Quantitative literacy: Difference between revisions

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==Health care==
==Health care==
Health care numeracy is problematic. It is confounded by scientific journals not well presenting quantitative results.<ref name="pmid12038920">{{cite journal |author=Nuovo J, Melnikow J, Chang D |title=Reporting number needed to treat and absolute risk reduction in randomized controlled trials |journal=JAMA |volume=287 |issue=21 |pages=2813–4 |year=2002 |month=June |pmid=12038920 |doi= |url=http://jama.ama-assn.org/cgi/pmidlookup?view=long&pmid=12038920 |issn=}}</ref>
Health care numeracy is problematic. Health care providers<ref name="pmid3701813">{{cite journal| author=Bergman DA, Pantell RH| title=The impact of reading a clinical study on treatment decisions of physicians and residents. | journal=J Med Educ | year= 1986 | volume= 61 | issue= 5 | pages= 380-6 | pmid=3701813 | doi= | pmc= | url= }} </ref><ref name="pmid7315859">{{cite journal| author=Berwick DM, Fineberg HV, Weinstein MC| title=When doctors meet numbers. | journal=Am J Med | year= 1981 | volume= 71 | issue= 6 | pages= 991-8 | pmid=7315859 | doi= | pmc= | url= }} </ref><ref name="pmid15175211">{{cite journal| author=Phelps MA, Levitt MA| title=Pretest probability estimates: a pitfall to the clinical utility of evidence-based medicine? | journal=Acad Emerg Med | year= 2004 | volume= 11 | issue= 6 | pages= 692-4 | pmid=15175211 | doi= | pmc= | url= }} </ref><ref name="pmid9576412">{{cite journal| author=Reid MC, Lane DA, Feinstein AR| title=Academic calculations versus clinical judgments: practicing physicians' use of quantitative measures of test accuracy. | journal=Am J Med | year= 1998 | volume= 104 | issue= 4 | pages= 374-80 | pmid=9576412 | doi= | pmc= | url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=sumsearch.org/cite&retmode=ref&cmd=prlinks&id=9576412  }} </ref><ref name="pmid11934776">{{cite journal| author=Steurer J, Fischer JE, Bachmann LM, Koller M, ter Riet G| title=Communicating accuracy of tests to general practitioners: a controlled study. | journal=BMJ | year= 2002 | volume= 324 | issue= 7341 | pages= 824-6 | pmid=11934776 | doi= | pmc=PMC100792 | url= }} </ref> and patients<ref name="pmid15150208">{{cite journal| author=Epstein RM, Alper BS, Quill TE| title=Communicating evidence for participatory decision making. | journal=JAMA | year= 2004 | volume= 291 | issue= 19 | pages= 2359-66 | pmid=15150208 | doi=10.1001/jama.291.19.2359 | pmc= | url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=sumsearch.org/cite&retmode=ref&cmd=prlinks&id=15150208  }} </ref><ref name="pmid8554250">{{cite journal| author=Friedmann PD, Brett AS, Mayo-Smith MF| title=Differences in generalists' and cardiologists' perceptions of cardiovascular risk and the outcomes of preventive therapy in cardiovascular disease. | journal=Ann Intern Med | year= 1996 | volume= 124 | issue= 4 | pages= 414-21 | pmid=8554250 | doi= | pmc= | url= }} </ref><ref name="pmid9673608">{{cite journal| author=Hamm RM, Smith SL| title=The accuracy of patients' judgments of disease probability and test sensitivity and specificity. | journal=J Fam Pract | year= 1998 | volume= 47 | issue= 1 | pages= 44-52 | pmid=9673608 | doi= | pmc= | url= }} </ref><ref name="pmid8271086">{{cite journal| author=Malenka DJ, Baron JA, Johansen S, Wahrenberger JW, Ross JM| title=The framing effect of relative and absolute risk. | journal=J Gen Intern Med | year= 1993 | volume= 8 | issue= 10 | pages= 543-8 | pmid=8271086 | doi= | pmc= | url= }} </ref><ref name="pmid1443954">{{cite journal| author=Naylor CD, Chen E, Strauss B| title=Measured enthusiasm: does the method of reporting trial results alter perceptions of therapeutic effectiveness? | journal=Ann Intern Med | year= 1992 | volume= 117 | issue= 11 | pages= 916-21 | pmid=1443954 | doi= | pmc= | url= }} </ref><ref name="pmid8271086">{{cite journal| author=Malenka DJ, Baron JA, Johansen S, Wahrenberger JW, Ross JM| title=The framing effect of relative and absolute risk. | journal=J Gen Intern Med | year= 1993 | volume= 8 | issue= 10 | pages= 543-8 | pmid=8271086 | doi= | pmc= | url= }} </ref><ref name="pmid9412301">{{cite journal| author=Schwartz LM, Woloshin S, Black WC, Welch HG| title=The role of numeracy in understanding the benefit of screening mammography. | journal=Ann Intern Med | year= 1997 | volume= 127 | issue= 11 | pages= 966-72 | pmid=9412301 | doi= | pmc= | url= }} </ref> both have problems with quantitative reasoning. Some of the difficulty is doe to interpreting relative versus absolute measures of efficacy.<ref name="pmid7950558">{{cite journal| author=Bucher HC, Weinbacher M, Gyr K| title=Influence of method of reporting study results on decision of physicians to prescribe drugs to lower cholesterol concentration. | journal=BMJ | year= 1994 | volume= 309 | issue= 6957 | pages= 761-4 | pmid=7950558 | doi= | pmc=PMC2541000 | url= }} </ref><ref name="pmid14687273">{{cite journal| author=Sheridan SL, Pignone MP, Lewis CL| title=A randomized comparison of patients' understanding of number needed to treat and other common risk reduction formats. | journal=J Gen Intern Med | year= 2003 | volume= 18 | issue= 11 | pages= 884-92 | pmid=14687273 | doi= | pmc=PMC1494938 | url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=sumsearch.org/cite&retmode=ref&cmd=prlinks&id=14687273  }} </ref> The problem is confounded by scientific journals not well presenting quantitative results.<ref name="pmid12038920">{{cite journal |author=Nuovo J, Melnikow J, Chang D |title=Reporting number needed to treat and absolute risk reduction in randomized controlled trials |journal=JAMA |volume=287 |issue=21 |pages=2813–4 |year=2002 |month=June |pmid=12038920 |doi= |url=http://jama.ama-assn.org/cgi/pmidlookup?view=long&pmid=12038920 |issn=}}</ref>


