Stat 10, UCLA
Chapter 2 Solutions

  1. The statement is false - the data do not show that if you have to fly, it is safer to do so on a commuter airline. We cannot compare the numbers given - we need to compare rates. To decide what the data DO show, we need to know how many people flew on commuter airlines versus scheduled carriers, and then we can calculate the rates and compare.

    1. False
    2. False - in both cases look at the theft rates.

    1. They studied the groups separately to eliminate the effects of the confounding factors of age and gender. Age and sex are possible confounders; these should be controlled for.
    2. That is not an appropriate conclusion because there are confounding factors. For example, those who recently stopped smoking may have done so on doctor's orders, because they had severe health problems. This is an observational study, so causative statements cannot be made. Many people quit smoking because they are sick. These people should not be compared to a group who are still healthy enough to smoke.

  2. Zinc sulfate should not be given to treat this disease because the double-blind experiment shows no effect. It seems likely that the apparent effect for the single-blind study is caused by either physician bias or the possibility that the physicians broke the blind by communicating (perhaps unintentionally) the patients' treatment status with them. The results from the double-blind study are more reliable as they are without the possible doctor bias; doctor bias may be present in the single blind study.
  3. The subjects the question refers to who do not improve in the first half of the trial likely assume they are receiving the placebo. Then, when they switch pills halfway through the trial, they probably think that they are now receiving the treatment; simply because they were receiving a placebo for the first half of the trial. The improvement in these subjects is likely due to a placebo effect.
    1. This is an observational study - the patients chose to be on oral contraceptives.
    2. Age, education, and marital status are variables that are known to have associations with cervical cancer and pill use. They adjusted for these variables to try to eliminate problems due to these confounding factors.
    3. They are likely to be more sexually active than non-users. This is related to marital status, but marital status doesn't tell the whole story.
    4. The conclusions are not justified by the study. There are several possible confounding factors that were not adjusted for. For example, the number of sexual partners is likely to be higher of pill-users than non-pill users, and it could be that cervical cancer is a sexually transmitted disease.

    1. The experiments did not confirm the results of the observational studies - the observational studies suggested that fresh fruits and vegetables might lower rates of colon and lung cancer, whereas the randomized, controlled experiments found no relationship and the opposite relationship for colon cancer and lung cancer respectively.
    2. This is true - for example, the people who eat lots of fruit and vegetables probably exercise more, they may be wealthier, they may be younger, all of which may be associated with lower colon and lung cancer rates.
    3. This is false - the experiments were randomized - there should be no confounding factors.
    1. This was an observational study - mothers get to choose their behavior.
    2. Yes, there was an association - fatter children tended to have more ``controlling'' mothers.
    3. That would explain the association, but it is not the only possible explanation.
    4. A gene would not explain the association unless the gene were also linked to ``controlling'' behavior of the mothers, which is conceivable but seems unlikely.
    5. Perhaps when mothers see their children getting fat, they become more ``controlling''. This is a causal relationship but in the opposite sense of the one on part (c). Or, there could be other confounding factors. For example, perhaps ``type A'' mothers have some genetic factor that leads to their children being fat and also causes the mothers to be ``controlling.
    6. No, the data do not support the advice, because there is insufficient evidence of a causal relationship.
    1. Treatment: those prisoners who complete boot camp. Control: everyone else, including those who start but do not complete boot camp, and those who don't even try it.
    2. Observational study.
    3. False. The data found an association. But there are certainly confounding factors, not the least of which is the psychological makeup of those prisoners who complete boot camp.

  4. False. Democrats could be concentrated in wards with low turnout, as in the following example (Simpson's paradox in all its glory).

      Democrats Republicans
      Registered Turnout Registered Turnout
    Ward A 1000 100 100 5
    Ward B 100 60 1000 500
    Total 1100 160 1100 505
        (14.5%)   (45.9%)