IDL DEMO




	The IDL demo is organized around the analysis of the New Jersey Pick-It Lottery Data described in "S, An Interactive Environment for Data Analysis and Graphics" by Richard Becker and John Chambers (Wadsworth, 1984).

	The New Jersey Pick-It lottery is a numbers game. Each ticket costs 50 cents, and gives the purchaser an opportunity to choose a number between 0 and 999. Half the money bet on any particular day is reserved as the prize; the rest goes to the state government. Each day one number is chosen at random, and all those who selected that number share the prize.

	The data itself consists of two pieces of information, the winning number and the payoff, for each of 254 drawing between May 1975 and March 1976. It is organized as a 254 x 2 data matrix. Two other similar data sets exist (for the drawing between Nov 1976 and Sept 1977 and between Dec. 1980 and Sept. 1981) for later comparison.

	The first question to address is whether the lottery is fair (i.e. are the winning number uniformly distributed?). This is investigated by producing a histogram for the winning number. 

  (WIDTH 392 HEIGHT 276 PLOT {(READPLOT)(RIGHTMENU {(READMENU)(ITEMS ((Layout PLOT.SKETCH.CREATE 
"Create a sketch of the PLOT") (Redraw REDRAWPLOTWINDOW "Redraw plot") (Rescale RESCALEPLOT 
"Rescale plot axes" (SUBITEMS (X% Axis (RESCALEPLOT (QUOTE X)) "Rescale X axis" (SUBITEMS (Automatic (
RESCALEPLOT (QUOTE X)) "Rescale automatically") (Manual (MANUALRESCALE (QUOTE X)) "Rescale manually"))
) (Y% Axis (RESCALEPLOT (QUOTE Y)) "Rescale Y axis" (SUBITEMS (Automatic (RESCALEPLOT (QUOTE Y)) 
"Rescale automatically") (Manual (MANUALRESCALE (QUOTE Y)) "Rescale manually"))))) (Extend 
TOGGLEEXTENDEDAXES "Extend plot axes on/off" (SUBITEMS (X% Axis (TOGGLEEXTENDEDAXES (QUOTE X)) 
"Extend X axis on/off") (Y% Axis (TOGGLEEXTENDEDAXES (QUOTE Y)) "Extend Y axis on/off"))) (Labels 
WHICHLABEL "Relabel plot" (SUBITEMS (Title (ASKFORLABEL (QUOTE TOP)) "Title plot") (Left (ASKFORLABEL 
(QUOTE LEFT)) "Label left of plot") (Bottom (ASKFORLABEL (QUOTE BOTTOM)) "Label bottom of plot") (
Right (ASKFORLABEL (QUOTE RIGHT)) "Label right of plot"))) (Tics TOGGLETICS "Tics on or off" (SUBITEMS
 (Top (TOGGLETICS (QUOTE TOP)) "Top tics on/off") (Left (TOGGLETICS (QUOTE LEFT)) "Left tics on/off") 
(Bottom (TOGGLETICS (QUOTE BOTTOM)) "Bottom tics on/off") (Right (TOGGLETICS (QUOTE RIGHT)) 
"Right tics on/off"))) (Undelete UNDELETEPLOTOBJECT "Undelete last deleted object" (SUBITEMS (Top (
