a. Incorrect – see response option e for how this should be worded. The specific interval from this study is not part of the long-run behavior of the confidence interval.
b. Correct – this could be a truly null finding or an example of Type II error
c. Incorrect – the confidence interval includes the null; we are not able to reject the null hypothesis
d. Incorrect – the confidence interval enables us to assess both precision and significance. Because it crosses the null, the results are not statistically significant.
e. Correct
f. Incorrect – statistical significance is not an assessment of bias. Understanding bias requires knowing the study design and procedures.
The null hypothesis would be: In the target population, there is no difference in the number of side effects associated with Drug A or Drug B.
Question 3
The mean birth weight in the control group was 3,450 grams, and in the treatment group it was 3,410 grams. The p value was 0.12.
The null hypothesis for this comparison is that mean birth weight is the same in both treatment groups.
Because the p-value is greater than our pre-specified alpha=0.05,
we can conclude that the birth weight among pregnancies in each group does not statistically differ.
A p-value of 0.12 is the probability that, assuming the null hypothesis is true in the target population,
we would observe a difference in birth weight as large as or larger than 40 grams in repeated samples from that same population.
Question 4
Assuming that misoprostol is not associated with reduction of postpartum hemorrhage (the null hypothesis),
the probability of observing a reduction in hemorrhage of this magnitude or more extreme due to chance (random sampling variability) alone is less than 0.01%.
Therefore, we reject the null hypothesis that there is no association between postpartum hemorrhage and misoprostol use at an alpha of 0.05.
Question 5
There is a 30% probability of observing the test statistic associated with an odds ratio of 3.6 or a more extreme association by chance alone if pesticide poisoning is not associated with suicidal thoughts in the source population, assuming no bias and a correct statistical model.
Question 6
True
False, in this case the lower one sided p value refers to the probability of observing relative risks less than or equal to 4.7
True
Question 7
Yes, it is essentially correct.
Question 8
True
False
True
True
False
Question 9
The differences in richness and total stem densities between the two areas were so small that they could easily occur by chance if population means were identical.
Question 10
The main assumption is that the null hypothesis is true.
Question 11
Its chief limitation is the use of a purely arbitrary cutoff for deciding whether or not to reject the null hypothesis.
Question 12
Type I error is incorrectly rejecting the null hypothesis when the null is true. Type II error is failing to reject the null hypothesis when the alternative is true.
Question 13
- Alpha: Probability (i.e. over many repeated samples) of making a type I error (alternately stated, the probability of rejecting the null hypothesis when it is true)
- Beta: Probability of making a type II error (alternately stated, the probability of not rejecting the null given that that the alternative is true).
- Power: 1- beta; long-term probability of rejecting a false null hypothesis (alternately stated, the probability of correctly rejecting the null hypothesis when the alternative hypothesis is true)
Question 14
a.
Study population: The 75 students who satisfied the inclusion criteria and actually participated in the study.
Actual population: The 185 students who responded to the flyers and satisfied the inclusion criteria. (This includes everyone who was eligible and willing to participate in the study if chosen.)
Target population: Students who live in the selected undergraduate dorm. This definition of the study’s target population could be different – remember that the target population may depend on the investigator’s aims!
b.
Possibilities: All Berkeley undergrads, all 18-22-year-olds in California, all 18-22-year-olds in the U.S. This would really depend on the investigator’s goals and the generalizability of the study population.
c.
The internal validity of her study. The study population was not representative of the target population.
d.
Random error. Random error can be reduced in the design phase (by increasing sample size – to be discussed in the final third of the course) and can only be estimated in terms of magnitude in the analysis phase
Question 15
Chance is an uncontrollable force that seems to have no assignable or predictable cause.
Precision is the lack of random error. It is defined as either the state or quality of being exact or the ability of a measurement to be consistently reproduced.
Statistical inference is a method for generalizing results from a sample to a parent population.
Question 16
Systematic error occurs if there is a difference between the bulls-eye of the target you think you are shooting at and the bulls-eye that you are actually shooting at. Random error occurs if your shot at the bulls-eye you are actually aiming at does not hit the bulls-eye.
Consideration of validity should take precedence over consideration of precision because it is more important to be estimating the parameter you want to estimate than to get a tight (i.e., precise) confidence interval around a parameter that you don’t want to estimate.
An example in which the study population is not a subset of the source population:
A sample from a study population of persons who attend a clinic for sexually transmitted diseases. These people may or may not have an STD and may or may not be exposing themselves to STD's. For example, some of these subjects may have partners who are not infected, and thus may not be at risk themselves. If they are not at risk, they are not part of the source population, but we may not know that.
An example in which the study population is a subset of the source population:
In a typical cohort study, even though every member of the initial study population is also in the source population the initial sample may change in the course of the study. The initial sample may suffer from exclusions, withdrawals, non-response, or loss-to-follow-up. The final study population is then only those individuals who are willing and able to stay in such a study - a population that may not represent either the initial study population or the source population as well as we might wish.
Yes, if the source population differs from the study population, it is still possible that the study sample can provide an estimate of effect close to the target parameter in the source population. The reason: random error may result in such an estimate.
You cannot assess external validity based on the design/results of a single study because external validity is about applying our conclusions to an external population beyond the study's restricted interest. Such inferences require judgments about other findings and their connection to the study's findings, conceptualization of the disease process and related biological processes, and comparative features of the source population and the external population.
Question 17
The normal distribution is used for continuous variables, and the binomial and Poisson distributions are used for discrete variables with two mutually exclusive outcomes. In addition, the Poisson distribution is usually reserved for rare events.
Question 18
a. Lengths of newly hatched pythons
Question 19
(continuous)
(binary/dichotomous)
(continuous)
(binary/dichotomous)
(binary/dichotomous)
(continuous)
(binary/dichotomous)
Question 20
(normal)
(binomial)
(poisson)
(normal)
(normal)
(binomial)
(binomial)
(normal)
(poisson)
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