LCL and UCL of percentages and difference of percentages
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LCL and UCL of percentages and difference of percentages
 
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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/health-54902908". * "https://www.cnn.com/2020/11/16/health/moderna-vaccine-results-coronavirus/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://spssx-discussion.1045642.n5.nabble.com/ ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD
Art Kendall
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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 |
Re: LCL and UCL of percentages and difference of percentages
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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: 30-Oct-2014 . * Author: Bruce Weaver, [hidden email] . * ======================================================== . * Compute the confidence interval for a binomial proportion using: [1] Clopper-Pearson "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 = 1-p. compute z = probit(1-alpha/2). * ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~. * Clopper-Pearson "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(1-alpha/2,n-x+1,x). IF x LT n upper1 = 1 - idf.beta(alpha/2,n-x,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,n-1). - 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*(1-p))**0.5 . COMPUTE #x3 = 2*(n+z**2) . COMPUTE lower4 = (#x1 - #x2) / #x3 . COMPUTE upper4 = (#x1 + #x2) / #x3 . * ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~. * Jeffreys method shown on the IBM-SPSS website at * http://www-01.ibm.com/support/docview.wss?uid=swg21474963 . compute lower5 = idf.beta(alpha/2,x+.5,n-x+.5). compute upper5 = idf.beta(1-alpha/2,x+.5,n-x+.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: Clopper-Pearson "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://www-01.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 "Clopper-Pearson: Lower" upper1 "Clopper-Pearson: 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/health-54902908". >> * >> " >> https://www.cnn.com/2020/11/16/health/moderna-vaccine-results-coronavirus/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://spssx-discussion.1045642.n5.nabble.com/ >> >> ===================== >> To manage your subscription to SPSSX-L, send a message to >> > LISTSERV@.UGA > (not to SPSSX-L), with no body text except the >> command. To leave the list, send the command >> SIGNOFF SPSSX-L >> For a list of commands to manage subscriptions, send the command >> INFO REFCARD >> > > > -- > Jon K Peck > jkpeck@ > > ===================== > To manage your subscription to SPSSX-L, send a message to > LISTSERV@.UGA > (not to SPSSX-L), with no body text except the > command. To leave the list, send the command > SIGNOFF SPSSX-L > 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 e-mail, please use the address shown above. -- Sent from: http://spssx-discussion.1045642.n5.nabble.com/ ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L 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." PLEASE NOTE THE FOLLOWING: 1. My Hotmail account is not monitored regularly. To send me an e-mail, please use the address shown above. 2. The SPSSX Discussion forum on Nabble is no longer linked to the SPSSX-L listserv administered by UGA (https://listserv.uga.edu/). |
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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 Z-Tests and confidence intervals for Proportions and differences in Proportions: For One-Sample, Paired-Samples, Independent-Samples 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 |
Re: LCL and UCL of percentages and difference of percentages
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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://spssx-discussion.1045642.n5.nabble.com/ ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD
Art Kendall
Social Research Consultants |
Re: LCL and UCL of percentages and difference of percentages
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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 SPSSX-l list members came to the rescue again. ----- Art Kendall Social Research Consultants -- Sent from: http://spssx-discussion.1045642.n5.nabble.com/ ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD
Art Kendall
Social Research Consultants |
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