UNDELETEPLOTOBJECT (QUOTE TOP)) "Undelete last deleted object") (Select (UNDELETEPLOTOBJECT (QUOTE 
SELECT)) "Select object to undelete") (Above (UNDELETEPLOTOBJECT (QUOTE ABOVE)) 
"Undelete all objects above selected object") (All (UNDELETEPLOTOBJECT (QUOTE ALL)) 
"Undelete all deleted objects"))) (Fixed% Menu TOGGLEFIXEDMENU "Fix Plot menu") ("Change bins" 
HISTOGRAM.CHANGEBINS "Change number of bins" (SUBITEMS (Reset (HISTOGRAM.RESET T) 
"Reset range and bin interval to original value"))) ("Summary" HISTOGRAM.SUMMARY 
"Attach quantile summary" (SUBITEMS (Long (HISTOGRAM.SUMMARY T) "Long summary") (Short 
HISTOGRAM.SUMMARY "Short summary"))) ("Display quantiles" HISTOGRAM.DISPLAYQUANTILES 
"Overlay graph of some quantiles") ("IT _ Batch" HISTOGRAM.GETBATCH "Bind IT to the Batch displayed"))
 WHENSELECTEDFN PLOT.WHENSELECTEDFN WHENHELDFN DEFAULTMENUHELDFN WHENUNHELDFN CLRPROMPT MENUPOSITION 
NIL MENUOFFSET NIL MENUFONT NIL
 TITLE NIL CENTERFLG NIL MENUROWS NIL MENUCOLUMNS NIL ITEMHEIGHT 32767 ITEMWIDTH 32767 MENUBORDERSIZE 
NIL MENUOUTLINESIZE NIL CHANGEOFFSETFLG NIL)}
MIDDLEMENU DEFAULT OTHERMENUS (BINMENU  {(READMENU)(ITEMS (("Values" HISTOGRAM.VALUES 
"Inspect values in bin")) WHENSELECTEDFN PLOT.WHENSELECTEDFN WHENHELDFN DEFAULTMENUHELDFN WHENUNHELDFN
 CLRPROMPT MENUPOSITION NIL MENUOFFSET NIL MENUFONT NIL
 TITLE NIL CENTERFLG NIL MENUROWS NIL MENUCOLUMNS NIL ITEMHEIGHT 32767 ITEMWIDTH 32767 MENUBORDERSIZE 
NIL MENUOUTLINESIZE NIL CHANGEOFFSETFLG NIL)})
LEFTMARGIN {~MARGIN T DEFAULT  "Frequency" }
TOPMARGIN {~MARGIN NIL DEFAULT  "Histogram of Winning numbers" }
RIGHTMARGIN {~MARGIN NIL DEFAULT NIL }
BOTTOMMARGIN {~MARGIN T DEFAULT  "Winning numbers" }
PLOTSCALE {~PLOTSCALE  {~AXISINTERVAL  0.0  1000.0 }  {~AXISINFO NIL HISTOGRAM.TICFN }  {~TICINFO  0.0
  1000.0  200.0 6 }  {~AXISINTERVAL  0.0  17.5 }  {~AXISINFO NIL NIL }  {~TICINFO  0.0  17.5  2.5 8 } 
}
 PLOTOBJECTS ({(READPLOTOBJECT)( OBJECTSUBTYPE FILLEDRECTANGLE OBJECTDATA ( OBJECTLEFT 950.0 
OBJECTBOTTOM 0.0 OBJECTWIDTH 50.0 OBJECTHEIGHT 14.0 BORDERWIDTH 1 TEXTURE 4680 ) OBJECTMENU BINMENU
 OBJECTLABEL "14 Obs. between 950.0 and 1000.0" OBJECTUSERDATA (FROMHISTOGRAM? T
LOWMARK  950.0
HIGHMARK  1000.0
))}
{(READPLOTOBJECT)( OBJECTSUBTYPE FILLEDRECTANGLE OBJECTDATA ( OBJECTLEFT 900.0 OBJECTBOTTOM 0.0 
OBJECTWIDTH 50.0 OBJECTHEIGHT 13.0 BORDERWIDTH 1 TEXTURE 4680 ) OBJECTMENU BINMENU
