Chapter 1 Problem Set: Statistics
The 4 scales of measurement:
NOMINAL: Used to categorize data into mutually exclusive categories or groups. ORDINAL: Used to measure variables in a natural order, such as rating or ranking. They provide meaningful insights into attitudes, preferences, and behaviors by understanding the order of responses. INTERVAL: Used to measure variables with equal intervals between values. This type of measurement is often used for temperature and time, allowing for precise comparisons and calculations. RATIO: Allows for comparisons and computations such as ratios, percentages, and averages. Great for research in fields like science, engineering, and finance, where you need to use ratios, percentages, and averages to understand the data.
A set of three scores consists of the values 3, 7, and 2.
Σ(2X)² = 248 Explanation: To compute the values of these equations, you need to compute values in the following order of precedence: 1.Perform any operation within parentheses. 2.Perform any exponentiation (such as squaring). 3.Perform any multiplication or division. 4.Perform any summations (Σ). 5. Complete any additional addition or subtraction in left to right order. X 2X (2X)² 32(3) = 6(2(3))² = 3672(7) = 14(2(7))² = 19622(2) = 4(2(2))² = 16 For Σ(2X)², since multiplication is in the parentheses, you first multiply each number by two and then square. Finally, you sum, so Σ(2X)² = (2 x 3)² + (2 x 7)² + (2 x 2)² = 248.
A set of three scores consists of the values 3, 7, and 2.
Σ2X - 2 = [we just keep dancin' like we're] 22 Explanation: To compute the values of these equations, you need to compute values in the following order of precedence: 1.Perform any operation within parentheses. 2.Perform any exponentiation (such as squaring). 3.Perform any multiplication or division. 4.Perform any summations (Σ). 5.Complete any additional addition or subtraction in left to right order. X 2X 32(3) = 672(7) = 1422(2) = 4 For Σ2X - 2, there are no parentheses and no exponents, so the first operation you consider is the multiplication of each value by two. Next, you will sum these values, so Σ2X = 2(3) + 2(7) + 2(2) = 24. Finally, subtract two to get Σ2X - 2 = 22.
When measuring weight on a scale that is accurate to the nearest 0.1 pound, what are the real limits for the weight of 131 pounds?
130.95-131.05 Explanation: Remember that the real limits are always halfway between adjacent categories. In the first case, the precision of the scale is 0.5 pounds, so the scores will be 0.5 pounds apart, therefore the real limits should be half of 0.5 (0.25) above and below the score (225). Thus, the real limits for 225 are 224.75-225.25. In the second case, the precision of the scale is 0.1 pounds, so the scores will be 0.1 pounds apart, therefore the real limits should be half of 0.1 (0.05) above and below the score (131). Thus, the real limits for 131 are 130.95-131.05.
When measuring weight on a scale that is accurate to the nearest 0.5 pound, what are the real limits for the weight of 225 pounds?
224.75-225.25 Explanation: Remember that the real limits are always halfway between adjacent categories. In the first case, the precision of the scale is 0.5 pounds, so the scores will be 0.5 pounds apart, therefore the real limits should be half of 0.5 (0.25) above and below the score (225). Thus, the real limits for 225 are 224.75-225.25. In the second case, the precision of the scale is 0.1 pounds, so the scores will be 0.1 pounds apart, therefore the real limits should be half of 0.1 (0.05) above and below the score (131). Thus, the real limits for 131 are 130.95-131.05.
What is an example of a statistic in the study?
34%, the average percentage of conceptually similar words mistakenly thought to be on the original list by the 75 students
A psychology professor wants to know whether age is related to memory quality in current first-year students at his small college. Participants in the study (first-year students at his college) complete an online memory task. The students are first shown a list of 60 words. Next they are shown a list that includes five new words that are conceptually similar to words on the original list. Then they are asked to identify the words on the second list that appeared on the original list. He uses the percentage of new but conceptually similar words that were mistakenly thought to be on the original list as his measure of memory quality. He also asks the students to report several characteristics such as their age, gender, and verbal SAT score. Each of the 750 first-year students (338 males and 412 females) at his school volunteered to participate. The professor chose 75 students at random to complete the memory task and answer the questions. The average percentage of new but conceptually similar words that were mistakenly thought to be on the original list was 34%. The professor infers that if all 750 first-year students had completed the study, the results would show that an average of 34% (plus or minus sampling error) of new words were mistakenly identified as original words because they were conceptually similar.
