The Basics Of Item Response Theory Using R Statistics For Social And Behavioral Sciences 1st Edition Frank B. Baker , Seock-Ho Kim - Solutions

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Interval- and ratio-level numbers can be _____ or _____.
Make a stem-and-leaf display and comment on the shape of the distribution for these data: 183, 192, 203, 203, 211, 219, 220, 227, 228, 228, 229, 230, 233, 234, 234, 248, 249, 254, and 266.
This graph shows the depression scores of the 772 residents surveyed in Practice Problem 2.15. Determine the shape of the data set.
Here is a graph for the religious affiliation of the 53 students surveyed in Practice Problem 2.14. Determine the shape of the data set.
What does it mean if a frequency distribution is positively skewed?
Describe the normal curve in terms of symmetry, modality, and kurtosis.
For what levels of measurement can one describe the shape of a frequency distribution?
A psychologist administered a continuous measure of depression to a representative sample of 772 residents of a midwestern state. Scores on the depression scale can range from 0 to 60 and higher scores indicate more depression. There were 423 with scores in the 0–9 range, 210 in the 10–19
A religion professor at a large university took a sample of 53 students and asked them what their religious faith was. Nine reported they were Muslim, 4 Buddhist, 2 Hindu, 16 Christian, 10 Jewish, 6 atheist, and 6 reported being other religions. Make a graph for these data.
A psychologist administered a continuous measure of depression to a representative sample of 772 residents of a midwestern state. Scores on the depression scale can range from 0 to 60 and higher scores indicate more depression. There were 423 with scores in the 0–9 range, 210 in the 10–19
A religion professor at a large university took a sample of 53 students and asked them what their religious faith was. Nine reported they were Muslim, 4 Buddhist, 2 Hindu, 16 Christian, 10 Jewish, 6 atheist, and 6 reported being other religions. Make a graph for these data.
Where do the bars go up and come down for each interval on a histogram?
Match these two types of data, continuous and discrete, with the three types of graphs (bar graphs, histograms, and frequency polygons).
Below are sets of consecutive intervals from frequency distributions for continuous variables. For the second interval in each set, the one in bold, tell the real lower limit; the real upper limit; the interval width, i; and the interval midpoint, m.a. 15–19; 20–24; 25–29b. 205–245;
For each variable, determine if it is continuous or discrete.a. The amount of snowfall, in inches, recorded during winter in a cityb. The number of days, in the past 30, on which a person has consumed any alcoholc. A person’s level of depression, as measured by the percentage of questions on a
If there were five cases in the interval 45–49 of a grouped frequency distribution for a continuous variable and their original raw scores were unknown, what value(s) should be assigned to them?
How does a continuous number differ from a discrete number?
Below are final grades, in order, from an upper-level psychology class. Make a grouped frequency distribution to show the distribution of grades. Use an interval width of 10 and start the lowest interval at 50. Be sure to include midpoint, frequency, cumulative frequency, percentage, and cumulative
An exercise physiologist has first-year college students exercise and then measures how many minutes it takes for their heart rates to return to normal. Make an ungrouped frequency distribution that shows frequency, cumulative frequency, percentage, and cumulative percentage for the following
What is the formula to calculate a midpoint for an interval in a grouped frequency distribution?
How many intervals should a grouped frequency distribution have?
How should a frequency distribution be organized for a nominal variable like type of religion?
What information does a cumulative frequency provide?
Under what conditions should an ungrouped frequency distribution be made? A grouped frequency distribution?
A sociologist believes that physical distress in cities leads to social distress. She measures physical distress by seeing how much graffiti there is. Based on this, she classifies cities as being high, moderate, or low in terms of physical distress. She randomly samples cities in North America
Explanatory variable is to outcome variable as:a. controlled is to manipulated.b. relationship is to cause and effect.c. statistic is to parameter.d. parameter is to statistic.e. none of the above
A researcher gives a different amount of X to different subjects and then measures how much Y each subject produces. She finds that subjects who got more X produce more Y, and subjects who got less X produce less Y. She also finds no other variable that can account for the different amounts of Y
Every 10 years, the U.S. Census Bureau attempts to collect information from all Americans. Assuming that they are successful, would it be a statistic or a parameter if the Census Bureau reported that 12.2% of Americans identify themselves as of African descent?
The admissions committee at a college does not distinguish between different types of high school extracurricular activities. As far as it is concerned, being a member of the tiddlywinks club is equivalent to being student council president. On the admission form to the college, applicants are
A neuroscientist believes that proteins form plaques in the brain that cause Alzheimer’s disease. He gets a sample of older adults, measures the nanograms per liter of protein in spinal fluid, and measures short-term memory as the percentage of words in a list that are recalled.
A political scientist is curious as to what influences voting behavior on taxes for school districts. She obtains a sample of voters and divides them, randomly, into three groups. One group serves as the control group, nothing is done to them. To one experimental group, she gives information about
A consumer behavior researcher is curious as to whether, in terms of the monetary value of Christmas presents received, it makes a difference if a child is naughty or nice. She has parents classify their children as naughty or nice, then calculates how much the parents spent on Christmas presents
An economist believed that as nations become wealthier, they produce more greenhouse gases. He took a country and found both its gross domestic product (GDP) and the total tons of CO2 emissions for each year over the past 50 years.
