Confidence Interval for Standardized Difference Between ...



Confidence Interval for Standardized Difference Between Means, Independent SamplesHere are results from a independent samples t test. One group consists of mice (Mus musculus) who were reared by mice, the other group consists of mice who were reared by rats (Rattus norvegicus). The dependent variable is a the difference between the number of visits the mouse made to a tunnel that smelled like another mouse and the number of visits to a tunnel that smelled like rat.-------------------------------------------------------------------------------------------------- The SAS System 1 Independent Samples T-Tests on Mouse-Rat Tunnel Difference Scores Foster Mom is a Mouse or is a Rat The TTEST Procedure Variable: v_diff Mom N Mean Std Dev Std Err Minimum Maximum Mouse 32 14.8125 9.0320 1.5966 0 31.0000 Rat 16 -1.3125 8.4041 2.1010 -17.0000 17.0000 Diff (1-2) 16.1250 8.8321 2.7043 Mom Method Mean 95% CL Mean Std Dev 95% CL Std Dev Mouse 14.8125 11.5561 18.0689 9.0320 7.2410 12.0078 Rat -1.3125 -5.7907 3.1657 8.4041 6.2082 13.0070 Diff (1-2) Pooled 16.1250 10.6816 21.5684 8.8321 7.3393 11.0930 Diff (1-2) Satterthwaite 16.1250 10.7507 21.4993 Method Variances DF t Value Pr > |t| Pooled Equal 46 5.96 <.0001 Satterthwaite Unequal 32.141 6.11 <.0001 Equality of Variances Method Num DF Den DF F Value Pr > F Folded F 31 15 1.15 0.7906Notice that you are given a pooled variances confidence interval and a separate variances confidence interval. These are in raw units, not standardized units.We may get a better feel for the size of the effect if we standardize it. I have two programs available to do this.Program Onetitle 'Compute 95% Confidence Interval for d, Standardardized Difference Between Two Independent Population Means';Data CI;**********************************************************************************;Replace tttt with the computed value of the independent samples t test.Replace dd with the degrees of freedom for the independent samples t test.Replace n1n with the sample size for the first group.Replace n2n with the sample size for the second group.***********************************************************************************;t= 5.96 ;df = 46 ;n1 = 32 ;n2 = 16 ;***********************************************************************************;g = t/sqrt(n1*n2/(n1+n2));ncp_lower = TNONCT(t,df,.975);ncp_upper = TNONCT(t,df,.025);d_lower = ncp_lower*sqrt((n1+n2)/(n1*n2));d_upper = ncp_upper*sqrt((n1+n2)/(n1*n2));output; run; proc print; var g d_lower d_upper; run;The Output Obs g d_lower d_upper 1 1.82487 1.11164 2.52360Notice that both sides of the confidence interval indicate that the effect is quite large.Program 2*This program computes a CI for the effect size in a between-subject design with two groups. m1 and m2 are the means for the two groupss1 and s2 are the standard deviations for the two groupsn1 and n2 are the sample sizes for the two groupsprob is the confidence level;*Downloaded from James Algina’s webpage at ;data;m1=14.8125 ;m2= -1.3125 ;s1=9.032 ;s2=8.4041 ;n1=32 ;n2=16 ;prob=.95;v1=s1**2;v2=s2**2;pvar=((n1-1)*v1+(n2-1)*v2)/(n1+n2-2);se=sqrt(pvar*(1/n1+1/n2));nchat=(m1-m2)/se;es=(m1-m2)/(sqrt(pvar));df=n1+n2-2;ncu=TNONCT(nchat,df,(1-prob)/2);ncl=TNONCT(nchat,df,1-(1-prob)/2);ll=(sqrt(1/n1+1/n2))*ncl;ul=(sqrt(1/n1+1/n2))*ncu;output;proc print;title1 'll is the lower limit and ul is the upper limit';title2 'of a confidence interval for the effect size';var es ll ul;run;The Output ll is the lower limit and ul is the upper limit 2 of a confidence interval for the effect size Obs es ll ul 1 1.82572 1.11239 2.52453The minor differences between these results and those shown earlier are due to rounding error from the value of t.Do it with SPSSWuensch’s Stats LessonsKarl L. Wuensch, East Carolina University, Dept. of Psychology, 3. September, 2011. ................
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