750 students, The students' percentage of new but conceptually similar words that were mistakenly thought to be on the original list, and the 75 students. Explanation: A variable is a characteristic or condition that changes or has different values for different individuals. Some of the variables for this study include the students' ages and the students' percentage of new but conceptually similar words that were mistakenly thought to be on the original list.
Fill in the missing values in the X - 1 column and the (X - 1)² column of the following table, and then calculate Σ(X - 1)².
A: 1 2 0 0 B: 1 3 0 0 C: 2 0 1 1 D: 1 5 0 0 E: 3 4 2 4 Σ(X - 1)² = 5 Explanation: For father A, X - 1 = 0. So, (X - 1)² = 0² = 0. For father D, X = 1. So, X - 1 = 1 - 1 = 0 and (X - 1)² = 0² = 0. Σ(X - 1)² is the sum of all of the values in the column (X - 1)², including the numbers 0 and 0 that were just added. Thus, Σ(X - 1)² = 0 + 0 + 1 + 0 + 4 = 5.
An anthropologist is looking at the role of fathers in child rearing in the rural Southeast. She asks the fathers how many times a week they feed and diaper their newborn infants. On her first day of work, the anthropologist interviews five fathers and gets the results shown in the first three columns of the following table. In this table, fill in the missing values in the XY column, and then calculate ΣXY.
A: 1 2 2 B: 1 3 3 C: 2 0 0 D: 1 5 5 E :3 4 12 ΣXY = [i dont know about you, but i'm feelin'] 22 Explanation: For father B, X = 1 and Y = 3. So, XY = 1 x 3 = 3. For father E, X = 3 and Y = 4. So, XY = 3 x 4 = 12. ΣXY is the sum of all of the values in the column XY, including the numbers 3 and 12 that were just added. Thus, ΣXY = 2 + 3 + 0 + 5 + 12 = 22.
Fill in the missing values in the Y² column of the following table, and then calculate ΣY².
A: 1 2 4 B: 1 3 9 C: 2 0 0 D: 1 5 25 E: 3 4 16 ΣY² =54 Explanation: For father C, Y = 0. So, Y² = 0² = 0. For father E, Y = 4. So, Y² = 4² = 16. ΣY² is the sum of all of the values in the column Y², including the numbers 0 and 16 that were just added. Thus, ΣY² = 4 + 9 + 0 + 25 + 16 = 54.
Fill in the missing values in the Y - 1 column and the (Y - 1)² column of the following table, and then calculate Σ(Y - 1)².
A: 3 3 2 4 B: 3 1 0 0 C: 3 2 1 1 D: 2 2 1 1 E: 4 3 2 4 Σ(Y - 1)² =10 Explanation: For parent A, Y - 1 = 2. So, (Y - 1)² = 2² = 4. For parent D, Y = 2. So, Y - 1 = 2 - 1 = 1 and (Y - 1)² = 1² = 1. Σ(Y - 1)² is the sum of all of the values in the column (Y - 1)², including the numbers 4 and 1 that were just added. Thus, Σ(Y - 1)² = 4 + 0 + 1 + 1 + 4 = 10.
Fill in the missing values in the X² column of the following table, and then calculate ΣX².
A: 3 3 9 B: 3 1 9 C: 3 2 9 D: 2 2 4 E: 4 3 16 ΣX² =47 Explanation: For parent C, X = 3. So, X² = 3² = 9. For parent E, X = 4. So, X² = 4² = 16. ΣX² is the sum of all of the values in the column X², including the numbers 9 and 16 that were just added. Thus, ΣX² = 9 + 9 + 9 + 4 + 16 = 47.
Are elderly women living at home healthier than those living in a nursing home? This question was studied by a group of psychologists at the University of Delhi. [Tyagil, R., Kapoor, S., & Kapoor, A. K. (2008). Environmental influence and health status of the elderly. The Open Anthropology Journal, 1, 14-18.] For a sample of elderly women, data were collected on the following variables: •Heart Rate •Age Group (1 = 60 to 70 years; 2 = 71 to 80 years; 3 = 81+ years) •Body Weight •Environment (0 = nursing home; 1 = living with family) •Height Recognizing the measurement scale of the data collected on each variable is important because the type of data dictates the appropriate data summary methods and statistical procedures. Which variable(s) in the data set are measured using a ordinal scale?