===Comparing benefits of two treatments===
===Comparing benefits of two treatments===
Various formats including the [[number needed to treat]] have been tested to improve comprehension of quantitative comparisons of treatment benefit by patients<ref name="pmid14687273">{{cite journal |author=Sheridan SL, Pignone MP, Lewis CL |title=A randomized comparison of patients' understanding of number needed to treat and other common risk reduction formats |journal=J Gen Intern Med |volume=18 |issue=11 |pages=884–92 |year=2003 |month=November |pmid=14687273 |pmc=1494938 |doi= |url=http://www.blackwell-synergy.com/openurl?genre=article&sid=nlm:pubmed&issn=0884-8734&date=2003&volume=18&issue=11&spage=884 |issn=}}</ref><ref name="pmid17873258">{{cite journal |author=Schwartz LM, Woloshin S, Welch HG |title=The drug facts box: providing consumers with simple tabular data on drug benefit and harm |journal=Med Decis Making |volume=27 |issue=5 |pages=655–62 |year=2007 |pmid=17873258 |doi=10.1177/0272989X07306786 |url=http://mdm.sagepub.com/cgi/pmidlookup?view=long&pmid=17873258 |issn=}}</ref><ref name="pmid17310049">{{cite journal |author=Woloshin S, Schwartz LM, Welch HG |title=The effectiveness of a primer to help people understand risk: two randomized trials in distinct populations |journal=Ann. Intern. Med. |volume=146 |issue=4 |pages=256–65 |year=2007 |month=February |pmid=17310049 |doi= |url=http://www.annals.org/cgi/content/full/146/4/256 |issn=}}</ref><ref name="pmid18565218">{{cite journal |author=Stovring H, Gyrd-Hansen D, Kristiansen IS, Nexoe J, Nielsen JB |title=Communicating effectiveness of intervention for chronic diseases: what single format can replace comprehensive information? |journal=BMC Med Inform Decis Mak |volume=8 |issue= |pages=25 |year=2008 |pmid=18565218 |pmc=2467410 |doi=10.1186/1472-6947-8-25 |url=http://www.biomedcentral.com/1472-6947/8/25 |issn=}}</ref><ref name="pmid18402680">{{cite journal |author=Dolan JG, Iadarola S |title=Risk communication formats for low probability events: an exploratory study of patient preferences |journal=BMC Med Inform Decis Mak |volume=8 |issue= |pages=14 |year=2008 |pmid=18402680 |pmc=2330036 |doi=10.1186/1472-6947-8-14 |url=http://www.biomedcentral.com/1472-6947/8/14 |issn=}}</ref><ref name="pmid9412301">{{cite journal |author=Schwartz LM, Woloshin S, Black WC, Welch HG |title=The role of numeracy in understanding the benefit of screening mammography |journal=Ann. Intern. Med. |volume=127 |issue=11 |pages=966–72 |year=1997 |month=December |pmid=9412301 |doi= |url=http://www.annals.org/cgi/pmidlookup?view=long&pmid=9412301 |issn=}}</ref><ref name="pmid16174840">{{cite journal |author=Wen L, Badgett R, Cornell J |title=Number needed to treat: a descriptor for weighing therapeutic options |journal=Am J Health Syst Pharm |volume=62 |issue=19 |pages=2031–6 |year=2005 |month=October |pmid=16174840 |doi=10.2146/ajhp040558 |url=http://www.ajhp.org/cgi/pmidlookup?view=long&pmid=16174840 |issn=}}</ref> and by health care professionals<ref name="pmid11874195">{{cite journal |author=Sheridan SL, Pignone M |title=Numeracy and the medical student's ability to interpret data |journal=Eff Clin Pract |volume=5 |issue=1 |pages=35–40 |year=2002 |pmid=11874195 |doi= |url=http://www.acponline.org/journals/ecp/janfeb02/sheridan.htm |issn=}}</ref><ref name="pmid14512488">{{cite journal |author=Gigerenzer G, Edwards A |title=Simple tools for understanding risks: from innumeracy to insight |journal=BMJ |volume=327 |issue=7417 |pages=741–4 |year=2003 |month=September |pmid=14512488 |pmc=200816 |doi=10.1136/bmj.327.7417.741 |url=http://bmj.com/cgi/pmidlookup?view=long&pmid=14512488 |issn=}}</ref><ref name="pmid16174840">{{cite journal |author=Wen L, Badgett R, Cornell J |title=Number needed to treat: a descriptor for weighing therapeutic options |journal=Am J Health Syst Pharm |volume=62 |issue=19 |pages=2031–6 |year=2005 |month=October |pmid=16174840 |doi=10.2146/ajhp040558 |url=http://www.ajhp.org/cgi/pmidlookup?view=long&pmid=16174840 |issn=}}</ref>.
