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Silver Member 
Hi I tried searching the board but didnt find anything. Is there a way to calculate the median or standard deviation of a data set in WebFocus ? Thanks StephenThis message has been edited. Last edited by: Kerry,  

Silver Member 
Stephen , This is an old problem for WF. I just calculated standard deviation yesterday with WF 5.2.1 on AIX (self service application) Unfortunately you have to write the formula using the prefix ASQ. AVE. and then SQRT. it would be better for you to use "Sorting with multiple Display Command" (see Manual) Paolo  

Silver Member 
Hmmm. Thanks Ill give it a try. Stephen  

Platinum Member 
The formula for Standard Deviation in an example.. TABLE FILE CAR SUM ASQ.WEIGHT AVE.WEIGHT CNT.WEIGHT COMPUTE STD=((ASQ.WEIGHTAVE.WEIGHT *AVE.WEIGHT) **.5) /CNT.WEIGHT ; END The reason its not a function in WebFocus is that often the denominator has to be (N1) and not N as in this example.  

Platinum Member 
The formula for MEDIAN is shown in this example.. TABLE FILE CAR PRINT WEIGHT NOPRINT COMPUTE MEDIAN=MEDIAN +1 ; WHERE TOTAL MEDIAN EQ 9 ; BY WEIGHT END Note that the number of values has to be known in advance (9). But you can find this out automatically , eg TABLE FILE CAR RRINT WEIGHT AND HOLD END SET &COUNT = &LINES ; TABLE FILE CAR PRINT WEIGHT NOPRINT COMPUTE MEDIAN=MEDIAN +1 ; WHERE TOTAL MEDIAN EQ &LINES ; BY WEIGHT END  

Platinum Member 
Slight error in median. TABLE FILE CAR RRINT WEIGHT AND HOLD END SET &COUNT = &LINES ; TABLE FILE CAR PRINT WEIGHT NOPRINT COMPUTE MEDIAN=MEDIAN +1 ; WHERE TOTAL MEDIAN EQ &COUNT ; BY WEIGHT END if the &COUNT is even then often it and the next value is used and averaged.  

Silver Member 
Great thanks.  

Expert 
Stephen, these need to be manual calculations, which imho is a good thing, bcause you can calc stats at levels within the data set, and not just for the entire data set. You can also check the shape of your distribution so that you know if your SD means anything at all,and youcancalc your own confidence limits, while you're at it. So it takes a few passes at the data to do this. Here's what works for me: For SD: you'll need your sample size N and you can get this as an &var ,if you want,by counting lines when you prepare your dataset, and you'll need to be able to exponentiate. Remember that in focus X**Y will perform whatever exponentiation you need, and X**.5 for example will take the square root. You can use one of the SD formulae and the Confidence Limit formulae that you'll find in Excel Help, to remind you how to set it all up. For Median: you'll need to order your data set, then use the LIST verb to number them, take the max of that LIST column, cut it in half, and then mark your data set where the values change from below that mark to above it, MAKING YOUR OWN decision about what to do if your median falls between two values, and proceed accordingly. I like to do these things manually, because I can then compute weighted medians, which is most common, or rank the groups of my entire data set inorder of , say, Confidence, Or present a report of member variance compared to group variance, and show the bad guys at the top of the list. Bored yet?  

<Pietro De Santis> 
Yikes! I hope I never have to do that!  
Member 
While Gerry's answer is (of course) correct, it's fairly simple, and uses TWO passes. The MEDIAN can be calculated with a single pass, and within sort fields, but it's a bit more complex. Below is annotated code, to allow this. It uses multiverb, as well as COMPUTEs, and WHERE TOTAL tests. * median is the 'middle' value (if odd number of values), or the * average of the two middle values (if even number) * when all the values are sorted TABLE FILE &FILE * use cnt. to get number of instances WRITE CNT.&FIELD NOPRINT COMPUTE * use this if even number of instances M1/I4=INT((CNT.&FIELD + 1)/2); NOPRINT COMPUTE * use this too for even. if odd number of instances  same as m1 M2/I4=INT((CNT.&FIELD + 2)/2); NOPRINT * sort field(s) within which to calculate median BY &BYFIELD * get details in sort fields and 'median'ed field order COMPUTE * concat all by fields to compute the xlist (for when to reset) BYFIELDS/A10=&BYFIELD; NOPRINT * use this compute to order the field within sorts COMPUTE XLIST/I5=IF BYFIELDS EQ LAST BYFIELDS THEN XLIST + 1 ELSE 1; NOPRINT * get cumulative values for median calculation * if count is odd, M1 = M2, and only one value. If even, need average COMPUTE C&FIELD/&FMT = IF M1 NE M2 THEN (LAST &FIELD + &FIELD)/2 ELSE &FIELD; AS 'MEDIAN,&FIELD' BY &BYFIELD BY &FIELD * only look at possible median values (m1 = m2 if odd, only m2 if even) WHERE TOTAL XLIST EQ M2 ENDThis message has been edited. Last edited by: <Mabel>,  

