Measure your progress

Perhaps you are thinking that you are having a great day. Well, let’s hope that you still feel that way after this “pop quiz” on measurement uncertainty terminology and symbols. Dr. Gooddata wants to see how much you’ve learned so far from this series. Hopefully, this quiz will be fun and educational rather than a downer for you. The answers to the questions appear later in this article, but no cheating.

1. In the equation X = (measured) - ( true). X is:
    a. the unknown quantity
    b. the uncertainty
    c. the error
    d. the horizontal axis
   Hint: There’s no uncertainty here.
2. The limit to which an error can go with some confidence is:
    a. unbounded
    b. the uncertainty
    c. the degrees of freedom
    d. inconsequential
   Hint: Forget about freedom of choice in this case.
3. A systematic uncertainty is one that:
    a. doesn’t change for an experiment or test
    b. arises from a random error source
    c. varies from one test to another
    d. relates only to hardware not procedures
   Hint: Pick the best answer to avoid random variability.
4. The degrees of freedom frequently associated with systematic uncertainties are:
    a. uncertain
    b. poorly defined
    c. infinity
    d. irrelevant
   Hint: It’s neither uncertain nor poor.
5. You need to calculate degrees of freedom for:
    a. random uncertainties taken alone
    b. the root-sum-square of systematic uncertainties when infinity cannot be assumed
    c. the result uncertainty when infinity cannot be assumed
    d. all the above
   Hint: Think inclusively.
6. The proper descriptor for the ith random uncertainty is:
    a. 
    b. 
    c. neither
    d. either
   Hint: Think average.
7. In ISO notation, Type A uncertainties:
    a. have no data to calculate standard deviation
    b. have data to calculate standard deviation
    c. don’t involve the standard deviation
    d. are higher than Type B uncertainties
   Hint: The data are the thing.
8. In ISO notation, Type B uncertainties:
    a. have no data to calculate standard deviation
    b. have data to calculate standard deviation
    c. don’t involve the standard deviation
    d. are higher than Type A uncertainties
   Hint: The data aren’t the thing.
9. When evaluating the combined effects of errors, you should:
    a. root-sum-square their estimates
    b. algebraically add their estimates
    c. use only the larger of the errors
    d. use only the smaller of the errors
   Hint: Sum’s such as they are.
10. When evaluating the combined effects of uncertainties, you should:
     a. root-sum-square their estimates
     b. algebraically add their estimates
     c. always give more weight to the random uncertainty
     d. always give more weight to the systematic uncertainty
    Hint: What does RSS stand for?
11. A “measurement uncertainty” estimate is:
     a. the error of an experiment
     b. an estimate of an experiment’s or test’s error
     c. a reason for legal action in border disputes
     d. an estimate of an experiment’s or test’s error limit with some confidence
    Hint: Long answers are only sometimes tricks.
12. When a temperature measurement is reported as 75°F  5°F, the 5°F is: 
     a. the experimental error
     b. an estimate of the experimental error
     c. twice the measurement uncertainty
     d. none of these
    Hint: Have no degree of uncertainty about this.
13. Random uncertainties are reported as:
     a. two standard deviations
     b. the random error
     c. one standard deviation
     d. one standard deviation of the average
    Hint: Remember that averages count.
14. Systematic uncertainties are reported as:
     a. two standard deviations
     b. the random error
     c. one standard deviation
     d. one standard deviation of the average
    Hint: Consider the number you are dealing with.
15. For ISO classifications of uncertainties, both Type A and Type B are:
     a. two standard deviations
     b. the random error
     c. one standard deviation
     d. one standard deviation of the average
    Hint: Averages are all that count here.
    The answers are (no cheating now, take the test then look at these answers): 1. c; 2. b; 3. a; 4. c; 5. d; 6. a; 7. b; 8. a; 9. b; 10. a; 11. d; 12. d; 13. d; 14. d; and 15. d.

How did you do?

Dr. Gooddata hopes that you aced this quiz (without checking out the answers first, of course). However, just in case you don’t agree with the answers, let’s go over the tough questions.