I am trying to help a colleague cobble together a quick lesson for
policymakers. 3 questions. 1) how to get CTABLES to show LCL and UCL of percentages 2) Does CTABLES use asymmetric confidence limits. 3) what conceptual takeaways are missing? * CNN data about Moderna Covid Vaccine copied down during broadcast. * find 95% confidence interval of difference of proportions when proportions are extreme. * including zero hits on one DV. * note the disciplinary difference in term 'cases'. * note this an actual control grouping not just comparison grouping. * further considerations at * "https://www.bbc.com/news/health54902908". * "https://www.cnn.com/2020/11/16/health/modernavaccineresultscoronavirus/index.html". * The DV is a dichotomy a special instance of the level of measurement. * Since there is only 1 possible interval, all intervals are identical. * There are many ways to look at such data. data list list /Group (f1)GroupSize(f5) Positive (f2) Severe(f2). BEGIN DATA 1 15000 90 11 2 15000 5 0 END DATA. VARIABLE LABELS Group 'Treatment group' GroupSize '# participants' Positive '# hits  individuals with positive tests' Severe '# hits  individuals with severe symptoms'. Value labels Group 1 'Placebo Control' 2 'Actual vaccine treatment'. WEIGHT BY GroupSize. * Custom Tables. CTABLES /VLABELS VARIABLES=Group Positive DISPLAY=NAME /TABLE Group [COUNT F40.0 COLPCT.COUNT PCT40.1 COLPCT.COUNT.LCL PCT40.1 COLPCT.COUNT.UCL PCT40.1] BY Positive /CATEGORIES VARIABLES=Group ORDER=A KEY=VALUE EMPTY=INCLUDE /CATEGORIES VARIABLES=Positive ORDER=A KEY=VALUE EMPTY=EXCLUDE /CRITERIA CILEVEL=95 /COMPARETEST TYPE=PROP ALPHA=0.05 ADJUST=BONFERRONI ORIGIN=COLUMN INCLUDEMRSETS=YES CATEGORIES=ALLVISIBLE MERGE=YES STYLE=APA SHOWSIG=NO. * Are differences in treatment vs control results readily attributable to chance? * How precise is the estimate of effectiveness? Is the uncertainty due to imprecision large enough to effect planning?  Art Kendall Social Research Consultants  Sent from: http://spssxdiscussion.1045642.n5.nabble.com/ ===================== To manage your subscription to SPSSXL, send a message to [hidden email] (not to SPSSXL), with no body text except the command. To leave the list, send the command SIGNOFF SPSSXL For a list of commands to manage subscriptions, send the command INFO REFCARD
Art Kendall
Social Research Consultants 
COLPCT.COUNT.LCL COLPCT.COUNT.UCL Yes, these are asymmetrical: Lower bound ( pi ) = IDF.BETA(α/ 2 ,^w'i +.5 , W '−w'i +.5 ), Upper bound ( pi ) = IDF.BETA(1− α / 2 ,w'i +.5 , W'−w'i +.5) See Algorithms doc for unmangled formula On Mon, Nov 16, 2020 at 8:28 AM Art Kendall <[hidden email]> wrote: I am trying to help a colleague cobble together a quick lesson for 
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What Jon shows there is the Jeffreys method. Some years ago, I wrote code to
compute CIs for binomial proportions using 5 methods, with Jeffreys as method 5. Here is a modified version of it using the binomial proportions that I think Art is interested in. HTH. * ======================================================== . * File: ciprop.SPS . * Date: 30Oct2014 . * Author: Bruce Weaver, [hidden email] . * ======================================================== . * Compute the confidence interval for a binomial proportion using: [1] ClopperPearson "exact" method [2] Wald method [3] Adjusted Wald method (Agresti & Coull, 1998) [4] Wilson score method [6] Jeffreys method . * Another method proposed by Ghosh (1979) is equivalent * to the the Wilson score method. DATA LIST LIST /x(f8.0) n(f8.0) confid(f5.3) . BEGIN DATA. 90 15000 .95 11 15000 .95 5 15000 .95 0 15000 .95 END DATA. compute alpha = 1  confid. compute p = x/n. compute q = 1p. compute z = probit(1alpha/2). * ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~. * ClopperPearson "exact" method. * See http://www.sigmazone.com/binomial_confidence_interval.htm. IF x EQ 0 lower1 = 0. IF x EQ n upper1 = 1. IF x GT 0 lower1 = 1  idf.beta(1alpha/2,nx+1,x). IF x LT n upper1 = 1  idf.beta(alpha/2,nx,x+1). * ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~. * Wald method (i.e., the usual normal approximation). * The Wald method breaks down if x = 0 or x = n. * So only attempt to use if 0 < x < n. NUMERIC lower2 upper2 (F5.4). DO IF RANGE(x,1,n1).  