr(ier));
|
||||
Cleanup;
|
||||
exit;
|
||||
end;
|
||||
*)
|
||||
|
||||
{
|
||||
WEdit.Text := Format('%.4f', [w]);
|
||||
ProbEdit.Text := Format('%.4f', [pw]);
|
||||
}
|
||||
|
||||
// Now do Lilliefors
|
||||
Calc_Lilliefors(data, skew, kurtosis, D, conclusion);
|
||||
|
||||
(*
|
||||
// Get unique scores and their frequencies
|
||||
n1 := 1;
|
||||
i := 1;
|
||||
freq[1] := 1;
|
||||
x[1] := data[1];
|
||||
repeat
|
||||
//again:
|
||||
for j := i + 1 to n do
|
||||
begin
|
||||
if data[j] = x[n1] then freq[n1] := freq[n1] + 1;
|
||||
@ -245,11 +370,10 @@ begin
|
||||
n1 := n1 + 1;
|
||||
x[n1] := data[i];
|
||||
freq[n1] := 1;
|
||||
//goto again;
|
||||
end;
|
||||
until i > n;
|
||||
|
||||
// now get skew and kurtosis of scores
|
||||
// Now get skew and kurtosis of scores
|
||||
mean := 0.0;
|
||||
variance := 0.0;
|
||||
for i := 1 to n do
|
||||
@ -262,7 +386,7 @@ begin
|
||||
stddev := sqrt(variance);
|
||||
mean := mean / n;
|
||||
|
||||
// obtain skew, kurtosis and z scores
|
||||
// Obtain skew, kurtosis and z scores
|
||||
M2 := 0.0;
|
||||
M3 := 0.0;
|
||||
M4 := 0.0;
|
||||
@ -279,10 +403,10 @@ begin
|
||||
skew := (n * M3) / ((n - 1) * (n - 2) * stddev * variance);
|
||||
kurtosis := (n * (n + 1) * M4) - (3 * M2 * M2 * (n - 1));
|
||||
kurtosis := kurtosis /( (n - 1) * (n - 2) * (n - 3) * (variance * variance) );
|
||||
SkewEdit.Text := Format('%.3f', [skew]);
|
||||
KurtosisEdit.Text := Format('%.3f', [kurtosis]);
|
||||
//SkewEdit.Text := Format('%.3f', [skew]);
|
||||
//KurtosisEdit.Text := Format('%.3f', [kurtosis]);
|
||||
|
||||
// obtain the test statistic
|
||||
// Obtain the test statistic
|
||||
for i := 1 to n1 do
|
||||
begin
|
||||
F1 := Norm(x[i]);
|
||||
@ -292,27 +416,20 @@ begin
|
||||
fval[i] := F1 / 2.0;
|
||||
end;
|
||||
|
||||
// cumulative proportions
|
||||
// Cumulative proportions
|
||||
jval[1] := freq[1] / n;
|
||||
for i := 2 to n1 do jval[i] := jval[i-1] + freq[i] / n;
|
||||
for i := 1 to n1 do DP[i] := abs(jval[i] - fval[i]);
|
||||
|
||||
// sort DP
|
||||
// Sort DP
|
||||
for i := 1 to n1-1 do
|
||||
begin
|
||||
for j := i+1 to n1 do
|
||||
begin
|
||||
if DP[j] < DP[i] then
|
||||
begin
|
||||
temp := DP[i];
|
||||
DP[i] := DP[j];
|
||||
DP[j] := temp;
|
||||
end;
|
||||
end;
|
||||
end;
|
||||
Exchange(DP[i], DP[j]);
|
||||
|
||||
DPP := DP[n1];
|
||||
D := DPP;
|
||||
StatEdit.Text := Format('%.3f', [D]);
|
||||
//StatEdit.Text := Format('%.3f', [D]);
|
||||
A0 := sqrt(n);
|
||||
C1 := A0 - 0.01 + (0.85 / A0);
|
||||
D15 := 0.775 / C1;
|
||||
@ -320,15 +437,142 @@ begin
|
||||
D05 := 0.895 / C1;
|
||||
D025 := 0.995 / C1;
|
||||
t2 := D;
|
||||
if t2 > D025 then ConclusionEdit.Text := 'Strong evidence against normality.';
|
||||
if ((t2 <= D025) and (t2 > D05)) then ConclusionEdit.Text := 'Sufficient evidence against normality.';
|
||||
if ((t2 <= D05) and (t2 > D10)) then ConclusionEdit.Text := 'Suggestive evidence against normality.';
|
||||
if ((t2 <= D10) and (t2 > D15)) then ConclusionEdit.Text := 'Little evidence against normality.';
|
||||
if (t2 <= D15) then ConclusionEdit.Text := 'No evidence against normality.';
|
||||
if t2 > D025 then conclusion := 'Strong evidence against normality.';
|
||||
if ((t2 <= D025) and (t2 > D05)) then conclusion := 'Sufficient evidence against normality.';
|
||||
if ((t2 <= D05) and (t2 > D10)) then conclusion := 'Suggestive evidence against normality.';
|
||||
if ((t2 <= D10) and (t2 > D15)) then conclusion := 'Little evidence against normality.';
