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Experimental Design Exam 3
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Terms in this set (13)
coded value formula
x=(ei-((emin+emax)/2)/((max-emin)/2)
Why is coding important (in terms of ANOVA)
Coding influences the effect tests; more specifically, the effect tests are most sensitive and therefore
more reliable when performed using coded factors.
Number of model degrees of freedom
total number of independent parameters, not including the intercept
Total corrected df
model df+ error df
minimal number of required runs
(N-1)= total corrected df
What is a 2^k design and what is it used for?
Factorial design where each factor is studied at 2 levels.
Used in 2 types of experiments: factor screening experiments and first phase of response surface methodology (RSM) to determine path of steepest ascent
When should you use fractional 2^k vs full 2^k
Fractional factorial is used when factors are greater than 3 or 4. For factor screening where only interested in main effects and binary interactions. For path of steepest ascent, we use 1st order model that includes only main effects. Not interested in higher order cross effects.
Importance of coding factors in design and analysis of experiments
protect confidential and proprietary information
provide convenient shorthand for labeling values
makes experiments "blind" so experimental human subjects,experimentalists, and data analysis experts do not know details and won't be biased
scale continuous factor values and make them dimensionless-should always be done with continuous factors because statistical tests are more reliable and parameter estimates more meaningful when working with coded factors
There are six possible cereal-marshmallow combinations. Explain why twelve batches of treats should
be prepared from scratch instead of only six.
We want to replicate in a way that captures as many of the real sources of random error as possible.
Making 12 batches instead of 6 is better because this will capture some of the variability that arises when
two people try to make treats from exactly the same recipe but do not get exactly the same results. It's
reasonable to expect that such variability could be important and so we should replicate in a way that
captures this.
In a factor-screening experiment with a relatively large number of factors (k), explain why it is neither necessary
nor desirable to perform a full factorials 2k design.
So a full factorial design is not necessary because we aren't interested in exploring high-order effects, and it's
not desirable because a full factorial experiment may require a large number of runs.
Why do (OFAT) designs suck?
poor exploration of design space
Explore effects of each factor at only one level of all other factors
cannot discover cross effects
What is a 2k design and for what type of experiment is it used? What determines whether you should use a
fractional factorial 2k design instead of a full factorial 2k design?
A 2k design is a factorial design in which each of the k factors is studied at only two levels. These designs may
sometimes include center points, which adds a third level for continuous factors. These designs are commonly
used in two types of experiments: factor-screening experiments and in the first phase of the response surface
methodology (RSM) for determining the path of steepest ascent.
When the number of factors (k) is greater than 3 or 4, a full factorial design will generate more (possibly much
more) information than you need. For factor-screening experiments, we typically are only interested in main
effects and binary interactions (cross effects). For determining a path of steepest ascent, we first the 1st-order
model that includes only main effects. We are therefore not interested in higher-order cross effects; e.g., if k = 5,
then we would often not be interested in 3-way interactions and almost surely would not be interested in 4-way
or 5-way interactions. Thus, a fractional factorial design will provide all we need.
When calculating the path of steepest ascent, explain why it is important to use the prediction equation
obtained using coded factors.
After fitting the first-order model, we need to set a step size for the factor that has the strongest main
effect on the response. If the factors are not coded, it's difficult to tell which factor has the strongest
effect; for example, looking at the prediction equation obtained using non-coded factors, the regression
coefficient for C is larger than the regression coefficient for M, which might suggest C has a stronger
effect... but this is bogus because these regression coefficients don't have the same units and so any
comparison of their numerical values is meaningless. We can, however, compare regression coefficients
in the model constructed using coded factors, and from this equation we see that M has the stronger effect
and therefore we sh'ould start by setting a step size for M.
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