COMPUTE #se = SQRT(p*q/n).  COMPUTE lower2 = MAX(0,p  z*#se).  COMPUTE upper2 = MIN(1,p + z*#se). END IF. * ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~. * Adjusted Wald method due to Agresti & Coull (1998). COMPUTE #p = (x + z**2/2) / (n + z**2). COMPUTE #q = 1  #p. COMPUTE #se = SQRT(#p*#q/(n+z**2)). COMPUTE lower3 = MAX(0, #p  z*#se). COMPUTE upper3 = MIN(1, #p + z*#se). * ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~. * Wilson score method (Method 3 in Newcombe, 1998) . * Code adapted from Robert Newcombe's code posted here: http://archive.uwcm.ac.uk/uwcm/ms/Robert2.html . COMPUTE #x1 = 2*n*p+z**2 . COMPUTE #x2 = z*(z**2+4*n*p*(1p))**0.5 . COMPUTE #x3 = 2*(n+z**2) . COMPUTE lower4 = (#x1  #x2) / #x3 . COMPUTE upper4 = (#x1 + #x2) / #x3 . * ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~. * Jeffreys method shown on the IBMSPSS website at * http://www01.ibm.com/support/docview.wss?uid=swg21474963 . compute lower5 = idf.beta(alpha/2,x+.5,nx+.5). compute upper5 = idf.beta(1alpha/2,x+.5,nx+.5). * ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~. * Format variables and list the results of all methods . FORMATS p q lower1 to upper5 (f5.4). LIST var x n confid p lower1 to upper5 . * Method 1: ClopperPearson "exact" method. * Method 2: Wald method (i.e., the usual normal approximation) . * Method 3: Adjusted Wald method (using z**2/2 and z**2 rather than 2 and 4). * Method 4: Wilson score method (from Newcombe paper). * Method 5: Jeffreys method (http://www01.ibm.com/support/docview.wss?uid=swg21474963). * Data from Newcombe (1998), Table I. VARIABLE LABELS x "Successes" n "Trials" p "p(Success)" confid "Confidence Level" lower1 "ClopperPearson: Lower" upper1 "ClopperPearson: Upper" lower2 "Wald: Lower" upper2 "Wald: Upper" lower3 "Adj Wald: Lower" upper3 "Adj Wald: Upper" lower4 "Wilson score: Lower" upper4 "Wilson score: Upper" lower5 "Jeffreys: Lower" upper5 "Jeffreys: Upper" . * OMS. OMS /SELECT TABLES /IF COMMANDS=['Summarize'] SUBTYPES=['Case Processing Summary'] /DESTINATION VIEWER=NO. SUMMARIZE /TABLES=x n p confid lower1 TO upper5 /FORMAT=VALIDLIST NOCASENUM TOTAL /TITLE='Confidence Intervals for Binomial Proportions' /MISSING=VARIABLE /CELLS=NONE. OMSEND. * ======================================================== . Jon Peck wrote > COLPCT.COUNT.LCL COLPCT.COUNT.UCL > Yes, these are asymmetrical: > Lower bound ( pi ) = IDF.BETA(α/ 2 ,^w'i +.5 , W '−w'i +.5 ), > Upper bound ( pi ) = IDF.BETA(1− α / 2 ,w'i +.5 , W'−w'i +.5) > See Algorithms doc for unmangled formula > > On Mon, Nov 16, 2020 at 8:28 AM Art Kendall < > Art@ > > wrote: > >> I am trying to help a colleague cobble together a quick lesson for >> policymakers. >> >> 3 questions. >> 1) how to get CTABLES to show LCL and UCL of percentages >> 2) Does CTABLES use asymmetric confidence limits. >> 3) what conceptual takeaways are missing? >> >> * CNN data about Moderna Covid Vaccine copied down during broadcast. >> * find 95% confidence interval of difference of proportions when >> proportions >> are extreme. >> * including zero hits on one DV. >> * note the disciplinary difference in term 'cases'. >> * note this an actual control grouping not just comparison grouping. >> * further considerations at >> * "https://www.bbc.com/news/health54902908". >> * >> " >> https://www.cnn.com/2020/11/16/health/modernavaccineresultscoronavirus/index.html >> ". >> * The DV is a dichotomy a special instance of the level of measurement. >> * Since there is only 1 possible interval, all intervals are identical. >> * There are many ways to look at such data. >> data list list /Group (f1)GroupSize(f5) Positive (f2) Severe(f2). >> BEGIN DATA >> 1 15000 90 11 >> 2 15000 5 0 >> END DATA. >> VARIABLE LABELS >> Group 'Treatment group' >> GroupSize '# participants' >> Positive '# hits  individuals with positive tests' >> Severe '# hits  individuals with severe symptoms'. >> Value labels Group 1 'Placebo Control' 2 'Actual vaccine treatment'. >> WEIGHT BY GroupSize. >> >> >> * Custom Tables. >> CTABLES >> /VLABELS VARIABLES=Group