|
||||
if (t2 <= D15) then conclusion := 'No evidence against normality.';
|
||||
*)
|
||||
|
||||
Cleanup;
|
||||
lReport := TStringList.Create;
|
||||
try
|
||||
lReport.Add('NORMALITY TESTS FOR '+ TestVarEdit.Text);
|
||||
lReport.Add('');
|
||||
lReport.Add('Shapiro-Wilkes Test Results');
|
||||
lReport.Add(' W: %8.5f', [w]); // WEdit.Tex
|
||||
lReport.Add(' Probability: %8.5f', [pw]); // ProbEdit.Text
|
||||
lReport.Add('');
|
||||
lReport.Add('Lilliefors Test Results');
|
||||
lReport.Add(' Skew: %8.5f', [skew]); // SkewEdit.Text
|
||||
lReport.Add(' Kurtosis: %8.5f', [kurtosis]); // KurtosisEdit.Text
|
||||
lReport.Add(' Test Statistic: %8.5f', [D]); // StatEdit.Text
|
||||
lReport.Add(' Conclusion: %s', [conclusion]);
|
||||
|
||||
FReportFrame.DisplayReport(lReport);
|
||||
finally
|
||||
lReport.Free;
|
||||
end;
|
||||
|
||||
PlotData(data);
|
||||
end;
|
||||
|
||||
function TNormalityFrm.Norm(z : double) : double;
|
||||
var
|
||||
p: double;
|
||||
begin
|
||||
z := abs(z);
|
||||
p := 1.0 + z * (0.04986735 + z * (0.02114101 + z * (0.00327763 +
|
||||
z * (0.0000380036 + z * (0.0000488906 + z * 0.000005383)))));
|
||||
p := p * p;
|
||||
p := p * p;
|
||||
p := p * p;
|
||||
Result := 1.0 / (p * p);
|
||||
end;
|
||||
|
||||
procedure TNormalityFrm.PlotData(AData: DblDyneVec);
|
||||
var
|
||||
i, n: Integer;
|
||||
ser: TChartSeries;
|
||||
begin
|
||||
n := Length(AData) - 1; // take care of unused value at index 0
|
||||
ser := FChartFrame.PlotXY(ptSymbols, nil, nil, nil, nil, '', clBlack);
|
||||
ser.AxisIndexX := 1;
|
||||
ser.AxisIndexY := 0;
|
||||
|
||||
// Add data manually
|
||||
for i := 1 to n do
|
||||
ser.AddXY(AData[i], i / (N+1));
|
||||
|
||||
FChartFrame.Chart.Legend.Visible := false;
|
||||
FChartFrame.SetTitle('Probability Plot of ' + TestVarEdit.Text);
|
||||
FChartFrame.SetXTitle(TestVaredit.Text);
|
||||
FChartFrame.SetYTitle('Cumulative probability');
|
||||
end;
|
||||
|
||||
|
||||
{ Extracts the data values from the data grid and stores them in a float array.
|
||||
Note that, because the Shapiro-Wilks function has been implemented for 1-based
|
||||
arrays the data array is considered to be 1-based although the 0-index element
|
||||
is present as well. }
|
||||
function TNormalityFrm.PrepareData(const VarName: String): DblDyneVec;
|
||||
var
|
||||
selCol: Integer;
|
||||
i, n: Integer;
|
||||
begin
|
||||
// Find data column in the grid
|
||||
selcol := 0;
|
||||
for i := 1 to NoVariables do
|
||||
if OS3MainFrm.DataGrid.Cells[i, 0] = VarName then
|
||||
begin
|
||||
selcol := i;
|
||||
break;
|
||||
end;
|
||||
if selCol = 0 then
|
||||
begin
|
||||
Result := nil;
|
||||
MessageDlg('No variable selected.', mtError, [mbOK], 0);
|
||||
exit;
|
||||
end;
|
||||
|
||||
// Place values into the data array
|
||||
SetLength(Result, NoCases+1);
|
||||
|
||||
n := 0;
|
||||
for i := 1 to NoCases do
|
||||
begin
|
||||
if not ValidValue(i, selcol) then
|
||||
continue;
|
||||
inc(n);
|
||||
if not TryStrToFloat(OS3MainFrm.DataGrid.Cells[selcol, i], Result[n]) then
|
||||
begin
|
||||
Result := nil;
|
||||
ErrorMsg('Non-numeric value encountered.');
|
||||
exit;
|
||||
end;
|
||||
end;
|
||||
|
||||
SetLength(Result, n + 1); // Take care of unused element at index 0
|
||||
end;
|
||||
|
||||
|
||||
procedure TNormalityFrm.Reset;
|
||||
var
|
||||
i: integer;
|
||||
begin
|
||||
TestVarEdit.Text := '';
|
||||
VarList.Items.Clear;
|
||||
for i := 1 to NoVariables do
|
||||
VarList.Items.Add(OS3MainFrm.DataGrid.Cells[i,0]);