Various formats including the [[number needed to treat]] have been tested to improve comprehension of quantitative comparisons of treatment benefit by patients<ref name="pmid14687273" /><ref name="pmid17873258">{{cite journal |author=Schwartz LM, Woloshin S, Welch HG |title=The drug facts box: providing consumers with simple tabular data on drug benefit and harm |journal=Med Decis Making |volume=27 |issue=5 |pages=655–62 |year=2007 |pmid=17873258 |doi=10.1177/0272989X07306786 |url=http://mdm.sagepub.com/cgi/pmidlookup?view=long&pmid=17873258 |issn=}}</ref><ref name="pmid17310049">{{cite journal |author=Woloshin S, Schwartz LM, Welch HG |title=The effectiveness of a primer to help people understand risk: two randomized trials in distinct populations |journal=Ann. Intern. Med. |volume=146 |issue=4 |pages=256–65 |year=2007 |month=February |pmid=17310049 |doi= |url=http://www.annals.org/cgi/content/full/146/4/256 |issn=}}</ref><ref name="pmid18565218">{{cite journal |author=Stovring H, Gyrd-Hansen D, Kristiansen IS, Nexoe J, Nielsen JB |title=Communicating effectiveness of intervention for chronic diseases: what single format can replace comprehensive information? |journal=BMC Med Inform Decis Mak |volume=8 |issue= |pages=25 |year=2008 |pmid=18565218 |pmc=2467410 |doi=10.1186/1472-6947-8-25 |url=http://www.biomedcentral.com/1472-6947/8/25 |issn=}}</ref><ref name="pmid18402680">{{cite journal |author=Dolan JG, Iadarola S |title=Risk communication formats for low probability events: an exploratory study of patient preferences |journal=BMC Med Inform Decis Mak |volume=8 |issue= |pages=14 |year=2008 |pmid=18402680 |pmc=2330036 |doi=10.1186/1472-6947-8-14 |url=http://www.biomedcentral.com/1472-6947/8/14 |issn=}}</ref><ref name="pmid9412301"/><ref name="pmid16174840">{{cite journal |author=Wen L, Badgett R, Cornell J |title=Number needed to treat: a descriptor for weighing therapeutic options |journal=Am J Health Syst Pharm |volume=62 |issue=19 |pages=2031–6 |year=2005 |month=October |pmid=16174840 |doi=10.2146/ajhp040558 |url=http://www.ajhp.org/cgi/pmidlookup?view=long&pmid=16174840 |issn=}}</ref> and by health care professionals<ref name="pmid11874195">{{cite journal |author=Sheridan SL, Pignone M |title=Numeracy and the medical student's ability to interpret data |journal=Eff Clin Pract |volume=5 |issue=1 |pages=35–40 |year=2002 |pmid=11874195 |doi= |url=http://www.acponline.org/journals/ecp/janfeb02/sheridan.htm |issn=}}</ref><ref name="pmid14512488">{{cite journal |author=Gigerenzer G, Edwards A |title=Simple tools for understanding risks: from innumeracy to insight |journal=BMJ |volume=327 |issue=7417 |pages=741–4 |year=2003 |month=September |pmid=14512488 |pmc=200816 |doi=10.1136/bmj.327.7417.741 |url=http://bmj.com/cgi/pmidlookup?view=long&pmid=14512488 |issn=}}</ref><ref name="pmid16174840">{{cite journal |author=Wen L, Badgett R, Cornell J |title=Number needed to treat: a descriptor for weighing therapeutic options |journal=Am J Health Syst Pharm |volume=62 |issue=19 |pages=2031–6 |year=2005 |month=October |pmid=16174840 |doi=10.2146/ajhp040558 |url=http://www.ajhp.org/cgi/pmidlookup?view=long&pmid=16174840 |issn=}}</ref>.
 