Age Group Explanation: Ordinal data exhibits the same properties as nominal data, but the data also provide a ranking of the elements in the data set. For example, postoperative hospital patients are often asked to rate their level of pain on a scale from 0 to 10, with 0 indicating no pain and 10 indicating excruciating, unbearable pain. Like nominal data, ordinal data may be numeric or nonnumeric. Age Group in this data set is ranked and measured on an ordinal scale. This measure is an ordinal one because age group has three different categories based on age. Because the age categories provide a ranking from younger to older, the scale is ordinal.
Michelle Kweder, a student at the University of Massachusetts Boston, summed up her feelings about taking statistics with the following status update: "I've decided that learning statistics is like bungee jumping with dental floss." The truth is that, while some statistical procedures may be completely new to you, you already have a good intuitive sense of how to use statistics. In fact, you probably already know how to use statistical information to inform your decisions. By way of example, do you think bungee jumping is a safe sport? (Note: This is an exploratory exercise. There are no right or wrong answers for this question. Choose your response based on your general impression or your knowledge of the sport.)
Bungee jumping is NOT safe. Explanation: Each person has a different propensity for risk. Some people make decisions based on a gut feeling, while others want to get their hands on concrete information that they can evaluate.
In each of the following situations, data are obtained by conducting a research study. Classify each research study as Experimental or Correlational.
CORRECTIONAL: A student is interested in how well majors in the social sciences do monetarily in the real world. She collects data from a sample of college graduates who majored in the social sciences, recording their specific majors, their current jobs, and their salaries for the previous year. CORRECTIONAL: A psychologist is interested in gender and cognition. She collects data on a large sample of siblings, recording their gender, birth order, and IQ. EXPERIMENTAL: An economist is interested in the demand behavior of rats. Rats in a rat lab have two levers in their cages. Pressing one lever dispenses Tom Collins mix (without alcohol); pressing the other lever dispenses the same amount of a sodium saccharin solution. Psychologists obtain data on the demand behavior by altering the total number of presses the rats are allotted and the number of presses required to dispense each of the fluids. Explanation: In an experimental study, researchers manipulate and control an independent variable to study its effect on a dependent variable. Researchers can examine the influence of the independent variable on the dependent variable without worrying about whether other extraneous variables also influenced the dependent variable. They do this typically by randomly assigning who gets which value of the independent variable (such as who gets which treatment). The rat study is an example of an experimental study. The independent variables are the total presses and the number of presses for each of the fluids, and the dependent variables are the quantities of each fluid consumed. In a correlational study, researchers are typically trying to figure out whether and how two variables are related by measuring and observing their values. Researchers in correlational studies do not manipulate the values of any variables. Instead, they observe the values of the variables and use statistical methods to determine if certain values of one variable are more likely to be associated with certain values of another variable. Since the researchers do not control, for example, who gets the treatment and who does not, a cause-and-effect relationship cannot be inferred from a correlational study. The salary and IQ studies are examples of correlational studies.
Rogers, Farlow, and colleagues (1998) conducted an experiment to investigate whether donepezil improved cognitive function in patients with mild to moderate Alzheimer's disease (AD). A total of 1,775 patients were randomly assigned to treatment with either donepezil or a placebo (a look-alike pill with no pharmacological effect). Cognitive function, as measured by the Alzheimer's Disease Assessment Scale (ADAS-cog), was significantly improved in patients taking donepezil compared with the placebo group at weeks 12, 18, and 24. [Source: Rogers, S. L., Farlow, M. R., Doody, R. S., et al. (1998). A 24-week, double-blind, placebo controlled trial of donepezil in patients with Alzheimer's disease. Neurology, 50, 136-145.]
Cognitive function is a construct that is being tested in this experiment, and the experimenters have operationally defined it as the score on ADAS-cog scale . Explanation: The construct is the attribute the researchers care about. Typically constructs—such as intelligence or health—cannot be directly measured. Instead, the researcher identifies a measurement procedure, the operational definition, that is intended to represent the construct of interest. For example, researchers might use an IQ test to measure the construct intelligence, while they might use blood pressure, cholesterol level, number of visits to the doctor or hospital, or a self-report of health status—or even some combination of these measures—to measure the construct health. Cognitive function is a construct that is being tested in this experiment, and the experimenters have operationally defined it as the score on ADAS-cog scale.
Suppose a researcher compiled a data set consisting of the following variables for a sample of 100 homeowners. For each variable, select whether it is discrete or continuous.
