Hello Ian! This is just an answer not the answer,but it will give you some elements ,Ihope: your data seem to variate around a mean;i think you can make the hypothesis your data are gaussian.The two samples are independant.(unless for example S1+S2 = T...) So you have to compare the two means of the two samples.Therefore the question is: Do the 2 samples come from the same population? note : S1b=mean(S1) S2b=mean(S2) sigma=std error (unknown) of the population here n1=n2
H0 : "come from the same populations" S1b-S2b~N(ES1-ES2,sigma�/n1 + sigma�/n2) under H0, T=[(S1b-S2b)-(ES1-ES2)] / [sigma*sqrt(1/n1+1n2)] = (S1b-S2b) / (sigma*sqrt(1/n1+1/n2)) (ok?ES1=ES2 by H0...) and T ~ N(0,1) let's estimate sigma: s1,s2 std of the samples (you've calculated it) Homoscedasticity implies to calculate sigma� with the two samples;theorem gives: n1.s� = sigma�*Xhi�(n1-1) n2.s2�=sigma�*Xhi�(n2-1) let's call Xhi�=K therefore, (n1*s1�+n2*s2�)/(n1+n2-2) = sigma�*((K1+K2) / n1+n2-2)) and T / (sqrt(K1+K2) / (n1+n2-2)) ~ t(n1+n2-2) , the student variable because of the ratio of N(0,1) by the square root of a normalized Xhi� Conclusion : Calculate this : (S1b-S2b) / sqrt((1/n1+1/n2)*(n1*s1�+n2*s2�)/(n1+n2-2)) and compare it with the t-student variable with (n1+n2-2) degrees of liberty at the risk alpha you want : 5%,maybe 1% here... The conclusion of |t(1%)|<|T| is : " The 2 samples don't come from different populations , and the risk to make a mistake by sayong it is <1%" PS: my english is a litlle bit poor...sorry @+ "Iain Toft" <[EMAIL PROTECTED]> a �crit dans le message de news: [EMAIL PROTECTED] > I'm no stats expert but would like to solve the following problem. > > Given two sets of scores... > > S1 = [38.37388112, 38.37471969, 38.40682618, 38.37863674, ..., > 38.39506964] > S2 = [22.40683282, 22.23267916, 22.08881316, 24.96633041, ..., > 21.8635192] > > I'd like some statistical evidence to show the scores attained in S2 > are inferior to those in S1. I can show the mean,min,max,stdev but > would like something with a little more clout. > > Each score in S2 was obtained in the same trial as S1 (that is the > scorer in S2 was competing against and in the same game/trial as the > scorer of S1). In this example S2 is clearly inferior in score, > however for other examples the difference is less prominent (in terms > of mean). How can I determine if scorer S2 is inferior to S1, from > what I can fathom out I need some kind of t test? > > There are 50 trials. > > Obvious two questions... > 1) What is a t test? > 2) How do I interpret the results? > > Thanks in advance, > Iain . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
