Math 143 C/E, Spring 2001
IPS Reading Discussion Questions
Chapter 3, Section 2 (pp. 237-250)



  1. What is bias? Give an example of how an experiment can be biased.

    Bias is a predisposition to one outcome or option over others. In terms of a statistical study, one does not want a biased design since a predisposition for one outcome over others stands in the way of getting the truth about the question the study was meant to answer.

    Suppose we wish to know whether one arrangement of keys, say, the standard U. S. keyboard layout (aka QWERTY), on a computer keyboard allows for faster typing than another arrangement, say, the Dvorak layout. We might give two groups of people a certain amount of time to practice with the layout assigned to them and then do a speed test. Nevertheless, if all of the people in both groups are experienced typists using the QWERTY layout, there is a bias in favor of that layout over the other.

  2. What is a placebo? How does the use of a placebo in a blind experiment provide a control against bias? Describe how an experiment that is double blind provides further control against bias.

    A placebo is a treatment (like a salt tablet) that is known to have no physiological effect. When people are receiving treatment that they think may improve some medical condition, it has been observed that the psychological effects alone can bring improved health. Thus an experiment that is meant to determine whether a certain drug combats a certain illness is likely to be biased towards the affirmative conclusion if the control group knows it is not receiving any treatment. Giving the control group a placebo (so that the subjects in that group have the same psychological benefit as those in the treatment group) eliminates the bias and makes it possible to conclude that any change in outcome between groups is due to some other variable. Such a study is called a blind study. There is still the possibility that a researcher who knows which patients are in each of the two (control and treatment) groups may treat members of one group differently than those of the other, and there are situations in which this may also introduce a bias. Such a risk is removed when even the researcher doesn't know who is in what group (i.e., a double blind study).

  3. What is the big advantage of a controlled experiment over an observational study? Give an example of a study for which, despite the advantage you just mentioned, an experiment is inappropriate (perhaps because no experiment would be practical, or maybe an experiment in this case would be unethical, etc.).

    Only through an experiment can one establish a cause-and-effect relationship between the treatment and the observed response. A particularly interesting example is the effect of cigarette smoking on lung cancer. To establish causation, one would have to select people (probably at birth), have certain ones smoke for a number of years and forbid the others from smoking, and then monitor each subject for lung cancer. Such an experiment would obviously be unethical. All of the evidence we have about the relationship between the two comes from (numerous) observational studies, and, as a result, the U. S. Surgeon General's Office has taken years to progress to the point of saying, ``smoking cigarettes causes cancer".

  4. Figure 3.3 (p. 245) diagrams the design of experiment described in Example 3.8. How many factors distinguish the groups, and what are they? Describe the treatment (that is, give the level of each factor) for each group.

    There is just one factor (categorical variable) distinguishing the groups, that being the type of assistance the utility company provides in monitoring energy usage. There are three values (levels) of monitoring assistance: installing a meter in the house that shows the members of the household their energy use, providing information and charts for people to monitor their own use, and no assistance at all.

  5. Why is it so important to randomly assign experimental units to treatment groups? Would the goals of randomization be realized if replication were not taken seriously in the design of the study (that is, say, if all treatment groups had very few subjetcs)?

    Random assignment is the best way to control the effect that lurking variables (unforseen factors) might have on the outcome of the experiment, as it more often than not divides up experimental units evenly who have similar values for those lurking variables. The ``more often than not" statement is put on more secure footing when there are many units/subjects in the study.

  6. What is block design? If you were studying the effects of a low-fat diet on the growth of 9-year-old children in the U. S. , what are some of the blocks you would pay special attention to as you divided up subjects into treatment groups? If randomization is supposed to take care of making the two groups (the low-fat diet children and the ``normal" diet children) roughly equal, why might we want to bother with blocking?

    When certain groups of experimental units are noted to be similar in a fashion that is thought may have an effect on the outcome, one may employ block design by dividing people from these groups (blocks) up evenly among treatments. In the particular case of the nutrition study proposed above, it seems particularly reasonable to consider gender blocks. (There may be other important ones as well.)

    It is true that we use randomization so that all variables (not just gender) have values (such as "Male", "Female") that are evenly represented in the various groups. While there is no better way of achieving such parity, randomness is not a sure way to get it. There will almost certainly be occasions when values of certain variables appear more often in one group than the other. When we foresee that this variable may have nontrivial effect on the outcome, it seems reasonable to take special care to distribute things evenly.

  7. An experimental design that uses ``either two matched individuals or the same individual to receive each of two treatments" (Utts, Seeing through Statistics, 2nd Ed.) is called a matched-pair design. In which of these two categories does the matched-pairs example (Example 3.10) on p. 247 belong?

    It is an example of the latter. The various regions of the field in which a pole with sticky boards is placed are all give two treatments, a yellow board and a green board.