 OBJECTLABEL "13 Obs. between 900.0 and 950.0" OBJECTUSERDATA (FROMHISTOGRAM? T
LOWMARK  900.0
HIGHMARK  950.0
))}
{(READPLOTOBJECT)( OBJECTSUBTYPE FILLEDRECTANGLE OBJECTDATA ( OBJECTLEFT 850.0 OBJECTBOTTOM 0.0 
OBJECTWIDTH 50.0 OBJECTHEIGHT 11.0 BORDERWIDTH 1 TEXTURE 4680 ) OBJECTMENU BINMENU
 OBJECTLABEL "11 Obs. between 850.0 and 900.0" OBJECTUSERDATA (FROMHISTOGRAM? T
LOWMARK  850.0
HIGHMARK  900.0
))}
{(READPLOTOBJECT)( OBJECTSUBTYPE FILLEDRECTANGLE OBJECTDATA ( OBJECTLEFT 800.0 OBJECTBOTTOM 0.0 
OBJECTWIDTH 50.0 OBJECTHEIGHT 10.0 BORDERWIDTH 1 TEXTURE 4680 ) OBJECTMENU BINMENU
 OBJECTLABEL "10 Obs. between 800.0 and 850.0" OBJECTUSERDATA (FROMHISTOGRAM? T
LOWMARK  800.0
HIGHMARK  850.0
))}
{(READPLOTOBJECT)( OBJECTSUBTYPE FILLEDRECTANGLE OBJECTDATA ( OBJECTLEFT 750.0 OBJECTBOTTOM 0.0 
OBJECTWIDTH 50.0 OBJECTHEIGHT 12.0 BORDERWIDTH 1 TEXTURE 4680 ) OBJECTMENU BINMENU
 OBJECTLABEL "12 Obs. between 750.0 and 800.0" OBJECTUSERDATA (FROMHISTOGRAM? T
LOWMARK  750.0
HIGHMARK  800.0
))}
{(READPLOTOBJECT)( OBJECTSUBTYPE FILLEDRECTANGLE OBJECTDATA ( OBJECTLEFT 700.0 OBJECTBOTTOM 0.0 
OBJECTWIDTH 50.0 OBJECTHEIGHT 8.0 BORDERWIDTH 1 TEXTURE 4680 ) OBJECTMENU BINMENU
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LOWMARK  700.0
HIGHMARK  750.0
))}
{(READPLOTOBJECT)( OBJECTSUBTYPE FILLEDRECTANGLE OBJECTDATA ( OBJECTLEFT 650.0 OBJECTBOTTOM 0.0 
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LOWMARK  650.0
HIGHMARK  700.0
))}
{(READPLOTOBJECT)( OBJECTSUBTYPE FILLEDRECTANGLE OBJECTDATA ( OBJECTLEFT 600.0 OBJECTBOTTOM 0.0 
OBJECTWIDTH 50.0 OBJECTHEIGHT 8.0 BORDERWIDTH 1 TEXTURE 4680 ) OBJECTMENU BINMENU
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LOWMARK  600.0
HIGHMARK  650.0
))}
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OBJECTWIDTH 50.0 OBJECTHEIGHT 6.0 BORDERWIDTH 1 TEXTURE 4680 ) OBJECTMENU BINMENU
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LOWMARK  550.0
HIGHMARK  600.0
))}
{(READPLOTOBJECT)( OBJECTSUBTYPE FILLEDRECTANGLE OBJECTDATA ( OBJECTLEFT 500.0 OBJECTBOTTOM 0.0 
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{(READPLOTOBJECT)( OBJECTSUBTYPE FILLEDRECTANGLE OBJECTDATA ( OBJECTLEFT 450.0 OBJECTBOTTOM 0.0 
OBJECTWIDTH 50.0 OBJECTHEIGHT 13.0 BORDERWIDTH 1 TEXTURE 4680 ) OBJECTMENU BINMENU
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LOWMARK  450.0
HIGHMARK  500.0
))}
{(READPLOTOBJECT)( OBJECTSUBTYPE FILLEDRECTANGLE OBJECTDATA ( OBJECTLEFT 400.0 OBJECTBOTTOM 0.0 