DISCRETE: The number of college football games ever attended DISCRETE: The number of sons or daughters DICRETE: Shirt size CONTINUOUS: Height in inches CONTINUOUS:Miles driven in the last year Explanation: A continuous variable is one that theoretically can have an infinite number of values between adjacent units on the scale. A discrete variable is one in which there are no possible values between adjacent units on the scale. The number of college football games ever attended, the number of sons or daughters, and the number of siblings are counts (0, 1, 2, ...). They are discrete variables, because there is a finite number of possible values between any two counts. For example, between 1 and 3, there is only one possible value: 2. Shirt size is not a count, but there is also a finite number of possible values between any two values, so it is also a discrete variable. Measurements such as weight, length, temperature, and elapsed time are continuous variables, because they are not limited to a finite set of values. Picture a number line; a measurement can lie anywhere along a segment or segments of the number line. Height in inches and miles driven in the last year are examples of continuous variables.
Are elderly women living at home healthier than those living in a nursing home? This question was studied by a group of psychologists at the University of Delhi. [Tyagil, R., Kapoor, S., & Kapoor, A. K. (2008). Environmental influence and health status of the elderly. The Open Anthropology Journal, 1, 14-18.] For a sample of elderly women, data were collected on the following variables: •Heart Rate •Age Group (1 = 60 to 70 years; 2 = 71 to 80 years; 3 = 81+ years) •Body Weight •Environment (0 = nursing home; 1 = living with family) •Height Recognizing the measurement scale of the data collected on each variable is important because the type of data dictates the appropriate data summary methods and statistical procedures. Which variable(s) in the data set are measured using a nominal scale?
Environment and Age Group Explanation: A nominal scale consists of a set of categories that have different names. Measurements on a nominal scale label and categorize observations, but they do not make any quantitative distinctions between observations. In this data set, Environment is measured on a nominal scale. This measure is a nominal one because there are two different environments which categorize the observations without making any qualitative distinctions (a nursing home is not more or less than living with family).
At the end of the study, the sociologist had a sample of 500 expectant parents. He estimates that there are 6 million expectant parents in the United States.
Given this information, N = 6,000,000 Explanation: The letter N is used to specify how many scores are in a set. An uppercase letter N identifies the number of scores in a population and a lowercase letter n identifies the number of scores in a sample. The sample (n) is the 500 expectant parents that the sociologist interviewed. The population (N) is the 6 million expectant parents in the United States.
At the end of the study, the anthropologist had a sample of 250 fathers. She estimates that there are probably 300,000 fathers of young children in the rural Southeast.
Given this information, n = 250 Explanation: The letter N is used to specify how many scores are in a set. An uppercase letter N identifies the number of scores in a population and a lowercase letter n identifies the number of scores in a sample. The sample (n) is the 250 fathers that the anthropologist interviewed. The population (N) is the 300,000 fathers of young children in the rural Southeast.
What is an example of the professor using descriptive statistics?
He characterizes the first-year students at the college as consisting of 338 males and 412 females.
What is an example of the professor using inferential statistics?
He infers that if all 750 students had done the experiment, the results would show that an average of 34% (plus or minus sampling error) of new words were mistakenly identified as original words because they were conceptually similar. Explanation: In descriptive statistics, statistical procedures are used to summarize, organize, and simplify data. In inferential statistics, sample data are used to make inferences about populations. In this study, the professor uses descriptive statistics when he characterizes the first-year students at the college as consisting of 338 males and 412 females, as well as when he reports that the average percentage of new but conceptually similar words that were mistakenly thought to be on the original list was 34%. He uses inferential statistics when he infers that if all 750 first-year students at his college had done the experiment, the results would show 34% of new words mistakenly identified as original words because they were conceptually similar.
Are elderly women living at home healthier than those living in a nursing home? This question was studied by a group of psychologists at the University of Delhi. [Tyagil, R., Kapoor, S., & Kapoor, A. K. (2008). Environmental influence and health status of the elderly. The Open Anthropology Journal, 1, 14-18.] For a sample of elderly women, data were collected on the following variables: •Heart Rate •Age Group (1 = 60 to 70 years; 2 = 71 to 80 years; 3 = 81+ years) •Body Weight •Environment (0 = nursing home; 1 = living with family) •Height Recognizing the measurement scale of the data collected on each variable is important because the type of data dictates the appropriate data summary methods and statistical procedures. Which variable(s) in the data set are measured using a ratio scale?
