Exercises - Measurements, Sampling, Studies, and Experiments

  1. Decide which of the 4 levels of measurement (nominal, ordinal, interval, or ratio) is most appropriate in each case:

    1. Water usage measurements (in gallons) from someone's home
    2. Types of books (mystery, non-fiction, fantasy, sci-fi, etc.)
    3. Movie ratings (1 to 5 stars)
    4. Temperatures in $C^{\circ}$ of water temperatures at various lakes in Georgia
    5. Social Media Companies (Facebook, Instagram, Snapchat, etc.)
    6. Garbage (in tons) that washes up on the West Coast beaches of the United States.
    7. Years in which the average temperature in July in Atlanta exceeded $90^{\circ}$
    8. Responses to the survey question "How easily can you breath when walking briskly? (1 - Very easily, 2 - Somewhat easily, 3 - With some difficulty, 4 - with great difficulty)" given to patients at a doctor's office.
    1. ratio
    2. nominal
    3. ordinal
    4. interval
    5. nominal
    6. ratio
    7. interval
    8. ordinal

  2. Identify the sample, population, and whether or not the sample is likely to be representative of the population, for each case below:

    1. A health magazine publishes a health survey and some of its readers complete the survey.

    2. A random selection of 753 Americans is surveyed by Gallup, finding that 91% do not support human cloning.

    3. Some people responded to the following request: "Dial 1-800-HUG-TREE to participate in a telephone poll on the damage industry is doing to the environment ($1.75 per minute. Average call: 2 minutes. You must be 18 years old.)"

    1. sample = the readers that complete the survey; population = health magazine subscribers; probably not representative as it is a voluntary response sample

    2. sample = the 753 Americans; population = Americans; probably representative

    3. sample = those that responded; the population is not clearly defined -- perhaps, it is the group of people that heard the request; definitely unlikely to be representative (cost will prohibit some from participating, age will prohibit others, there is strong bias in the question itself (e.g., "tree huggers", assumed damage to environment by industry). People with strong beliefs may respond, but few others.

  3. Explain any problems that exist in the situations described below.

    1. In a survey of attitudes regarding capital punishment, the following question is asked: "Agree or disagree: the taking of a human life can never be condoned."

    2. Employees must use their company id numbers to log into a website to take a survey. One of the questions on the survey asks "Have you ever used company resources for personal profit?"

    3. Mars Inc. (a candy manufacturer) conducts a study to determine if chocolate added to one's daily diet has health benefits.

    4. A phone poll is conducted to determine whether or not people find telemarketers a nuisance.

    5. Pollsters interview one member of each household in a neighborhood. One of their questions is "Do you frequent the local park at least once a month?".

    6. Twenty patients of a geriatric specialist are randomly selected to participate in a study of a new drug to decrease arthritic pain. Ten are given the new drug once a day, the other ten patients are not given anything and simply observed as a control group.

    7. Azalea bushes can be difficult to keep alive, as they require just the right amount of water (not too little, and not too much). An experiment seeks to determine the effect of a new blend of fertilizer on the flowering of Azalea bushes over the leading existing blend. In a large plot of land, twenty azalea bushes are planted at twenty randomly selected locations. Ten are fertilized with the new blend, while the remainder ten are fertilized with the leading existing blend. The number of flowers produced by each plant in one year is then counted. Of the ten locations with plants fertilized with the new blend, seven historically stay fairly wet due to the lay of the land. Of the ten locations with plants fertilized with the existing blend, only three locations stay fairly wet.

    1. Responses will likely be biased towards agreement due to the wording of the question.

    2. People may not tell the truth, if they are worried that the id numbers they have to provide to log into the survey could be used to link them to admitted actions of wrong-doing in the survey.

    3. The company funding the study has a strong interest in being able to say that chocolate has health benefits. This could be used to increase sales. There may be pressure on the researchers to conclude only positive results even if they are not really present.

    4. If one finds telemarketers a nuisance, one will probably be less likely to answer the phone to participate in the poll.

    5. There is a possibility that people who live in large households are under-represented in the sample. This is especially true since parks offer a source of entertainment that is relatively cheap -- which is a benefit for people that live in large households and wish to do things together.

    6. As currently designed, positive results may be from the effectiveness of the new drug, or they may be due to the placebo effect. There is no way to determine which is the root cause. To counteract this, the other 10 should be given a sugar pill and told it is the new drug.