In practicing [[evidence-based medicine]], framing bias is best avoided by using numeracy with absolute measures of efficacy.<ref name="pmid21792695">{{cite journal| author=Perneger TV, Agoritsas T| title=Doctors and Patients' Susceptibility to Framing Bias: A Randomized Trial. | journal=J Gen Intern Med | year= 2011 | volume=  | issue=  | pages=  | pmid=21792695 | doi=10.1007/s11606-011-1810-x | pmc= | url= }} </ref><ref name="pmid21768582">{{cite journal| author=Woloshin S, Schwartz LM| title=Communicating data about the benefits and harms of treatment: a randomized trial. | journal=Ann Intern Med | year= 2011 | volume= 155 | issue= 2 | pages= 87-96 | pmid=21768582 | doi=10.1059/0003-4819-155-2-201107190-00004 | pmc= | url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=sumsearch.org/cite&retmode=ref&cmd=prlinks&id=21768582  }} </ref>


===Comparing accuracy of diagnostic methods===
===Comparing accuracy of diagnostic methods===
Various formats have been tested to improve comprehension of quantitative comparisons of diagnostic accuracy.<ref name="pmid16061916">{{cite journal |author=Puhan MA, Steurer J, Bachmann LM, ter Riet G |title=A randomized trial of ways to describe test accuracy: the effect on physicians' post-test probability estimates |journal=Ann. Intern. Med. |volume=143 |issue=3 |pages=184–9 |url=http://www.annals.org/cgi/content/full/143/3/184|year=2005 |pmid=16061916 |doi= |issn=}}</ref><ref name="pmid7898300">{{cite journal |author=Poses RM ''et al.''|title=You can lead a horse to water--improving physicians' knowledge of probabilities may not affect their decisions |journal=Medical Decision Making |volume=15  |pages=65–75 |year=1995 |pmid=7898300 |doi=}}</ref>
Various formats have been tested to improve comprehension of quantitative comparisons of diagnostic accuracy.<ref name="pmid16061916">{{cite journal |author=Puhan MA, Steurer J, Bachmann LM, ter Riet G |title=A randomized trial of ways to describe test accuracy: the effect on physicians' post-test probability estimates |journal=Ann. Intern. Med. |volume=143 |issue=3 |pages=184–9 |url=http://www.annals.org/cgi/content/full/143/3/184|year=2005 |pmid=16061916 |doi= |issn=}}</ref><ref name="pmid7898300">{{cite journal |author=Poses RM ''et al.''|title=You can lead a horse to water--improving physicians' knowledge of probabilities may not affect their decisions |journal=Medical Decision Making |volume=15  |pages=65–75 |year=1995 |pmid=7898300 |doi=}}</ref>
<ref name="pmid11874195"/>
==Footnotes==
<small>
<references>


==References==
</references>
<references/>
</small>

Revision as of 12:58, 20 August 2024

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In education and literacy, quantitative literacy (also called numeracy) is "the knowledge and skills required to apply arithmetic operations, either alone or sequentially, using numbers embedded in printed materials; for example, balancing a checkbook, figuring out a tip, completing an order form, or determining the amount of interest from a loan advertisement."[1]

Quantitative literacy is important in politics[2][3] and health care[4][5].

