Deck 1: An Overview of Statistical Concepts

Question 1

You suspect that the salary of study participants might be skewed. A statistician told you that the skewed data should not be described by a mean. Why?

Answer 1

In a skewed data set, the mean is likely to be pulled towards the tail and does not provide a robust measure of the center. A median would be more appropriate.

Question 2

In preparing a grant, you meet with a biostatistician to discuss sample sizes. The biostatistician tells you that if you want more power, you will have to increase your sample size. Explain why this is the case. Provide additional alternatives for increasing the power of the study without changing the sample size.

Answer 2

As the sample size gets larger, the alternative sampling distribution gets skinnier. As a result, the null and alternative distributions become more separated. When there is a discernable difference between the two distributions, it is easier to reject the null hypothesis correctly, and thus increases the power of the study. Alternatively, as the a level increases, the statistical power also increases.

Question 3

Which of the following statements is considered a null hypothesis?

A) The children who watch more than 2 hours of TV have the same weight gain as children who watch TV less than 2 hours.
B) Smoking is related to poorer health status.
C) There is a greater amount of fatigue in health-care professionals in urban areas.
D) Increases in activity are associated with decreases in cognition.

Answer 3

The children who watch more than 2 hours of TV have the same weight gain as children who watch TV less than 2 hours.

Question 4

Power, type 1 and type 2 errors are all related, which of the following statements is NOT true?

A) Probability of type 2 error = 1-power.
B) If the probability of type 1 error increases, the power also increases.
C) Probability of type 1 error is inversely related to the probability of type 2 error.
D) Probability of type 1 error increases with the probability of type 2 error.

Question 5

Suppose you are told that your BMI is 32, the 70th percentile for your age and sex. Interpret this percentile.

Question 6

A 2-year study was conducted to investigate bicycle safety at a city's 10 most congested intersections. The primary variable of interest was the number of accidents that involved a bicycle. Describe the number of accidents involving a bicycle as a continuous and ordinal variable.

Question 7

Central limit theorem states that the distribution of _________ will be normally distributed with large enough samples regardless of the shape of the population distribution.

A) a sample size
B) sample means
C) a continuous random variable
D) a discrete random variable

Question 8

Which of the following is most likely a type 2 error?

A) Correctly concluding that an effect exists.
B) Correctly concluding that no effect exists.
C) Falsely concluding that an effect exists.
D) Falsely concluding that no effect exists.

Question 9

Briefly describe the difference between a bar graph and a histogram. Consider your own area of interest. Provide an example where a bar graph would be most appropriate. Provide an example where a histogram would be most appropriate.

Question 10

A study was conducted to investigate whether the use of vitamins during prostate cancer treatment would improve the prostate-specific antigen (PSA). PSA in study patients was measured before treatment and four months after treatment. Suppose the change in PSA is 3.0 and there is a p-value of 0.07. How would you interpret this result?

Question 11

Which of the following is NOT an advantage of a retrospective study?

A) Sample size required is relatively small compared to that of a prospective study.
B) Efficient when the outcome is rare.
C) Efficient when the outcome requires a long time to develop.
D) Investigators have control over the way the variables are collected.

Question 12

How does the shape of the sampling distribution of means with sample sizes of N=10 and N=100 differ? How are they the same?

Question 13

John waited 30 minutes to be treated in an emergency room. A 30-minute wait is in the 20th percentile of the wait time. Did he have a comparatively long- or short wait time? Interpret this percentile.

Question 14

Consider a study where the majority of the study subjects have high body mass index (BMI) and only a few have low BMI. When a histogram is constructed to describe the distribution of BMI, what shape of the distribution is most likely to be observed (right-skewed, left-skewed, or symmetric)?

Question 15

Twenty fibromyalgia patients are asked to register their pain on a visual analog scale (VAS), where 0 represents no pain and 5 represents the worst pain imaginable. The responses are {0, 0, 0, 1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5}.a.What are the frequency distribution and probability distribution of this sample? b.What are the mean, median, and mode for the VAS?

Question 16

In the following scenarios, state which type of error (type 1 or type 2) you would want to change in a hypothesis test to reduce errors.

A)You are investigating an effect of drug A indicated for patients who risk death if not treated. The drug will be used to replace a therapy that has serious side effects. The study is testing the hypotheses:
Null hypothesis: drug A is not effective.
Research hypothesis: drug A is effective.
B)Many studies are investigating different experimental strategies for increasing bone density in osteoporotic women. Suppose a new therapy has been discovered to increase bone density in mice. It is possible that this therapy could be effective in humans.
The study is testing the hypotheses:
Null hypothesis: drug A is not effective.
Research hypothesis: drug A is effective.

Question 17

A study was conducted to examine the gender difference in daily smoking prevalence.

A)State the null and research hypotheses for this test.
B)Suppose the p-value associated with the test is 0.04. What can you conclude?

Question 18

A group of investigators are interested in conducting a clinical trial to determine whether taking bio-identical treatments prevents postmenopausal osteoporosis in women. They obtained a list of physicians in the region and recruited their patients by mailing out response cards to all eligible women; 60% of the cards were returned and 75% of those respondents entered the study. They were equally divided into the treatment group and placebo group, and were followed for 5 years to determine if they develop osteoporosis. Identify the population, sample, sampling frame, and type of study.

Question 19

An outbreak of food poisoning occurred at a high school a few hours after 100 students ate lunch at the school's cafeteria. Most of them developed symptoms including nausea, vomiting, and diarrhea. An investigation was conducted to identify the contaminated food source. Interviews were conducted with students who ate at the cafeteria, and a food history was collected. Describe this study design (case-control, cohort, cross-sectional). Explain.

Question 20

Suppose an investigator is comparing different infertility treatments. She hypothesizes that treatment A is better than treatment B. Describe what type 1 and type 2 errors would mean in this situation.