%Traditional versus Piaget clear all close all % randn('state',0) % trad = round(normrnd(84.1, 9,[1 16])) % piaget = round(normrnd(88.1, 15,[1 14])) trad =[80 69 85 87 74 85 95 84 ... 87 86 82 91 79 100 83 85]; piaget =[ 100 89 87 76 93 68 99 ... 100 78 99 100 74 76 97]; X1bar = mean(trad) %84.5 X2bar = mean(piaget) %88.2857 s1 = std(trad) %7.3847 s2 = std(piaget) %11.6515 n1= 16; n2 = 14; %========================= F = s1^2/s2^2 %F =0.4017 pval1 = 2*fcdf(F, n2-1, n1 -1) %pval1 =0.1063 % decide sigma_1^2 = sigma_2^2 test by % pooled standard deviation sp = sqrt( ( (n1-1)*s1^2 + (n2-1)*s2^2)/(n1 + n2 - 2) ) %sp =9.6044 % t = (X1bar - X2bar)/(sp * sqrt(1/n1 + 1/n2)) %t=-1.0771 % pval = tcdf(t, n1 + n2 - 2) %pval=0.1453 % tcrit = tinv(0.05, n1 + n2 - 2) %tcrit=-1.7011 %=============================================================== %============================================================== disp('Let''s NOT assume equal variances') vt = var(trad); vp = var(piaget); T = (X1bar-X2bar)/sqrt(var(trad)/n1+var(piaget)/n2) df = (vt/n1+vp/n2)^2/((vt/n1)^2/(n1-1)+(vp/n2)^2/(n2-1)) pvalue = tcdf(T,df)