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Topic Sample Size for 2-level Fractional Factorial

Sample Size for 2-level Fractional Factorial

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This topic contains 3 replies, has 2 voices, and was last updated by  Robert Butler 2 months, 2 weeks ago.

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  • #670122 Reply

    Hi
    Could you please help me with sample size calculation in Minitab?
    I want to conduct 2-level fractional factorial design.
    -I know the SD of a response.
    -I want to achieve 80% of power (P).
    -Number of variables is known – k.
    And I want to detect the smallest effect of d=20%.
    So that if we perform a response optimization, then calculate the maximum desirable values of response, the d of 20% would be the difference between the best performer and a response when treatment at its low levels (-1 -1 -1 -1 -1 …).

    Do I need to calculate a sample size for ANOVA or Regression in this case?
    I have information from P. Mathews book DOE with Minitab on how to calculate:
    -Sample size to determine the slope with specified confidence
    -Sample size to determine the regression constant with specified confidence
    -Sample size to determine the predicted value with specified confidence
    -Sample size to determine the a slope different from zero with specified confidence

    Thanks

    • This topic was modified 2 months, 2 weeks ago by  Gustav.
    • This topic was modified 2 months, 2 weeks ago by  Katie Barry.
    #670205 Reply

    Question: How many variables are we talking about?
    Question: What kind of a fraction? Half rep, quarter rep, saturated?
    Question: How do you know that the response will be at its absolute minimum for the design space when the setting are all at their low levels?
    Question: The standard deviation of the response is based on what?
    Question: What makes you think that the standard deviation of the response will remain invariant across the design space?

    My personal opinion – I’ve run hundreds of designs in my career and I’ve never bothered to worry about sample sizes for the design. I focus on what I can do with the time/money/effort I am allowed to apply to the construction/execution/analysis of the design.

    In almost every instance the results of the design were such that it was much easier to find the optimum and run a small separate analysis to confirm the predicted optimum to whatever level of power I happen to be interested in checking. Also in almost every instance the actual delta between minimum and maximum responses was such that no one really cared much about power issues.

    #671124 Reply

    How many variables are we talking about?

    4 variables.

    What kind of a fraction? Half rep, quarter rep, saturated?

    Resolution 4

    How do you know that the response will be at its absolute minimum for the design space when the setting are all at their low levels?

    Variables are categorical. Type: Yes/No

    The standard deviation of the response is based on what?

    Based on previous researches by other researchers in that field.

    What makes you think that the standard deviation of the response will remain invariant across the design space?

    Unfortunately, the question is not clear for me.

    The response is done via survey (0-100) about prototype by people-testers, so I think about how to minimize the sample size. I even think about showing to one tester all the variants but somehow block the difference within testers… Any suggestions about that?

    #671231 Reply

    Your last sentence gives me pause “I even think about showing to one tester all the variants but somehow block the difference within testers…” This sentence coupled with the statement “The response is done via survey (0-100)” gives the impression that what you have done is build some kind of device in which there are 4 components that can either be included or excluded within that device. This, in turn, would suggest the construction of 8 items all of which are to be rated(?) on a scale from 0-100.

    If the above is an accurate description of what you have done then by stating you believe the situation where none of the 4 variables are present constitutes a minimum response means the presence of any of the 4 variables are only beneficial and any interaction with respect to presence/absence of combinations of the variables will always be synergistic and never antagonistic. That is a large assumption but it is one that would be easy to check.

    Again, if the above is correct then what you would want to do would be to randomizes the order of presentation of all of the devices to each tester/rater and have each tester/rater judge all 8 devices. This will drastically shrink the number of needed raters but it will require that you have the capability to perform and understand the methods of repeated measures regression analysis.

    You would run the repeated measures regression analysis with the repeated subject being the individual tester/rater and look at a model involving all main effects and two way interactions. Using backward elimination regression methods you could identify the reduced model (a model containing only significant terms (P< .05)) and you could also run a least squares means assessment of specific pairwise comparisons with appropriate corrections for the multiple comparisons.

    There are ways to compute samples sizes for repeated measures analysis but, to the best of my knowledge, none of them are easy to perform and I can’t offer any references with respect to finding them.

    Assuming that you have the capability to run a repeated measures analysis and can understand the output then a much easier approach would be to identify a sample that would meet the usual restraints of time/money/effort and test that sample. You could run an interim analysis of the data after the results were in for some fraction of the total number of testers. You might find the results of the interim analysis are such that additional testing is unnecessary.

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