Re: ANOVA question

*To*: mathgroup at smc.vnet.net*Subject*: [mg112495] Re: ANOVA question*From*: Ray Koopman <koopman at sfu.ca>*Date*: Fri, 17 Sep 2010 06:42:34 -0400 (EDT)*References*: <i6spqq$mh9$1@smc.vnet.net>

On Sep 16, 2:59 am, "Stuart Nettleton" <Stuart.Nettle... at uts.edu.au> wrote: > Hi, > Would anyone be able to refer me to a two-way ANOVA method for > Mathematica where the cell variables may be random variables? My > problem is that I have a population of student satisfaction results > for a large teaching program and two samples from that population, > representing courses (which also contribute to the program result). > There are Likert scale measurements on eight variables resulting in > a mean and standard deviation for each. Student t comparison of each > sample to the population on each variable suggests that there is no > significant difference. However, this may be a Type 1 error. For > example, all of the sampleA variables are consistently higher than > the respective population variables. All of the sampleB variables > are lower than the population. > Can I establish for each sample whether the variables considered > together may constitute a significant difference? > The structure of the data below is as follows: SampleA1 provides > measurement mean and standard deviation for each of the eight > variables. SampleA2 provides the sample size and participation rate > for the sample (for example, 65 is a particpation of 53% of the > potential respondents). SampleB and population have the same structure. > > sampleA1 = {{4.00, 0.83}, {4.18, 0.75}, {4.23, 0.69}, {3.88, 1.02}, > {3.89, 0.90}, {4.03, 0.73}, {4.27, 0.76}, {4.16, 0.80}, {4.14, 0.79}}; > sampleA2 = {65, 0.53}; > sampleB1 = {{3.46, 0.93}, {3.57, 1.07}, {3.45, 1.17}, {3.47, 1.05}, > {3.30, 1.11}, {3.47, 1.03}, {3.98, 0.93}, {3.85, 0.94}, {3.78, 1.04}}; > sampleB2 = {455, 0.51}; > population1 = {{3.86, 0.41}, {3.79, 0.47}, {3.69, 0.48}, {3.67, 0.48}, > {3.68, 0.49}, {3.68, 0.51}, {3.94, 0.58}, {3.86, 0.61}, {3.84, 0.60}}; > population2 = {401, 0.50}; > > Any thoughts would be appreciated. > > Many thanks, > Stuart 1. You talk about 8 variables, but show 9 {mean,sd} pairs. Is one of them some sort summary? 2. So in sample A you approached 122 or 123 people, and 65 of them agreed to respond to the question? And similarly ly in sample B and population? 3. What do you mean by "population"? In particular, does it include responses that ought to be in A or B? 4. To consider all three groups simultaneously, you need to do a Multivariate ANOVA (MANOVA), which looks at linear composites of the 8 measures. To compare any two groups, MANOVA reduces to ordinary linear regression with the dependent measures as predictors, and group (dummy coded) as the d.v.