A personality psychologist has kindergarten teachers use an empathy scale that ranges from 0 (not at all empathetic) to 100 (extremely high levels of empathy) to rate their students. Thirteen years later, when the students are ready to graduate from high school, he tracks them down and rates their
Ever notice that some college students buy all the books for class, complete all the readings, do all the homework, and so on? These students usually end up with better grades as well. An education professor decided to investigate if these more conscientious students received better grades because
Some football players put streaks of black paint under their eyes because they believe that it helps them see better in sunny conditions and react more quickly. A sensory psychologist wants to see if this is really true. He gathers a group of volunteers and randomly divides them in two. Half get
The local police department has come to a criminologist to help it evaluate a new type of disposable, plastic handcuffs. They are just as effective as metal handcuffs in terms of immobilizing someone who has been arrested and they are cheaper than metal handcuffs, but the police are concerned that
If you do round as you go, carry at least _____ decimal places.
The letter we use as an abbreviation for an outcome variable is _____. The abbreviation for the number of cases in a group is _____.The symbol for adding up a group of scores is _____, the uppercase Greek letter sigma.
If a summary statement is used to describe a group of cases, it is a(an) _____ statistic; if it is used to draw a conclusion about the larger population, it is a (an) _____ statistic.
A number characterizing a sample is called a (an) _____; a number characterizing a population is called a (an) _____.
A sample is a (an) _____ of a population.
A (an) _____ is the larger group of cases that a researcher is interested in studying.
Interval-level numbers have a (an) _____ zero point, and ratio-level numbers have a (an) _____ zero point.
Because interval-level numbers have _____, we can meaningfully speak of the distance between two scores.
The explanatory variable in quasi-experimental designs is called the _____ variable.
The _____ variable in _____ is called the dependent variable.
Though a quasi-experimental design looks like a (an) _____ design, it is really a (an) _____ design.
If two variables, X and Y, are found to be related in a correlational design, the three possible explanations for the relationship are: (a)_____, (b) _____, and (c) _____.
Round the following appropriately:a. 17.7854b. 9.7432c. 12.9845d. 8.3450e. 7.1205f. 53 g. 42
Given this data set (12, 8, 4, 6), calculate what is requested. Don’t forget the rules of rounding.a. Nb. ΣXc. ΣX 2d. (ΣX)2e. ΣX + 1f. Σ (X + 1)
According to the American Psychological Association, how many decimal places should a result have?
Following the order of operations, what does one do first in an equation?
What abbreviation do statisticians use for a summation sign?
A demographer is interested in the annual incomes of people who live in apartments. From the Census Bureau, she obtains a representative sample of 2,500 people living in apartments all across the United States and learns their annual incomes. She then reports that the average annual income of
The athletic director at a college is interested in how well female athletes perform academically. He interviews the women’s softball team, determines what their average GPA is, and reports that the women’s softball team has a GPA of 3.37. (a) Is this a statistic or a parameter? (b) Is this a
What is the name for a statistic that is used to draw a conclusion about a population from a sample?
What are Greek letters used as abbreviations for? Latin letters?
A personality psychologist developed a femininity scale. From the list of hundreds of behaviors that are considered feminine, he selected 10. For each of these 10 behaviors, a person completing the scale indicates if he or she engages in the behavior. Each “yes”answer is worth 1 point. Scores
Infants who are being reared by heterosexual couples are observed and classified as (a) being attached to the mother, (b) being attached to the father, (c) being attached to both, or (d) being attached to neither. Attachment is being measured at what level?
At the end of the semester, a professor surveys his students using the following scale with regard to how much of the assigned reading was done: 0 = none, 1 = a bit, 2 = about half, 3 = most, 4 = all. Amount of assigned reading completed is measured at what level?
Ivan Pavlov gathers a group of dogs, exposes each to its favorite food for 5 minutes, and measures how many milliliters of saliva each dog produces during the 5-minute period. Salivation is being measured at what level?
If a scale has an absolute zero point, what does a zero on the scale represent?
When a scale moves from ordinal to interval by adding equality of units, what additional information does that scale now provide?
List the four levels of measurement, in order from simplest to most complex.
A nutritionist is examining the role of fiber in gastrointestinal (GI)health. He believes that consuming fiber is good for GI health. He gathers a group of college students and asks each one the number of grams of fiber consumed per day. He also asks each one how many episodes of GI distress (upset
An educational researcher is interested in the effects of sleep on school performance. She classifies students as (a) getting an adequate amount of sleep or (b) not getting an adequate amount of sleep. Then she measures school performance by finding out their GPAs for a semester.
A psychologist gets a group of college students to come to his lab and randomly divides them into two groups. He has each group study a list of nonsense syllables for 15 minutes. One group, the massed group, studies for 15 minutes in a row. The other group, the spaced group, studies for three
In which types of studies does one need to worry about confounding variables?
