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# 2 x 3 factorial design

From Wikipedia

Factorial

In mathematics, the factorial of a positive integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example, 5 ! = 5 \times 4 \times 3 \times 2 \times 1 = 120 \ 0! is a special case that is explicitly defined to be 1. The factorial operation

File:Factorial Design.jpg - Wikipedia, the free encyclopedia

Sketch of 2^3 factorial design

Question:Hi, Please could someone confirm that I have got my description right ... I'm just getting more and more confused!!! I have conducted some research on school children using a questionnaire. I have given the questionnaire to 3 groups of children - 1 = Target group, 2 = comparison group, 3 = another comparison group. The questionnaire is divided into 5 domains that are analysed separately. I have used a 1-way ANOVA for each domain and have calculated the difference between the 3 groups. Therefore, I have conducted 5 separate 1-way ANOVAs. The analysis is strictly between-participants, as I am trying to see if there is a difference between the research group and comparison groups each time. My question is how I should describe the design in the Methods section of the report. Is it a FACTORIAL DESIGN? I'm assuming that the IVs are the 3 groups and the DVs are the questionnaire score in each of the 5 domains. I realise that I will need to report back 5 sets of results. The problem is that the more I look at this, the more confused I get ... I'm somewhat new to stats too, even if I quite like them most of the time! Thanks in advance!

Answers:Yes, you have a factorial experiment. A more rigorous test of your findings would be a multivariate ANOVA where you put all 5 domains in as DVs at once. This helps control for the fact that you have multiple tests, and the likelihood that one will be significant by chance. You can do 5 separate one-way ANOVAs, but I'd adjust the p-values accordingly for multiple comparisons if you want it to be completely legit. The choice of analysis probably depends on your purpose. E.g., a master's thesis would be held to higher standards than a class project.

Question:So I outlined the ANOVA table for a 3^4 design that is confounded in nine blocks: Source / Degrees of Freedom =================================== Blocks / 8 Main effects / 8 2-way interactions / 24 3-way interactions / 32 Error / 7 Total / 79 Given this information, how can I tell if the statistical design is practical?

Answers:I donno exactly but i think the error percentage should be the factor

Question:that will be assigned. Use MATLAB to compute S for x = 5 & n (number of terms) = 100. Write below the answer

Answers:Here's some code that does the job: x = 5; n = 100; sum = 1; for i = 1: n sum = sum + (-x)^i/factorial(i); end sum and it results in an answer of 0.0067. You should recognise S as an approximation of e^-x.

Question:What is the addition version of a factorial? plus instead of 5! being 1x2x3x4x5, it would be 1+2+3+4+5. Also, using the calculator under the accessories tab of computer, how does calculate ( using the addition version of the factorial ) say 22 ( with whatever symbol for the addition thinger ) - 17 ( whatever symbol )?