Term
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Definition
| the variation of factors we are not controlling, or possibly even considering |
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Term
| What are blocking factors? |
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Definition
| Controllable inputs that are not of primary interest |
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Term
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Definition
| inputs that are controllable during experimentation, but not during normal system operations |
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Term
| If one fails to find significance in hypothesis testing, it might still be possible to find significance if? (2 answers) |
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Definition
1) Additional test runs performed
2) Different levels analyzed
3) Different factors held constant |
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Term
| Given 1 factor with 2 levels, what type of test would you perform to determine if there is significance? What is the basic procedure of this type of test? |
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Definition
T-test.
1) Find avg. of y1 and y2
2) Find s1 and s2 w/ formula
3) Find s(p) given s1 and s2
4) Find t(o) from formula and look up t(crit) in a table
5) if t(o)>t(crit), there is significance at given alpha level |
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Term
| How, in general, do you perform a double blind experiment and account for blocking factors? |
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Definition
| There is a master experimenter who knows which levels are receiving "placebo" vs. the real thing. The thing being tested is coded in a way that only the master experimenter knows, and gives the people running the exp. numbers only so they do not know who is getting what. Blocking factors are accounted for by having the experimenter not know the gender or the nationality of the test subject. |
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Term
| Where do critical values come from and how can they be derived? |
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Definition
Crit. values derive from the assumption that all responses come from same distribution, and no effects assoc. w/ level changes being studied.
By repeating approx. 10,000 simulated experiments, we can find a typical large value that might happen by chance near the value we look up in a table. |
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Term
| Can we perform randomized experiments on a planetary scale? Why or why not? |
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Definition
| No, the scale is simply too large, therefore we would have to rely on planetary models and simulations. |
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Term
| Is randomization necessary to conclude direct empirical proof? |
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Definition
| Yes, without randomization, no direct empirical proof is possible- evidence is possible however |
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Term
| What does Tukey's Method do? |
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Definition
| Tukey's Method is a multiple comparison procedure similar to ANOVA + LSD combo. Based on a single step and designed to limit type 1 error. |
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Term
| Given 1 factor and more than 2 levels, what test is appropriate and what is basic procedure? |
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Definition
F-test.
1) Organize data into matrix- each column = a level
2) set data matrix = grand mean matrix + estimated effects matrix + residuals matrix
3) Calc. SS, df's, and MS for factors and residuals
4) Calculate F(o) and look up F(crit)
5) If F(o) > F(crit), we can conclude significance between the levels, but don't know which ones. |
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Term
| When ANOVA finds significance, how do we determine which levels are significantly better than other levels? Briefly describe the procedure. |
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Definition
LSD Test.
1) Calculate the absolute value of all y-bar difference combos.
2) Calculate LSD using formula.
3) Compare each absolute value calculated previously to this LSD value.
4) If a difference is greater than the LSD, than we can conclude significance between those two y-bar levels. |
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Term
| Why do t-tests sometimes show significance between 2 level comparisons, when an ANOVA does not? |
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Definition
| A type 1 error is highly likely when using t-tests on multiple level comparisons. ANOVA should be used in this case to avoid these falsified significance declarations. |
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Term
| Why is run order important? |
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Definition
| If the run order is not randomized, then we cannot generate empirical proof. The chance of systematic bias or error is likely without randomization. |
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Term
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Definition
| An average of measured values. |
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Term
| How do you calculate the "estimated effect" in an ANOVA test? |
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Definition
| The column average minus the grand mean (for balanced orthogonal designs). Difference between the model prediction conditioned on a level and the grand mean. |
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Term
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Definition
| The allocation of blocking factor levels including run order in an un-patterned way |
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Term
| What is a residual/ how is it calculated? |
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Definition
| The difference between the model prediction (column avg.) and the actual values. Aka "estimated error." |
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Term
| What is a fractional factorial experiment? |
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Definition
| A subset of a full factorial experiment. A randomized plan involving fewer than all combinations of relevant factor levels. |
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Term
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Definition
| A setting that a factor can assume. |
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Term
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Definition
| the difference in the avg. response when a factor is at the high level minus the avg. at the low level. |
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Term
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Definition
| not associated with any specific distributional assumption |
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Term
| What is a random variable? |
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Definition
| a number with an unknown value at the time of planning by the planner. |
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Term
| What is the purpose of a master guide sheet? |
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Definition
| To aid in experimental planning. |
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Term
| What is an empirical model? |
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Definition
| A quantitative input-output relationship derived from experimental data |
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Term
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Definition
| A value of alpha that makes the test statistic equal to the critical value |
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Term
| Why would Tukey's method be preferred over other approaches? |
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Definition
| Has a lower chance of making at least 1 type 1 error. (but higher type 2 rate) |
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