Positive DISPLAY=NAME >> /TABLE Group [COUNT F40.0 COLPCT.COUNT PCT40.1 COLPCT.COUNT.LCL PCT40.1 >> COLPCT.COUNT.UCL PCT40.1] >> BY Positive >> /CATEGORIES VARIABLES=Group ORDER=A KEY=VALUE EMPTY=INCLUDE >> /CATEGORIES VARIABLES=Positive ORDER=A KEY=VALUE EMPTY=EXCLUDE >> /CRITERIA CILEVEL=95 >> /COMPARETEST TYPE=PROP ALPHA=0.05 ADJUST=BONFERRONI ORIGIN=COLUMN >> INCLUDEMRSETS=YES >> CATEGORIES=ALLVISIBLE MERGE=YES STYLE=APA SHOWSIG=NO. >> >> * Are differences in treatment vs control results readily attributable to >> chance? >> * How precise is the estimate of effectiveness? Is the uncertainty due to >> imprecision large enough to effect planning? >> >> >> >> >> >>  >> Art Kendall >> Social Research Consultants >>  >> Sent from: http://spssxdiscussion.1045642.n5.nabble.com/ >> >> ===================== >> To manage your subscription to SPSSXL, send a message to >> > LISTSERV@.UGA > (not to SPSSXL), with no body text except the >> command. To leave the list, send the command >> SIGNOFF SPSSXL >> For a list of commands to manage subscriptions, send the command >> INFO REFCARD >> > > >  > Jon K Peck > jkpeck@ > > ===================== > To manage your subscription to SPSSXL, send a message to > LISTSERV@.UGA > (not to SPSSXL), with no body text except the > command. To leave the list, send the command > SIGNOFF SPSSXL > For a list of commands to manage subscriptions, send the command > INFO REFCARD   Bruce Weaver [hidden email] http://sites.google.com/a/lakeheadu.ca/bweaver/ "When all else fails, RTFM." NOTE: My Hotmail account is not monitored regularly. To send me an email, please use the address shown above.  Sent from: http://spssxdiscussion.1045642.n5.nabble.com/ ===================== To manage your subscription to SPSSXL, send a message to [hidden email] (not to SPSSXL), with no body text except the command. To leave the list, send the command SIGNOFF SPSSXL For a list of commands to manage subscriptions, send the command INFO REFCARD

Bruce Weaver bweaver@lakeheadu.ca http://sites.google.com/a/lakeheadu.ca/bweaver/ "When all else fails, RTFM." NOTE: My Hotmail account is not monitored regularly. To send me an email, please use the address shown above. 
The PROPOR extension command calculates binomial or Poisson CIs for proportions or differences in proportions. New in 27.0.1 is a PROPORTIONS procedure. It is described as ZTests and confidence intervals for Proportions and differences in Proportions: For OneSample, PairedSamples, IndependentSamples analyses. Found under the Analyze > Compare Means menu, the new Proportions procedure allows users to test for differences in population proportions and construct confidence intervals on observed differences using a variety of methods for each type of analysis. I haven't seen it yet as I am still on 27.0.0. On Mon, Nov 16, 2020 at 1:06 PM Bruce Weaver <[hidden email]> wrote: What Jon shows there is the Jeffreys method. Some years ago, I wrote code to 
In reply to this post by Jon Peck
Thanks.
I should download v 27. I'll just leave v24 on my PC and have both here.  Art Kendall Social Research Consultants  Sent from: http://spssxdiscussion.1045642.n5.nabble.com/ ===================== To manage your subscription to SPSSXL, send a message to [hidden email] (not to SPSSXL), with no body text except the command. To leave the list, send the command SIGNOFF SPSSXL For a list of commands to manage subscriptions, send the command INFO REFCARD
Art Kendall
Social Research Consultants 
In reply to this post by Bruce Weaver
Thanks again.
I passed along the previous version with just the notes/comments. I'll send this since the briefing is in about 1/2 hour. The SPSSXl list members came to the rescue again.  Art Kendall Social Research Consultants  Sent from: http://spssxdiscussion.1045642.n5.nabble.com/ ===================== To manage your subscription to SPSSXL, send a message to [hidden email] (not to SPSSXL), with no body text except the command. To leave the list, send the command SIGNOFF SPSSXL For a list of commands to manage subscriptions, send the command INFO REFCARD
Art Kendall
Social Research Consultants 
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