Health care

Health care numeracy is problematic. Health care providers[6][7][8][9][10] and patients[11][12][13][14][15][14][16] both have problems with quantitative reasoning. Some of the difficulty is doe to interpreting relative versus absolute measures of efficacy.[17][18] The problem is confounded by scientific journals not well presenting quantitative results.[19]

Comparing benefits of two treatments

Various formats including the number needed to treat have been tested to improve comprehension of quantitative comparisons of treatment benefit by patients[18][20][21][22][23][16][24] and by health care professionals[25][26][24].

In practicing evidence-based medicine, framing bias is best avoided by using numeracy with absolute measures of efficacy.[27][28]

Comparing accuracy of diagnostic methods

Various formats have been tested to improve comprehension of quantitative comparisons of diagnostic accuracy.[29][30] [25]

Footnotes

  1. ↑ Irwin S. Kirsch, Ann Jungeblut, Lynn Jenkins, and Andrew Kolstad. (1993). Adult Literacy in America: a first look at the findings of the National Adult Literacy Survey, (NCES 93275). U.S. Department of Education.
  2. ↑ Best, Joel (2001). Damned lies and statistics: untangling numbers from the media, politicians, and activists. Berkeley: University of California Press. ISBN 0-520-21978-3. 
  3. ↑ Best, Joel (2004). More damned lies and statistics: how numbers confuse public issues. Berkeley: University of California Press. ISBN 0-520-23830-3. 
  4. ↑ Mark Kutner, Elizabeth Greenberg, Ying Jin, Christine Paulsen. (2006) The Health Literacy of America’s Adults: Results From the 2003 National Assessment of Adult Literacy. U.S. Department of Education.
  5. ↑ Schwartz, Lisa A.; Steven Woloshin (2008). Know Your Chances: Understanding Health Statistics. Berkeley: University of California Press. ISBN 0-520-25222-5. 
  6. ↑ Bergman DA, Pantell RH (1986). "The impact of reading a clinical study on treatment decisions of physicians and residents.". J Med Educ 61 (5): 380-6. PMID 3701813. [e]
  7. ↑ Berwick DM, Fineberg HV, Weinstein MC (1981). "When doctors meet numbers.". Am J Med 71 (6): 991-8. PMID 7315859. [e]
  8. ↑ Phelps MA, Levitt MA (2004). "Pretest probability estimates: a pitfall to the clinical utility of evidence-based medicine?". Acad Emerg Med 11 (6): 692-4. PMID 15175211. [e]
  9. ↑ Reid MC, Lane DA, Feinstein AR (1998). "Academic calculations versus clinical judgments: practicing physicians' use of quantitative measures of test accuracy.". Am J Med 104 (4): 374-80. PMID 9576412. [e]
  10. ↑ Steurer J, Fischer JE, Bachmann LM, Koller M, ter Riet G (2002). "Communicating accuracy of tests to general practitioners: a controlled study.". BMJ 324 (7341): 824-6. PMID 11934776. PMC PMC100792. [e]
  11. ↑ Epstein RM, Alper BS, Quill TE (2004). "Communicating evidence for participatory decision making.". JAMA 291 (19): 2359-66. DOI:10.1001/jama.291.19.2359. PMID 15150208. Research Blogging.
  12. ↑ Friedmann PD, Brett AS, Mayo-Smith MF (1996). "Differences in generalists' and cardiologists' perceptions of cardiovascular risk and the outcomes of preventive therapy in cardiovascular disease.". Ann Intern Med 124 (4): 414-21. PMID 8554250. [e]
  13. ↑ Hamm RM, Smith SL (1998). "The accuracy of patients' judgments of disease probability and test sensitivity and specificity.". J Fam Pract 47 (1): 44-52. PMID 9673608. [e]
  14. ↑ 14.0 14.1 Malenka DJ, Baron JA, Johansen S, Wahrenberger JW, Ross JM (1993). "The framing effect of relative and absolute risk.". J Gen Intern Med 8 (10): 543-8. PMID 8271086. [e]
