       ANOVA question

• To: mathgroup at smc.vnet.net
• Subject: [mg112460] ANOVA question
• From: "Stuart Nettleton" <Stuart.Nettleton at uts.edu.au>
• Date: Thu, 16 Sep 2010 06:00:04 -0400 (EDT)
• Organization: University of Technology, Sydney

```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,
0.9}, {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

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