/* SAS program to accompany the blog post "Perceptions of probability" 
   by Rick Wicklin, published on The DO Loop blog 03MAY2017
    http://blogs.sas.com/content/iml/2017/05/03/perceptions-of-probability.html

Data and idea from from 
   https://github.com/zonination/perceptions/blob/master/numberly.csv
Original data discussed at
https://www.cia.gov/library/center-for-the-study-of-intelligence/csi-publications/books-and-monographs/psychology-of-intelligence-analysis/art15.html
*/
data Perception;
input AlmostCertainly HighlyLikely VeryGoodChance Probable	
      Likely Probably WeBelieve BetterThanEven AboutEven	
      WeDoubt Improbable Unlikely ProbablyNot LittleChance
      AlmostNoChance HighlyUnlikely ChancesAreSlight;
label AlmostCertainly="Almost Certainly" 
      HighlyLikely="Highly Likely" 
      Probable="Probable"
      Likely="Likely"
      Probably="Probably"
      VeryGoodChance="Very Good Chance"
      WeBelieve="We Believe" 
      BetterThanEven="Better Than Even" 
      AboutEven="About Even"	
      WeDoubt="We Doubt" 
      Improbable="Improbable"
      Unlikely="Unlikely"
      ProbablyNot="Probably Not" 
      LittleChance="Little Chance"
      AlmostNoChance="Almost No Chance" 
      HighlyUnlikely="Highly Unlikely" 
      ChancesAreSlight="Chances Are Slight";
datalines;
95	80	85	75	66	75	66	55	50	40	20	30	15	20	5	25	25
95	75	75	51	75	51	51	51	50	20	49	25	49	5	5	10	5
95	85	85	70	75	70	80	60	50	30	10	25	25	20	1	5	15
95	85	85	70	75	70	80	60	50	30	10	25	25	20	1	5	15
98	95	80	70	70	75	65	60	50	10	50	5	20	5	1	2	10
95	99	85	90	75	75	80	65	50	7	15	8	15	5	1	3	20
85	95	65	80	40	45	80	60	45	45	35	20	40	20	10	20	30
97	95	75	70	70	80	75	55	50	25	30	15	25	20	3	5	10
95	95	80	70	65	80	65	55	50	20	30	35	35	15	5	15	10
90	85	90	70	75	70	65	60	52	60	20	30	45	20	10	6	25
90	90	85	70	60	75	80	60	50	25	1	15	40	20	15	10	15
99	97	70	75	75	75	90	67	50	17	10	10	25	17	2	3	5
60	80	70	70	60	55	60	55	50	20	5	30	30	10	5	5	15
88.7	69	80	51	70	60	50	5	50	30	49	20	40	13	2	3	5
99	98	85	85	75	65	5	65	50	100	1	10	100	100	95	90	35
95	90	80	70	70	80	85	60	50	30	40	30	40	15	1	5	10
97	90	70	51	65	60	75	51	50	5	10	15	10	15	2	7	5
99	95	75	60	65	75	80	55	50	25	3	15	30	10	1	5	40
95	95	90	60	80	75	75	60	50	25	10	10	20	25	5	5	10
95	90	75	80	75	75	50	50.1	50	25	20	25	49.9	25	5	5	10
90	80	80	75	80	75	60	60	50	40	30	10	25	20	5	5	5
92	85	75	60	70	60	85	57	50	25	33	10	10	7	3	3	13
98	90	75	80	85	85	85	60	49	5	15	2	10	2	5	5	5
98	92	91	85	85	85	70	60	50	30	7	18	27	17	2	3	10
90	90	75	75	65	80	80	60	50	12	25	35	30	20	2	10	20
95	85	80	75	65	75	50	60	50	33	10	25	25	10	2	5	5
95	90	80	60	75	60	60	51	50	10	49	20	40	15	5	20	10
98	95	75	85	90	85	75	98	50	40	7	10	25	10	2	5	5
85	85	90	60	65	76	50	51	50	33	25	25	20	10	1	15	15
80	15	74	65	65	65	60	60	50	38	29	36	34	29	7	15	30
98	80	75	65	70	55	60	55	50	25	20	12	35	15	1	8	15
96	85	80	75	70	90	80	60	50	5	9	3	20	20	10	5	12
99	85	75	80	75	90	50	51	50	1	0.001	10	10	5	0.05	10	5
85	84	87	50	60	65	50	60	50	60	3	24	30	20	5	15	30
90	95	80	70	90	60	60	80	40	25	3	5	20	4	2	2	30
95	85	80	64	80	80	75	80	50	10	10	25	20	8	2	5	5
98	96	90	90	90	80	70	53	50	40	4	30	30	8	1	5	10
98	96	82	75	86	80	45	69	52	21	12	34	26	18	7	3	13
80	90	70	80	80	80	70	60	50	10	0	20	30	10	1	10	10
95	90	90	80	90	90	85	55	48	15	20	35	15	15	5	8	10
99	90	80	90	60	50	90	60	50	40	20	10	40	5	1	30	15
85	80	80	70	70	70	65	51	45	30	15	35	30	10	5	15	20
90	70	80	75	70	65	70	60	50	15	35	20	25	5	2	10	10
95	80	90	75	70	75	100	60	50	10	5	10	20	10	1	5	5
85	90	75	65	65	60	95	55	50	95	5	20	40	25	2	5	10
95	80	75	75	60	68	55	51	49	25	20	35	40	17	5	10	15
;

/* First sort variables by value of the median. See
   http://blogs.sas.com/content/iml/2014/09/08/order-variables-by-statistic.html */
%let Stat = Median; /* or mean, stddev, qrange, skew, etc */
proc means data=Perception &Stat STACKODSOUTPUT; 
 ods output Summary=StatOut;
run;
/* put ordered variable names into macro variable */
proc sql noprint;                              
 select Variable into :varlist separated by ' '
 from StatOut order by &Stat;
quit;

proc means data=Perception Q1 median Q3 nolabels; 
 var &varList;
run;

data Wide / view=Wide;     
retain &varlist;           /* reorder vars by statistic */
set Perception;
obsNum = _N_;              /* add ID for subject (observation) */
keep obsNum &varlist;
run;
 
/* transpose from wide to long data format; VARNAME is a categorical var */
proc transpose data=Wide name=VarName 
               out=Long(rename=(Col1=_Value_));
 by obsNum;
run;

/* Create the box plot
   1. sorted by medians
   2. no colors; use alternating bands instead
   3. systematic jitter instead of random jitter
   4. do not duplicate outliers
*/
ods graphics / height=700px width=500px subpixel;
title "Perceptions of Probability";
proc sgplot data=Long noautolegend;
   hbox _Value_ / category=_Label_ nooutliers nomean nocaps;  
   scatter x=_Value_ y=_Label_ / jitter transparency=0.5
                     markerattrs=GraphData2(symbol=circlefilled size=4);
   yaxis reverse discreteorder=data labelpos=top labelattrs=(weight=bold)
                     colorbands=even colorbandsattrs=(color=gray transparency=0.9)
                     offsetmin=0.0294 offsetmax=0.0294; /* half of 1/k, where k=number of catgories */
   xaxis grid values=(0 to 100 by 10);
   label _Value_ = "Assigned Probability (%)" _label_="Statement";
run;