Data and Sampling

1
Data and Sampling

• Engineering Experimental Design
• Winter 2003

2
Sampling

• Goal use statistics based on analysis of a
  sample to estimate the same characteristics for
  the whole population
• Random sampling best choice
• Likely to be representative of whole population
• Ironically, requires careful planning
• Uses a consistent, predetermined protocol

3
Questions

• True or false you can always get more accurate
  characterization of a population if you measure
  every element instead of sampling.
• Which is a better example of random sampling?
• The operator takes a sample at 10 past the hour
  every hour.
• The operator takes a sample once an hour at
  whatever time he gets a chance

4
In the refractive index determination . . .

• What sources of variability influenced the value
  of n when we made measurements at five different
  angles of incidence?
• Were those five measurements replicates? Could
  you use them to estimate uncertainty?
• What sources of variability go untested if you
  make five measurements at one angle of incidence?
  

5
Replicate Measurements

• Goal determine how much of the variability in y
  is due to the way the experiment is done, and not
  due to the factors you want to test.
• Your definition of replicate determines what
  effects are included in the uncertainty you
  determine.

6
Questions

• After carefully controlling all the chemical
  reagents and conditions during a reaction, the
  researcher weighs the product on an electronic
  balance five times, removing and replacing the
  reactant on the balance between weighings.
• What measurement is being replicated?
• What uncertainty or variability can be
  characterized by the standard deviation of the
  five weighings?
• What would you do to determine the uncertainty on
  the reaction yield?

7
Getting Uncertainty from Replicate Measurements

• With replicate measurements, the mean is commonly
  reported as the best estimate of the true value.
• Uncertainty may be described by standard
  deviations or confidence limits.
• 1 s.d. 68 c.l.
• 2 s.d. 95 c.l.
• Propagation of error on the calculation of the
  mean is NOT appropriate.
• Error propagation makes the uncertainty grow with
  more replicates. You should be more certain of
  your answer with more replicates, not less.

8
Questions

• In a study of the factors that affect CD
  readability, a researcher decides to test the
  effect of photoresist thickness on the depth of
  the holes etched on the surface of the CD. The
  research budget allows 20 CDs to be tested.
• Identify the independent variable(s).
• Identify the dependent variable(s).
• Identify the factor(s).
• Identify the response variable(s).
• Describe a replicate sample.

9
Questions

• In a study of the factors that affect CD
  readability, a researcher decides to test the
  effect of photoresist thickness on the depth of
  the pits etched on the surface of the CD. The
  research budget allows 20 CDs to be tested.
• Suppose it is known that for any fixed
  photoresist thickness, there is little or no
  variation in pit depth. Should the researcher
  test several photoresist thicknesses with few
  replicate samples, or use many replicate samples
  and test few photoresist thicknesses?

10
Questions

• In a study of the factors that affect CD
  readability, a researcher decides to test the
  effect of photoresist thickness on the depth of
  the pits etched on the surface of the CD. The
  research budget allows 20 CDs to be tested.
• Suppose it is known that for any fixed
  photoresist thickness, pit depth can vary
  substantially. Should the researcher test
  several photoresist thicknesses with few
  replicate samples, or use many replicate samples
  and test few photoresist thicknesses?

11
Experimental Design

• Goal make efficient use of time to learn about
  the predictable behavior and the random
  variability in your system
• A procedure and a test matrix
• A plan for the conditions to test and the number
  of samples to collect under each set of conditions

12
Questions

• Hardness measurements (in Mohs) of molded
  plastics in 4 test runs are shown above.
• Estimate the increase in hardness when you switch
  from Plastic A to Plastic B.
• Estimate the increase in hardness when you switch
  from Molding Machine 1 to 2.

13
Questions

• Hardness measurements (in Mohs) of molded
  plastics in 4 test runs are shown above.
• Which of these measurements are replicates?
• Is the increase in hardness when you switch from
  Plastic A to Plastic B significant? How do you
  know?