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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.
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