    7. Dead bushes don't flower, so clearly getting the right amount of water is a significant factor in the flowering of the bushes. One should consider randomized block design, blocked by the type of fertilizer and water present at each site.

  4. What is the difference between an observational study and an experiment?

    In an experiment, one actively assigns subjects/units to different treatment groups. In a study, observations and measurements are made, but there is no attempt to modify or treat the subjects being studied.

  5. Identify the type of sampling used in each case:

    1. A statistics student collects measurements of index finger lengths from her family members for a class project

    2. CNN organizes an exit poll in which specific polling stations are randomly selected and all voters are surveyed as they leave the premises.

    3. A wine taste test involves 4 different wines randomly selected from each of 3 different wineries.

    4. A test to ensure the maximum capacity for a foot stool involves testing "to destruction" every 100th stool from the assembly line (i.e., weight is added to each stool until it collapses)

    5. 4 of the many health plans available to the citizens of Georgia are randomly selected and all of their members are surveyed about their satisfaction

    6. The "Math:rand" function on the TI-83 calculator generates random decimal values between 0 and 1. A group of 70 people are assigned numbers 00 to 69. A random value is generated on the TI-83 calculator using the aforementioned function. If the first two digits of the random number match someone's assigned number, then that person is selected to be part of a sample. For example, if the number $0.35876397688$ was generated, person $35$ would be selected to be in the sample. If the first two digits don't match any of the assigned numbers, or if they correspond to someone already selected, nothing happens. This process is repeated until 10 people have been selected to form the entire sample.

    1. Convenience Sample

    2. Cluster Sample

    3. Stratified

    4. Systematic

    5. Cluster

    6. Simple Random Sample

  6. Decide if each of the below is an observational study or experiment. In the case of an observational study, identify it as retrospective, prospective, or cross-sectional. In the case of an experiment, identify the treatment groups.

    1. Between 1932 and 1972, the U.S. Public Health Service in collaboration with Tuskegee University, a historically black college in Alabama enrolled 622 impoverished, African-American sharecroppers in a program where they would be given free medical care and meals for 6 months. It was determined by the investigators that 431 of these men had previously contracted syphilis, but the men were never told this, nor were they treated for this condition (even given that by 1947, penicillin was known as a successful treatment against the disease). The intent was to to understand the natural progression of the disease. Numerous men in the study died of syphilis, 40 wives contracted the disease, and 19 children were born with congenital syphilis. The highly unethical nature of this program finally came to light in 1972, leading not only to its immediate termination, but also to the creation of federal laws and regulations requiring Institutional Review Boards (IRB) for the protection of human subjects in research endeavors.

    2. When an outbreak of Giardia occurred in Milton, MA, the Milton Health Department requested assistance from the epidemiologists in the MA Department of Public Health. The request for assistance was made some time after the start of the outbreak, and the outbreak was winding down by the time the Department of Public Health began their investigation. The outbreak was clearly concentrated among members of the Wollaston Golf Club in Milton, MA, which had two swimming pools, one for adults and a wading pool for infants and small children. Given what they knew about the usual mechanisms by which Giardia is transmitted, the investigators thought that contamination of the kiddy pool by a child shedding Giardia into their stool was the most likely source. The study was conducted by asking a people that frequented the Wollaston Golf Club to complete a questionnaire in which one of the key questions was "Did you spend any time in the kiddy pool?". Information as to whether or not these people had suffered from Giardia during the outbreak was also collected.

    3. In 1939, Mary Tudor working under the supervision of Wendell Johnson at the University of Iowa took 22 orphaned children that sufferred from stuttering and gave them feedback on their speech. Half the children were given positive feedback, and the others were given negative feedback. The test was trying to determine the effects of positive and negative feedback on speech. Some of the children who were belittled for their mistakes when speaking suffered serious psychological damage and some had problems with speaking for the rest of their lives. Johnson's colleagues were horrified at his treatment of the children, calling it the "Monster Study". The University of Iowa publicly apologized for the study in 2001. However, Patricia Zebrowski, University of Iowa assistant professor of speech pathology and audiology notes that the data that resulted is the "largest collection of scientific information" on the phenomenon of stuttering and that Johnson's work was the first to discuss the importance of the stutterer's thoughts, attitudes, beliefs, and feelings and continues to influence views on stuttering greatly.

    1. Observational Study (Prospective)

    2. Observational Study (Retrospective)

    3. Experiment; treatment groups consisted of the 11 children given positive feedback and the 11 children given negative feedback