|
||||
UpdateBtnStates;
|
||||
end;
|
||||
|
||||
|
||||
procedure TNormalityFrm.ResetBtnClick(Sender: TObject);
|
||||
begin
|
||||
Reset;
|
||||
end;
|
||||
|
||||
|
||||
|
||||
procedure TNormalityFrm.UpdateBtnStates;
|
||||
begin
|
||||
VarInBtn.Enabled := (VarList.ItemIndex > -1) and (TestVarEdit.Text = '');
|
||||
VarOutBtn.Enabled := (TestVarEdit.Text <> '');
|
||||
FReportFrame.UpdateBtnStates;
|
||||
FChartFrame.UpdateBtnStates;
|
||||
end;
|
||||
|
||||
|
||||
procedure TNormalityFrm.VarInBtnClick(Sender: TObject);
|
||||
var
|
||||
i: integer;
|
||||
@ -336,17 +580,25 @@ begin
|
||||
i := VarList.ItemIndex;
|
||||
if (i > -1) and (TestVarEdit.Text = '') then
|
||||
begin
|
||||
TestVarEdit.Text := VarList.Items.Strings[i];
|
||||
TestVarEdit.Text := VarList.Items[i];
|
||||
VarList.Items.Delete(i);
|
||||
end;
|
||||
UpdateBtnStates;
|
||||
end;
|
||||
|
||||
|
||||
procedure TNormalityFrm.VarListDblClick(Sender: TObject);
|
||||
begin
|
||||
VarInBtnClick(nil);
|
||||
end;
|
||||
|
||||
|
||||
procedure TNormalityFrm.VarListSelectionChange(Sender: TObject; User: boolean);
|
||||
begin
|
||||
UpdateBtnStates;
|
||||
end;
|
||||
|
||||
|
||||
procedure TNormalityFrm.VarOutBtnClick(Sender: TObject);
|
||||
begin
|
||||
if TestVarEdit.Text <> '' then
|
||||
@ -357,27 +609,6 @@ begin
|
||||
UpdateBtnStates;
|
||||
end;
|
||||
|
||||
function TNormalityFrm.Norm(z : double) : double;
|
||||
var
|
||||
p : double;
|
||||
begin
|
||||
z := abs(z);
|
||||
p := 1.0 + z * (0.04986735 + z * (0.02114101 + z * (0.00327763 +
|
||||
z * (0.0000380036 + z * (0.0000488906 + z * 0.000005383)))));
|
||||
p := p * p;
|
||||
p := p * p;
|
||||
p := p * p;
|
||||
Result := 1.0 / (p * p);
|
||||
end;
|
||||
|
||||
procedure TNormalityFrm.UpdateBtnStates;
|
||||
begin
|
||||
VarInBtn.Enabled := (VarList.ItemIndex > -1) and (TestVarEdit.Text = '');
|
||||
VarOutBtn.Enabled := (TestVarEdit.Text <> '');
|
||||
end;
|
||||
|
||||
initialization
|
||||
{$I normalityunit.lrs}
|
||||
|
||||
end.
|
||||
|
||||
|
||||
@ -25,7 +25,7 @@ procedure Exchange(var a, b: Double); overload;
|
||||
procedure Exchange(var a, b: Integer); overload;
|
||||
procedure Exchange(var a, b: String); overload;
|
||||
|
||||
procedure SortOnX(X, Y: DblDyneVec);
|
||||
procedure SortOnX(X: DblDyneVec; Y: DblDyneVec = nil; Z: DblDyneVec = nil);
|
||||
procedure SortOnX(X: DblDyneVec; Y: DblDyneMat);
|
||||
|
||||
function IndexOfString(L: StrDyneVec; s: String): Integer;
|
||||
@ -131,13 +131,15 @@ begin
|
||||
b := tmp;
|
||||
end;
|
||||
|
||||
procedure SortOnX(X, Y: DblDyneVec);
|
||||
procedure SortOnX(X: DblDyneVec; Y: DblDyneVec = nil; Z: DblDyneVec = nil);
|
||||
var
|
||||
i, j, N: Integer;
|
||||
begin
|
||||
N := Length(X);
|
||||
if N <> Length(Y) then
|
||||
raise Exception.Create('[SortOnX] Both arrays must have the same length');
|
||||
if (Y <> nil) and (N <> Length(Y)) then
|
||||
raise Exception.Create('[SortOnX] Arrays must have the same length.');
|
||||
if (Z <> nil) and (N <> Length(Z)) then
|
||||
raise Exception.Create('[SortOnX] Arrays must have the same length.');
|
||||
|
||||
for i := 0 to N - 2 do
|
||||
begin
|
||||
@ -146,7 +148,10 @@ begin
|
||||
if X[i] > X[j] then //swap
|
||||
begin
|
||||
Exchange(X[i], X[j]);
|
||||
Exchange(Y[i], Y[j]);
|
||||
if Y <> nil then
|
||||
Exchange(Y[i], Y[j]);
|
||||
if Z <> nil then
|
||||
Exchange(Z[i], Z[j]);
|
||||
end;
|
||||
end;
|
||||
end;
|
||||
|
||||
Reference in New Issue
Block a user