Heart Rate, Body Weight, and Height Explanation: To understand the ratio measurement scale, you first have to understand the interval measurement scale. If data are measured using an interval scale, differences between data values are meaningful. This is not the case with the pain rating scale discussed in the previous explanation; when a patient changes her pain level from a 4 to a 5, her pain increase may not be comparable to her pain increase when she changes her pain level from a 6 to a 7. Like interval data, ratio data has the property that differences among data values are meaningful, but the data also have the property that data values have meaningful ratios. This property stems from the fact that measurements are referenced to a true zero point that indicates the absence of the condition that is being measured. For example, temperature measured on the Kelvin scale is ratio data because the measurements are made with respect to a true zero (the absence of all thermal energy). Temperature measured on the Fahrenheit or Celsius scales is interval data because the measurements are not referenced to a true zero. As a result, 80 degrees Fahrenheit is not twice as hot as 40 degrees Fahrenheit, but 80 kelvin is twice as hot as 40 kelvin. In this data set, Heart Rate, Body Weight, and Height are measured on an interval scale that references a true zero (for example, heart rate is a ratio scale because no heart rate is not an arbitrary zero) and therefore, measured on a ratio scale.
Select the measurement scale in the right column that best matches the description in the left column. Note that each scale (nominal scale, ordinal scale, interval scale, and ratio scale) will be used exactly once.
INTERVALE SCALE: The values of data measured on this scale can be rank ordered and have meaningful differences between scale points. NOMINAL SCALE: The values of data measured on this scale cannot be rank ordered. ORDINAL SCALE: The values of data measured on this scale can be a number or a name, but they can be rank ordered. RATIO SCALE: The values of data measured on this scale can be rank ordered and have meaningful differences between scale points. For this scale, there is also an absolute zero point. Explanation: Data measured on a nominal scale have values that are labels or names usually representing categories, such as male and female. Sometimes these labels can be numbers, but those numbers are actually labels for the categories, as in 0 = male and 1 = female. Data measured on an ordinal scale may have values that look very similar to data measured on a nominal scale, except that these values can be rank ordered. For example, the highest level of education attained can be measured as 0 = grade school or lower, 1 = some high school, 2 = graduated from high school, 3 = attended some college, 4 = graduated from college, and so on. These values can be rank ordered ("graduated from high school" is a higher level of education than "grade school or lower"), but the distances between these different scale points are not the same across the whole scale (the "distance" between a 0 and a 1 is not the same as the "distance" between a 3 and a 4). Similarly, it is common for a respondent to be asked to rank a statement as never, sometimes, often, or always OR as disagree, disagree somewhat, neutral, agree somewhat, agree. These are also ordinal scales. There is an order to these rankings but the distance between the different points on the scale is not necessarily consistent. Data measured on an interval scale typically are numbers, not names, in which the differences between two values of the scale are meaningful. For example, temperature measured on the Fahrenheit or Celsius scales is interval data because there is a consistent difference between 40 and 41 degrees and 63 and 64 degrees. On the other hand, these measurements do not reference a true zero so 80 degrees Fahrenheit is not twice as hot as 40 degrees Fahrenheit. Finally, data measured on a ratio scale are data measured on an interval scale, but with the additional requirement that there is an absolute zero point. The number of years of schooling is measured on a ratio scale because zero years of schooling is a real value with real meaning—the person did not attend any school. A person who attends eight years of schooling did indeed attend school for twice as many years as someone who attended school for four years. Only when there is a real zero point are such ratios meaningful.
Rogers, Farlow, and colleagues (1998) conducted an experiment to investigate whether donepezil improved cognitive function in patients with mild to moderate Alzheimer's disease (AD). A total of 1,775 patients were randomly assigned to treatment with either donepezil or a placebo (a look-alike pill with no pharmacological effect). Cognitive function, as measured by the Alzheimer's Disease Assessment Scale (ADAS-cog), was significantly improved in patients taking donepezil compared with the placebo group at weeks 12, 18, and 24. [Source: Rogers, S. L., Farlow, M. R., Doody, R. S., et al. (1998). A 24-week, double-blind, placebo controlled trial of donepezil in patients with Alzheimer's disease. Neurology, 50, 136-145.]