In which type of study can one draw a conclusion about cause and effect?
In which studies are cases assigned to groups?
Name the three different types of studies.
A researcher has collected IQ scores from a sample of sixth graders.What are some questions she might want to ask of the data? How would the data be arranged to answer the questions?
What is the purpose of statistics?
Why aren’t the rules of rounding followed when reporting N, sample size?
Use the computer session to experiment with different combinations of testing goals, item characteristic curve models, and numbers of items. The goal is to be able to obtain test characteristic curves and test information functions that are optimal for the testing goals. It will be helpful to use
Construct a test that will have a horizontal test information function over the ability range of 2:0 to C2:0 having a maximum amount of information of 2:5.
Repeat the previous problem using the three-parameter model.
Construct a test that will have a nearly linear test characteristic curve whose midtrue score occurs at an ability level of zero. Use the Rasch model.
Construct a test having a test characteristic curve with a rather small slope and a test information function that has a moderately rounded appearance. Use either the two- or three-parameter model.
Construct a broad-range test under the three-parameter model that will have a horizontal test information function over the ability range of 1:0 to C1:0.
Construct a ten-item screening test to function at an ability level of C0:75 using a Rasch model.
Plot several test information functions on the same graph. It will be helpful to make rough sketches of the test information functions displayed and notes to indicate the nature of the mix of item parameter values. The goal is to be able to predict what the form of the test information function
Experiment a bit with different item characteristic curve models, parameter values, and number of items. To make things easier, you may use R command lines that lets the computer generate the values of the item parameters.
Use a model of your choice and select values of the item parameters such that the test information function approximates a horizontal line. Use a ten-item test.
Experiment with different types of models and item parameter values to see if you can determine what influences the distribution of the estimated abilities.
The intent of this exercise is to see if you can improve upon the previous estimate of the examinee’s ability parameter by proper selection of the test’s item parameters.(a) Use the number of items J D 5 and the number of replications R D 10.(b) Set up the ability parameter to one of the values
An example case earlier will be performed using the item characteristic curve model of your choice. The two-parameter model may be a good starting model.(a) Use the number of items J D 5 and the number of replications R D 10.(b) Set up the ability parameter to 0:5. Note that you may use a randomly
It would be possible to construct a test characteristic curve that decreases as ability increases. To do so would require items with negative item discrimination for the correct response to the items. Such a test would not be considered to be a good test because the higher an examinee’s ability
Shape of the test characteristic curve:(a) When J D 1, the true score ranges from 0 to 1 and the shape of the test characteristic curve is identical to that of the item characteristic curve for the single item.(b) The test characteristic curve does not always look like an item characteristic curve.
Relation of the true score and the ability level:(a) Given an ability level, the corresponding true score can be found via the test characteristic curve.(b) Given a true score, the corresponding ability level can be found via the test characteristic curve.(c) Both the true scores and ability are
Obtain the test characteristic curve for a test with five items using the following item difficulty and item discrimination parameters:
Obtain the test characteristic curve for a test with five items using the following item difficulty and item discrimination parameters:b1 D 1:0 b2 D 1:0 b3 D 1:0 b4 D 1:0 b5 D 1:0 a1 D 1:6 a2 D 1:9 a3 D 1:6 a4 D 1:9 a5 D 1:6 The majority of the test characteristic curve is compressed into a rather
Obtain the test characteristic curve for a test with five items using the following item difficulty and item discrimination parameters:b1 D 0:0 b2 D 0:0 b3 D 0:0 b4 D 0:0 b5 D 0:0 a1 D 0:4 a2 D 0:8 a3 D 0:4 a4 D 0:8 a5 D 0:4 The test characteristic curve is nearly a straight line with a rather
Obtain the test characteristic curve for a test with ten items using the following item difficulty parameters:b1 D 0:8 b2 D 0:5 b3 D 0:5 b4 D 0:0 b5 D 0:0 b6 D 0:0 b7 D 0:5 b8 D 0:5 b9 D 0:5 b10 D 0:8 The test characteristic curve has a well-defined S-shape much like an item characteristic curve.
Obtain the test characteristic curve for a test with ten items using the following item difficulty parameters:b1 D 3:0 b2 D 2:5 b3 D 2:0 b4 D 1:5 b5 D 1:0 b6 D 0:5 b7 D 0:0 b8 D 0:5 b9 D 1:0 b10 D 1:5 The resulting test characteristic curve has a nearly linear section from an ability level of 3 to
Obtain the test characteristic curve for a test with ten items by setting all item difficulty parameters to a value of b D 0:0. The test characteristic curve in this case looks just like an item characteristic curve for an item with b D 0:0. The vertical axis ranges from 0 to 10. The mid true score
Now experiment with various combinations of overlapping and nonoverlapping ability groups in conjunction with each of the three item characteristic curve models.
Under the three-parameter model (i.e., mdl
Under the Rasch model (i.e., mdl

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The Basics Of Item Response Theory Using R Statistics For Social And Behavioral Sciences 1st Edition Frank B. Baker , Seock-Ho Kim - Solutions

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