OBJECTWIDTH 50.0 OBJECTHEIGHT 16.0 BORDERWIDTH 1 TEXTURE 4680 ) OBJECTMENU BINMENU
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LOWMARK  400.0
HIGHMARK  450.0
))}
{(READPLOTOBJECT)( OBJECTSUBTYPE FILLEDRECTANGLE OBJECTDATA ( OBJECTLEFT 350.0 OBJECTBOTTOM 0.0 
OBJECTWIDTH 50.0 OBJECTHEIGHT 10.0 BORDERWIDTH 1 TEXTURE 4680 ) OBJECTMENU BINMENU
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LOWMARK  350.0
HIGHMARK  400.0
))}
{(READPLOTOBJECT)( OBJECTSUBTYPE FILLEDRECTANGLE OBJECTDATA ( OBJECTLEFT 300.0 OBJECTBOTTOM 0.0 
OBJECTWIDTH 50.0 OBJECTHEIGHT 14.0 BORDERWIDTH 1 TEXTURE 4680 ) OBJECTMENU BINMENU
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LOWMARK  300.0
HIGHMARK  350.0
))}
{(READPLOTOBJECT)( OBJECTSUBTYPE FILLEDRECTANGLE OBJECTDATA ( OBJECTLEFT 250.0 OBJECTBOTTOM 0.0 
OBJECTWIDTH 50.0 OBJECTHEIGHT 16.0 BORDERWIDTH 1 TEXTURE 4680 ) OBJECTMENU BINMENU
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LOWMARK  250.0
HIGHMARK  300.0
))}
{(READPLOTOBJECT)( OBJECTSUBTYPE FILLEDRECTANGLE OBJECTDATA ( OBJECTLEFT 200.0 OBJECTBOTTOM 0.0 
OBJECTWIDTH 50.0 OBJECTHEIGHT 16.0 BORDERWIDTH 1 TEXTURE 4680 ) OBJECTMENU BINMENU
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{(READPLOTOBJECT)( OBJECTSUBTYPE FILLEDRECTANGLE OBJECTDATA ( OBJECTLEFT 150.0 OBJECTBOTTOM 0.0 
OBJECTWIDTH 50.0 OBJECTHEIGHT 16.0 BORDERWIDTH 1 TEXTURE 4680 ) OBJECTMENU BINMENU
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LOWMARK  150.0
HIGHMARK  200.0
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{(READPLOTOBJECT)( OBJECTSUBTYPE FILLEDRECTANGLE OBJECTDATA ( OBJECTLEFT 100.0 OBJECTBOTTOM 0.0 
OBJECTWIDTH 50.0 OBJECTHEIGHT 15.0 BORDERWIDTH 1 TEXTURE 4680 ) OBJECTMENU BINMENU
 OBJECTLABEL "15 Obs. between 100.0 and 150.0" OBJECTUSERDATA (FROMHISTOGRAM? T
LOWMARK  100.0
HIGHMARK  150.0
))}
{(READPLOTOBJECT)( OBJECTSUBTYPE FILLEDRECTANGLE OBJECTDATA ( OBJECTLEFT 50.0 OBJECTBOTTOM 0.0 
OBJECTWIDTH 50.0 OBJECTHEIGHT 10.0 BORDERWIDTH 1 TEXTURE 4680 ) OBJECTMENU BINMENU
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LOWMARK  50.0
HIGHMARK  100.0
))}
{(READPLOTOBJECT)( OBJECTSUBTYPE FILLEDRECTANGLE OBJECTDATA ( OBJECTLEFT 0.0 OBJECTBOTTOM 0.0 
OBJECTWIDTH 50.0 OBJECTHEIGHT 16.0 BORDERWIDTH 1 TEXTURE 4680 ) OBJECTMENU BINMENU
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LOWMARK  0.0
HIGHMARK  50.0
))}
)  PLOTUSERDATA ( N 254
 NBINS 24
 INTFLG NIL
 SHADE 4680
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 COPYFN COPYHISTOGRAM
) )}
)