In this experiment, the independent variable is drug type , and the dependent variable is cognitive function . Explanation: The researcher's goal is to see whether differences in the independent variable coincide with differences in the dependent variable. That is, the researcher wants to know if the dependent variable is dependent on the independent variable. In an experiment, a researcher manipulates the independent variable, such as which treatment the participants receive, to see whether it changes the dependent variable, such as some measure of the severity of an illness. In this experiment, the independent variable is the drug type (whether the drug is donepezil or placebo), and the dependent variable is cognitive function.
You may or may not have used statistical information to inform your decision. In either case, you probably can recognize which types of information would be most useful to you for deciding whether or not bungee jumping is safe. Rank order the usefulness from 1 (most important) to 5 (least important) the following pieces of information for determining whether or not bungee jumping is safe. (Note: Remember, this is an exploratory exercise. There are no right or wrong answers.)
RANKING: 2. In some people, eyesight is impaired for months after bungee jumping. 5. Bungee jumping fatalities average 1 in 500,000 jumps. 1. The death ratio of playing tennis deaths compared to bungee jumping deaths is 5 to 1. 4. In one case, a 26-year-old woman's eyesight was still impaired 7 months after bungee jumping. 3. There were at least 18 bungee jumping fatalities between 1986 and 2002—a little more than 1 per year. Explanation: If you are going to evaluate concrete information, the most useful information is data such as: how common fatalities (or injuries) are, the rate of fatalities (or injuries) per a given number of jumps, the rate of fatalities (or injuries) compared to the rate of fatalities in other sports, the annual number of fatalities, and so on. These data are statistics—facts and figures that have been summarized in a precise numerical way so that we can create a clearer "big picture" of the situation. Information about the types of injuries (without any information about their frequencies) and information about isolated events are less helpful, because they cannot be generalized to form a bigger picture. If you do decide to try bungee jumping, you should know that good bungee jumping companies publish their safety statistics. These statistics should help you make a decision about which company to jump with.
What is the sample in the study?
The 75 students who participated in the study Explanation: A population is the set of all individuals, objects, or scores that the investigator is interested in studying. A sample is a subset of individuals selected from a population usually intended to represent the population in a research study. In this study, the population is the 750 first-year students at the professor's college. The sample is the 75 students who were chosen to complete the study.
What is the population in the study?
The 750 first-year students at the college Explanation: A population is the set of all individuals, objects, or scores that the investigator is interested in studying. A sample is a subset of individuals selected from a population usually intended to represent the population in a research study. In this study, the population is the 750 first-year students at the professor's college. The sample is the 75 students who were chosen to complete the study.
What is an example of a parameter in the study?
The actual average percentage of conceptually similar words that would be mistakenly recognized as being from the original list by the 750 first-year students Explanation: Data are the measurements or observations that are made on the subjects of an experiment. A statistic is a value, usually a numerical value, that describes a sample that is usually derived from measurements of the individuals in the sample. A parameter is a value, usually a numerical value, that describes a population that is usually derived from measurements of the individuals in the population. In this study the statistic is 34%, the average percentage of the new but conceptually similar words that were mistakenly thought to be on the original list by the 75 students. The actual average percentage of conceptually similar words that would be mistakenly recognized as being from the original list by the 750 first-year students is the parameter. The best estimate of this parameter is the statistic obtained from the 75 students, which is 34%.
In a study designed to examine the association of breakfast intake and body mass index (BMI), the National Heart, Lung, and Blood Institute Growth and Health Study recruited 2,379 adolescent girls. Frequency of breakfast consumption, dietary calcium and fiber, and BMI were recorded over a period of nine years. The study found that girls who ate breakfast more often tended to have a lower BMI [Source: J Am Diet Assoc. (2005) 105(6):938-45]. Which of the following conclusions can you make on the basis of this study?
The frequency of eating breakfast is associated with lower BMI in adolescent girls. Explanation: The data described is from an observational study in which participants were followed and monitored over the course of the study or simply observed or surveyed at one point in time. No variables were controlled, and no treatments were randomly assigned to participants. As a result, causation between the variables cannot be inferred from this study. You can only observe that an association or a relationship was found to exist; further conclusions may be drawn after conducting a randomized experimental study. Thus, the only listed conclusion you can make on the basis of this study is "The frequency of eating breakfast is associated with lower BMI in adolescent girls."
