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 -- UTS CRICOS Provider Code: 00099F DISCLAIMER: This email message and any accompanying attachments may contain confidential information. If you are not the intended recipient, do not read, use, disseminate, distribute or copy this message or attachments. If you have received this message in error, please notify the sender immediately and delete this message. Any views expressed in this message are those of the individual sender, except where the sender expressly, and with authority, states them to be the views the University of Technology, Sydney. Before opening any attachments, please check them for viruses and defects.