	As you can see the distribution of winning is fairly uniform, which indicates that the lottery is fair.

	If we were to play would we expect to win on the average? Since each ticket costs 50 cents and there are 1000 numbers, we need an average payoff of  500 dollars to win if we played repeatedly. Again a histogram of the payoffs will help us here.

 (WIDTH 401 HEIGHT 269 PLOT {(READPLOT)(RIGHTMENU {(READMENU)(ITEMS ((Layout PLOT.SKETCH.CREATE 
"Create a sketch of the PLOT") (Redraw REDRAWPLOTWINDOW "Redraw plot") (Rescale RESCALEPLOT 
"Rescale plot axes" (SUBITEMS (X% Axis (RESCALEPLOT (QUOTE X)) "Rescale X axis" (SUBITEMS (Automatic (
RESCALEPLOT (QUOTE X)) "Rescale automatically") (Manual (MANUALRESCALE (QUOTE X)) "Rescale manually"))
) (Y% Axis (RESCALEPLOT (QUOTE Y)) "Rescale Y axis" (SUBITEMS (Automatic (RESCALEPLOT (QUOTE Y)) 
"Rescale automatically") (Manual (MANUALRESCALE (QUOTE Y)) "Rescale manually"))))) (Extend 
TOGGLEEXTENDEDAXES "Extend plot axes on/off" (SUBITEMS (X% Axis (TOGGLEEXTENDEDAXES (QUOTE X)) 
"Extend X axis on/off") (Y% Axis (TOGGLEEXTENDEDAXES (QUOTE Y)) "Extend Y axis on/off"))) (Labels 
WHICHLABEL "Relabel plot" (SUBITEMS (Title (ASKFORLABEL (QUOTE TOP)) "Title plot") (Left (ASKFORLABEL 
(QUOTE LEFT)) "Label left of plot") (Bottom (ASKFORLABEL (QUOTE BOTTOM)) "Label bottom of plot") (
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 (Top (TOGGLETICS (QUOTE TOP)) "Top tics on/off") (Left (TOGGLETICS (QUOTE LEFT)) "Left tics on/off") 
(Bottom (TOGGLETICS (QUOTE BOTTOM)) "Bottom tics on/off") (Right (TOGGLETICS (QUOTE RIGHT)) 
"Right tics on/off"))) (Undelete UNDELETEPLOTOBJECT "Undelete last deleted object" (SUBITEMS (Top (
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"Undelete all deleted objects"))) (Fixed% Menu TOGGLEFIXEDMENU "Fix Plot menu") ("Change bins" 
HISTOGRAM.CHANGEBINS "Change number of bins" (SUBITEMS (Reset (HISTOGRAM.RESET T) 
"Reset range and bin interval to original value"))) ("Summary" HISTOGRAM.SUMMARY 
"Attach quantile summary" (SUBITEMS (Long (HISTOGRAM.SUMMARY T) "Long summary") (Short 
HISTOGRAM.SUMMARY "Short summary"))) ("Display quantiles" HISTOGRAM.DISPLAYQUANTILES 
"Overlay graph of some quantiles") ("IT _ Batch" HISTOGRAM.GETBATCH "Bind IT to the Batch displayed"))
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NIL MENUOFFSET NIL MENUFONT NIL
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NIL MENUOUTLINESIZE NIL CHANGEOFFSETFLG NIL)}
MIDDLEMENU DEFAULT OTHERMENUS (BINMENU  {(READMENU)(ITEMS (("Values" HISTOGRAM.VALUES 
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NIL MENUOUTLINESIZE NIL CHANGEOFFSETFLG NIL)})
LEFTMARGIN {~MARGIN T DEFAULT  "Frequency" }
TOPMARGIN {~MARGIN NIL DEFAULT  "Histogram of Payoffs" }
RIGHTMARGIN {~MARGIN NIL DEFAULT NIL }
BOTTOMMARGIN {~MARGIN T DEFAULT Payoffs }
PLOTSCALE {~PLOTSCALE  {~AXISINTERVAL  0.0  900.0 }  {~AXISINFO NIL HISTOGRAM.TICFN }  {~TICINFO  0.0 
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}
 PLOTOBJECTS ({(READPLOTOBJECT)( OBJECTSUBTYPE FILLEDRECTANGLE OBJECTDATA ( OBJECTLEFT 850.0 
OBJECTBOTTOM 0.0 OBJECTWIDTH 50.0 OBJECTHEIGHT 1.0 BORDERWIDTH 1 TEXTURE 4680 ) OBJECTMENU BINMENU
 OBJECTLABEL "1 Obs. between 850.0 and 900.0" OBJECTUSERDATA (FROMHISTOGRAM? T
LOWMARK  850.0
HIGHMARK  900.0
))}
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OBJECTWIDTH 50.0 OBJECTHEIGHT 1.0 BORDERWIDTH 1 TEXTURE 4680 ) OBJECTMENU BINMENU
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)

	The distribution is skew to the right with a few payoffs much greater than $500. 

	We would also like to know what winning numbers were associated with both the big and the small payoffs. This may be investigate with a scatterplot of payoff vs winning number.

 <<SCATTERPLOT>>

	Notice that the outliers all have in common a repeated digit in their winning number. This is readily explained when one discovers that there is a betting option (called a combination bet) in which the player wins if the digits of his chosen number turn up in ANY order (of course he is paid 1/6 th less). However this option demands that no digit be repeated. This is a popular option, hence the prize for a winning number with repeated digits tends to be split among fewer people. Also, winning numbers with leading zeros tend to have high payoffs.

	O.K., so we are armed and ready to go! Choose a number with repeated digits or one with a leading zero and watch the money roll in.

	Unfortunately, we are not the only ones who analyze betting records. We have data available for two subsequent time periods. We can compare the overall distribution of payoff for the three time periods via a boxplot display.

 <<BOXPLOT>>

	Thus, we find that others have also discovered the secret of maximizing payoff and we are faced with the conclusion that on the average we will not become rich playing the Pick-It lottery.
.
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