Silver Member 
Gerald , the formula is wrong. A wonderful old IBI Manual "Statistical Analyse" says that for computational puprposes is used: TABLE FILE CAR SUM ASQ.WEIGHT AVE.WEIGHT CNT.WEIGHT COMPUTE STD=( (ASQ.WEIGHTCNT.WEIGHT*AVE.WEIGHT*AVE.WEIGHT) **.5) /(CNT.WEIGHT 1); END Paolo  

Platinum Member 
Paulo, Nope, your formula would give a negative number. Actually you can take my formula and multiple by cnt.x/(cnt.x 1) to adjust for the degrees of freedom.  

Member 
Since we're talking FOCUS, you can get both standard deviation and variance with a LET, as follows: LET * Population variance PVAR = COMPUTE PVAR.<1>=(ASQ.<1>(AVE.<1>*AVE.<1>));; * sample variance ( population variance time N/(N1) SVAR = CNT.<1> NOPRINT COMPUTE # SVAR2 <1>; SVAR2= SVAR.<1>=(ASQ.<1>(AVE.<1>*AVE.<1>)) * (CNT.<1>/(CNT.<1>1)) ;; * population standard deviation PSDEV = PVAR <1> # NOPRINT COMPUTE PSDEV.<1>=SQRT(PVAR.<1>);; * sample standard deviation SSDEV = SVAR <1> # NOPRINT COMPUTE SSDEV.<1>=SQRT(SVAR.<1>);; END So, to get the POPULATION variance of WEIGHT, you'd use: PVAR WEIGHT to get the SAMPLE standard deviation, you'd use: SSDEV WEIGHTThis message has been edited. Last edited by: <Mabel>,  

Silver Member 
I'm sorry but I repeat that the formula is wrong. I try STDEVA1=(ASQ.var(AVE.var*AVE.var))*(CNT.var/(CNT.var1)) ; STDEV1=SQRT(STDEVA1); and STDEVA=(ASQ.var(CNT.var*(AVE.var)**2))/(CNT.var1)); STDEV=SQRT(STDEVA); on my sample : var 6,97 16,99 19,1 45,52 25,64 3,02 384,81 26,00 Then I test both with excel and the good formula is my formula STDEV. STDEV1= 411,04 STDEV= 129,47 ST.DEV (excel)= 129,4718873 Paolo  

Member 
Paolo, I'm not sure what your ENTIRE request was, but I took your data, loaded it into a file, and ran your code, as follows. I had to remove the final right paren (one too many), and got the following results: STDEVA1 STDEV1 STDEVA STDEV     16,762.95 129.47 2,261.45 .00 Seems correct to me, for the calculation we gave. Here's the code: TABLE FILE PAOLO SUM CNT.DATA NOPRINT COMPUTE STDEVA1=(ASQ.DATA(AVE.DATA*AVE.DATA))*(CNT.DATA/(CNT.DATA1)) ; STDEV1=SQRT(STDEVA1); STDEVA=(ASQ.DATA(CNT.DATA*(AVE.DATA)**2))/(CNT.DATA1); STDEV=SQRT(STDEVA); END Now, my Stats book defines VARIANCE (St. Dev. squared) as: (n * SUM(x**2)  (SUM(x))**2)/n**2 which can be rearranged as: (n * SUM(x**2))/n**2  (SUM(x)**2)/n**2 which becomes: SUM(x**2)/n  (SUM(x)/n)**2 The first term is the definition of ASQ; the second is the average squared. The last part is giving sample values (uses n1 instead of n instances). This is the calculation given.This message has been edited. Last edited by: <Mabel>,  

Member 
Not to belabor the point, but I found an old ANALYSE manual, dated 10/91. The formula for VARIANCE (Std. Dev. squared) is given as: (Sum(x**2)  n * ave.x**2)/(n1) That first term is ASQ.x * n, NOT ASQ.x Maybe THAT's what's causing the confusion.  

Silver Member 
Thanks to all for the input.  