Rogers, Farlow, and colleagues (1998) conducted an experiment to investigate whether donepezil improved cognitive function in patients with mild to moderate Alzheimer's disease (AD). A total of 1,775 patients were randomly assigned to treatment with either donepezil or a placebo (a look-alike pill with no pharmacological effect). Cognitive function, as measured by the Alzheimer's Disease Assessment Scale (ADAS-cog), was significantly improved in patients taking donepezil compared with the placebo group at weeks 12, 18, and 24. [Source: Rogers, S. L., Farlow, M. R., Doody, R. S., et al. (1998). A 24-week, double-blind, placebo controlled trial of donepezil in patients with Alzheimer's disease. Neurology, 50, 136-145.]
The individuals who are in the control condition are typically referred to as the control group. Here, the control group consists of patients taking the placebo . Explanation: The individuals who are in the control condition (the control group) are those who do not receive the experimental treatment. The use of a control group allows researchers to compare individuals who receive treatment to those who do not in order to determine whether the treatment is effective. Here, the control group consists of patients taking the placebo.
You want to find out whether caffeine mitigates the effect of alcohol on reaction time. To study this, you administer to your subjects a drink that is equivalent to three 12-ounce beers, followed by the equivalent of two cups of coffee. Then your subjects complete a simulated driving task in which they must follow a fixed speed limit while driving on a straight road. Wind periodically and randomly pushes the simulated vehicle right, left, or not at all. Speed is measured in miles per hour above or below the 60-mph speed limit, with 1 mph being the smallest unit on the scale. Suppose the first subject scores 9 mph. Determine the real limits of 9.
The lower real limit is: 8.5 The upper real limit is: 9.5 Explanation: Continuous variables may have an infinite number of values between adjacent units on the scale; all measurements made on a continuous variable are approximate. You cannot know the exact value of the speed, so you rely on the real limits that specify the range that includes the exact value. The real limits of a continuous variable are those values that are above and below the recorded value by one-half of the smallest measuring unit of the scale. In this case, the smallest measuring unit on the scale is 1 mph, so you can be sure that the exact value lies between 9 minus 0.5 mph and 9 plus 0.5 mph. Thus, the value 8.5 (9 minus 0.5) is the lower real limit, and 9.5 (9 plus 0.5) is the upper real limit.
The following research studies consist of two or more groups of scores being compared. For each, decide whether the study is experimental or nonexperimental, and then identify the dependent, independent, or quasi-independent variables. A researcher would like to find out more about the determinants of college achievement. He conducts a study on 437 college students in which he measures their IQ levels and their grades in college courses. The researcher created five different groups using the students' IQ levels and then compared the average grades among members in different groups.
This study is an example of a nonexperimental study. The grades of the college students is the dependent variable. IQ group assignment is the quasi-independent variable. Explanation: Research studies that compare groups of scores can be categorized as experimental studies or nonexperimental studies. In both types of studies, the researcher is attempting to discover whether differences in the values of one variable (the independent variable for experimental studies and the quasi-independent variable for nonexperimental studies) result in differences in the values of another variable (the dependent variable). In an experimental study, the researcher systematically manipulates the independent variable. In a nonexperimental study, the researcher does not or cannot manipulate the quasi-independent variable. One reason not to manipulate the quasi-independent variable is that it may not be ethical to do so, as in a study where the treatments (or groups being compared) are different levels of consumption of toxic substances. Another reason may be that the researcher does not have the ability or authority to do so, as in a study where the treatment values are the subjects' ages, genders, or IQs. In this study, the treatments are not really treatments, because the researcher does not assign an IQ range to each college student in the study. (He does not have the power to do so.) He only compares the differences in college grades among the IQ groups (treatments). Therefore, this is a nonexperimental study. This study was conducted to determine whether IQ group assignment is related to the grades of the college students. The grades of the college students is the dependent variable, and IQ group assignment is the quasi-independent variable.
Researchers at a medical school conducted a study to test the effectiveness of a new treatment for lung cancer. Of the 128 lung cancer patients in an affiliated hospital, 94 volunteered for the new treatment, while the remaining 34 declined and underwent traditional treatment instead. The survival rates for the two treatment groups were measured after 12 months.
This study is an example of a nonexperimental study. Whether a patient survives after 12 months is the dependent variable. The type of lung cancer treatment is the quasi-independent variable. Explanation: In this study, the researcher does not assign the patients to the traditional or the new treatment for lung cancer for the 128 lung cancer patients in the study. Therefore, this is not an experimental study. The study was conducted to determine whether the type of lung cancer treatment is related to whether a patient survives after 12 months. The quasi-independent variable is the type of lung cancer treatment, and the dependent variable is whether a patient survives after 12 months.