  15. ↑ Naylor CD, Chen E, Strauss B (1992). "Measured enthusiasm: does the method of reporting trial results alter perceptions of therapeutic effectiveness?". Ann Intern Med 117 (11): 916-21. PMID 1443954. [e]
  16. ↑ 16.0 16.1 Schwartz LM, Woloshin S, Black WC, Welch HG (1997). "The role of numeracy in understanding the benefit of screening mammography.". Ann Intern Med 127 (11): 966-72. PMID 9412301. [e]
  17. ↑ Bucher HC, Weinbacher M, Gyr K (1994). "Influence of method of reporting study results on decision of physicians to prescribe drugs to lower cholesterol concentration.". BMJ 309 (6957): 761-4. PMID 7950558. PMC PMC2541000. [e]
  18. ↑ 18.0 18.1 Sheridan SL, Pignone MP, Lewis CL (2003). "A randomized comparison of patients' understanding of number needed to treat and other common risk reduction formats.". J Gen Intern Med 18 (11): 884-92. PMID 14687273. PMC PMC1494938. [e]
  19. ↑ Nuovo J, Melnikow J, Chang D (June 2002). "Reporting number needed to treat and absolute risk reduction in randomized controlled trials". JAMA 287 (21): 2813–4. PMID 12038920. [e]
  20. ↑ Schwartz LM, Woloshin S, Welch HG (2007). "The drug facts box: providing consumers with simple tabular data on drug benefit and harm". Med Decis Making 27 (5): 655–62. DOI:10.1177/0272989X07306786. PMID 17873258. Research Blogging.
  21. ↑ Woloshin S, Schwartz LM, Welch HG (February 2007). "The effectiveness of a primer to help people understand risk: two randomized trials in distinct populations". Ann. Intern. Med. 146 (4): 256–65. PMID 17310049. [e]
  22. ↑ Stovring H, Gyrd-Hansen D, Kristiansen IS, Nexoe J, Nielsen JB (2008). "Communicating effectiveness of intervention for chronic diseases: what single format can replace comprehensive information?". BMC Med Inform Decis Mak 8: 25. DOI:10.1186/1472-6947-8-25. PMID 18565218. PMC 2467410. Research Blogging.
  23. ↑ Dolan JG, Iadarola S (2008). "Risk communication formats for low probability events: an exploratory study of patient preferences". BMC Med Inform Decis Mak 8: 14. DOI:10.1186/1472-6947-8-14. PMID 18402680. PMC 2330036. Research Blogging.
  24. ↑ 24.0 24.1 Wen L, Badgett R, Cornell J (October 2005). "Number needed to treat: a descriptor for weighing therapeutic options". Am J Health Syst Pharm 62 (19): 2031–6. DOI:10.2146/ajhp040558. PMID 16174840. Research Blogging.
  25. ↑ 25.0 25.1 Sheridan SL, Pignone M (2002). "Numeracy and the medical student's ability to interpret data". Eff Clin Pract 5 (1): 35–40. PMID 11874195. [e]
  26. ↑ Gigerenzer G, Edwards A (September 2003). "Simple tools for understanding risks: from innumeracy to insight". BMJ 327 (7417): 741–4. DOI:10.1136/bmj.327.7417.741. PMID 14512488. PMC 200816. Research Blogging.
  27. ↑ Perneger TV, Agoritsas T (2011). "Doctors and Patients' Susceptibility to Framing Bias: A Randomized Trial.". J Gen Intern Med. DOI:10.1007/s11606-011-1810-x. PMID 21792695. Research Blogging.
  28. ↑ Woloshin S, Schwartz LM (2011). "Communicating data about the benefits and harms of treatment: a randomized trial.". Ann Intern Med 155 (2): 87-96. DOI:10.1059/0003-4819-155-2-201107190-00004. PMID 21768582. Research Blogging.
  29. ↑ Puhan MA, Steurer J, Bachmann LM, ter Riet G (2005). "A randomized trial of ways to describe test accuracy: the effect on physicians' post-test probability estimates". Ann. Intern. Med. 143 (3): 184–9. PMID 16061916. [e]
  30. ↑ Poses RM et al. (1995). "You can lead a horse to water--improving physicians' knowledge of probabilities may not affect their decisions". Medical Decision Making 15: 65–75. PMID 7898300. [e]

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