Because of the intimate links bet een the 2 concepts authors no use statements like the 9 CI overlaps here the ould formerl have stated the difference is not statisticall sig nificant at the level lthough this interchangeabilit is technicall corre ID: 26235 Download Pdf

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Because of the intimate links bet een the 2 concepts authors no use statements like the 9 CI overlaps here the ould formerl have stated the difference is not statisticall sig nificant at the level lthough this interchangeabilit is technicall corre

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n the last decade, guidelines for the presentation of sta- tistical results in medical journals have emphasized confidence intervals (CIs) as an adjunct to, or even a replacement for, statistical tests and values. Because of the intimate links bet een the 2 concepts, authors no use statements like “the 9$% CI overlaps &” here the( ould formerl( have stated “the difference is not statisticall( sig- nificant at the $% level.” )lthough this interchangeabilit( is technicall( correct in 1-sample situations, it does not carr( over full( to comparisons involving 2 samples. ) fre-

quentl( encountered misconception is that if 2 independent 9$% CIs overlap each other, as the( do in ,ig. 1, then a statistical test of the difference ill not be statisticall( sig- nificant at the $% level. Wh( is this not necessaril( so. Consider the means in 2 independent groups, mean and mean , ith for simplicit( mean being the smaller of the 2. The 9$% CI for the mean in group ) is appro0imatel( given b( mean plus or minus t ice the standard error of the mean for that group, S2 , and correspondingl( for group B. ) mathematical check for hether these CIs overlap is given b( adding the

distance 2S2 (from mean to the upper bound of the CI) to 2S2 and comparing this sum ith the distance bet een the 2 means, that is, mean minus mean ) (,ig. 2). The CIs overlap hen [1] But overlapping confidence intervals do not demon- strate that group means are not statisticall( significantl( different from each other. In a 2-sample -test to compare 2 means, significance is attained at the &.&$ level if the sta- tistic e0ceeds the critical value of about 2, hich occurs hen the difference bet een the means e0ceeds t ice its standard error, namel(, if [2] This standard error reflects the fact

that the standard error of a difference involves summing the standard error of each esti- mate, but doing so b( “adding in quadrature,” for e0ample, [5] Thus, to evaluate the overlap of 2 9$% CIs and to deter- mine hether at the same time the difference bet een the If we†re so different, why do we keep overlapping? When 1 plus 1 doesn†t make 2 Rory Wolfe, James Hanley CMAJ • JAN. 8, 2002; 166 (1) 65 2002 Canadian Medical Association or its licensors PRACTICE Fig. 1: Group means with confidence intervals that overlap. Placebo/Group A Treated/Group B 10 15 20 25 Fig. 2: Confidence

intervals and comparison of 2 group means (hypothetical clinical trial data: SE A = SE B = 1.8, means differ by 3 SE; assuming > 30 and independent samples, the 2- sided value for testing the difference in means is approxi- mately 0.036). SE = standard error of the mean. 2 SE 2 SE mean mean Placebo/Group A Treated/Group B 10 15 20 25 mean mean < 2SE + 2SE mean mean > 2 (SE + SE 1 1 = (1 + 1 ) = 1.414

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means is significant at the &.&$ level, the follo ing rough rule can be used6 [7] If S2 and S2 are equal, the condition is as follo s6 [$] When one S2 is 2$% larger than the

other, the boundaries are 5.2 and 7.$ times the smaller S2. )s the lo er boundar( remains close to 5, 8oses as prompted to displa( group means ith error bars that ere 1.$ S2 around the mean in order to have a “b( e(e” test of significance bet een the 2 group means hile presenting the information in the 2 groups separatel(. Reference 1. 8oses 92. :raphical methods in statistical anal(sis. Annu Rev Public Health 19;7;;65&9-$5. RACTICE 66 JAMC 8 JANV. 2002; 166 (1) This article has been peer revie ed. Dr. Wolfe is ith the Department of 2pidemiolog( and ?reventive 8edicine, 8onash Universit(,

8elbourne, Aictoria, )ustralia. Dr. Banle( is ith the De- partment of 2pidemiolog( and Biostatistics, 8c:ill Universit(, 8ontreal, Cue. Contributors Both authors independentl( conceived of the material for this article. Both ere involved in riting the article, and both have seen and approved the final version. Competing interests Done declared. Correspondence to: Dr. Rory Wolfe, Department of Epidemiology and Preventive Medicine, Central and Eastern Clinical School, Monash University and the Alfred Hospital, Commercial Rd., Prahran, Victoria 3183, Australia; fax 61 3 9903 0556;

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