Silver Member 
I must apologize for myself, I used ASQ.x * n while I wrote ASQ.x without n My justification is that my query is very complex within multiple sort fields and I went wrong to copy in the mail Paolo  

Virtuoso 
I was looking for a standard deviation function myself. The above definition is exactly what wikipedia gives as: In FOCUS, that appears to translate to: COMPUTE STD = (ASQ.WEIGHT  (AVE.WEIGHT ** 2)) ** 0.5; WebFOCUS 8.1.03, Windows 764/200864, IBM DB2/400, Oracle 11g & RDB, MS SQLServer 2005, SAP, PostgreSQL 11, Output: HTML, PDF, Excel 2010 : Member of User Group Benelux :  

Gold member 
This is an example of the standard deviation code I have used for years. * File Standard_Deviation.fex LET * Population variance PVAR = COMPUTE PVAR.<1>=(ASQ.<1>(AVE.<1>*AVE.<1>));; * sample variance ( population variance time N/(N1) SVAR = CNT.<1> NOPRINT COMPUTE # SVAR2 <1>; SVAR2 = SVAR.<1>=(ASQ.<1>(AVE.<1>*AVE.<1>)) * (CNT.<1>/(CNT.<1>1)) ;; * population standard deviation PSDEV = PVAR <1> # NOPRINT COMPUTE PSDEV.<1>=SQRT(PVAR.<1>);; * sample standard deviation SSDEV = SVAR <1> # NOPRINT COMPUTE SSDEV.<1>=SQRT(SVAR.<1>);; END SET ASNAMES=ON TABLE FILE CAR SUM AVE.MPG AS AVE_MPG MIN.MPG AS MIN_MPG MAX.MPG AS MAX_MPG SSDEV MPG AS SD_MPG CNT.MPG AS N BY COUNTRY ON TABLE HOLD AS HLD_STATS END DEFINE FILE HLD_STATS SE_MPG/D16.6 = SD_MPG/SQRT(N); END TABLE FILE HLD_STATS SUM AVE_MPG MIN_MPG MAX_MPG SD_MPG N SE_MPG BY COUNTRY END  

Platinum Member 
Not a single word about ANALYSE that was supposed to be a SAS competitor. Ce que c'est que de nous ( Ashes to ashes, if you prefer ) Focus Mainframe 7.6.11 Dev Studio 7.6.11 and !!! PC Focus, Focus for OS/2, FFW Six, MSO  

Gold member 
ANALYSE code ran for many versions after it was no longer documented. I had to rewrite a lot of reports upon its demise.  

Platinum Member 
But it still works, if not maintained. The difficult point is that the Masters created by Analyse are not correct and Focus can't read the Data created by Analyse. I manually correct the master and I can have Analyse at Work. Of course, it's not very professional, but some old cowboys like to spit into a copper spitoon and drink an old scotch with old Focusians friends. Focusely and Cordially Focus Mainframe 7.6.11 Dev Studio 7.6.11 and !!! PC Focus, Focus for OS/2, FFW Six, MSO  

Virtuoso 
I just found out that this formula is incorrect! The definition of the formula (according to wikipedia) contains SUM((x  AVE.x) **2), which is not equivalent to SUM(x **2)  SUM(AVE.x **2)! Equivalent would be (if I remember my highschool math correctly): s = SUM(x**2  2*x*AVE.x + AVE.x**2) <=> s = SUM(x**2)  2*SUM(AVE.x)*SUM(x) + ASQ.x I think this is a correct implementation: TABLE FILE EXAMPLE SUM AVE.X AS X_AVE BY GROUP ON TABLE HOLD AS EXAMPLE_AVG FORMAT FOCUS INDEX GROUP END JOIN GROUP IN EXAMPLE TO GROUP IN EXAMPLE_AVG AS J0 DEFINE FILE EXAMPLE DEV/D20.2 = (X  X_AVG) **2; END TABLE FILE EXAMPLE COMPUTE DEV_AVG_SMP/D20.2 = DEV / (CNT.X 1); NOPRINT COMPUTE STDDEV_POP/D20.2 = AVE.DEV ** 0.5; COMPUTE STDDEV_SMP/D20.2 = DEV_AVG_SMP ** 0.5; BY GROUP END The complexity of this issue raises the question why there is no standard implementation in WebFOCUS! Do we have an ETA for that? It's dearly needed.This message has been edited. Last edited by: Wep5622, WebFOCUS 8.1.03, Windows 764/200864, IBM DB2/400, Oracle 11g & RDB, MS SQLServer 2005, SAP, PostgreSQL 11, Output: HTML, PDF, Excel 2010 : Member of User Group Benelux :  

Virtuoso 
Easier yet, but not always an option: use SQL passthru and calculate stddev there. That can be done more often than you'd think, because many databases support windowing aggregate functions these days, so you can do stuff like: SELECT stddev_samp(X) over (PARTITION BY GROUP) AS X_STDDEV, X FROM EXAMPLE ; Which is quite a bit more flexible than the "old": SELECT stddev_samp(X) AS X_STDDEV FROM EXAMPLE GROUP BY X ; WebFOCUS 8.1.03, Windows 764/200864, IBM DB2/400, Oracle 11g & RDB, MS SQLServer 2005, SAP, PostgreSQL 11, Output: HTML, PDF, Excel 2010 : Member of User Group Benelux :  

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