Exercise #1
As part of a test preparation course, students are asked to take a practice version of the Graduate Record Examination (GRE). This is a standardized test. Scores can range from 200 to 800 with a population mean on500 and a population standard deviation of 100.
Nominal. Sorry, this is incorrect. No groupings or classifications were described.
Ordinal. Sorry, this is incorrect. GRE scores have the property of identity and magnitude, so they do tell us lower or higher probability of success in graduate school. They also have the property of equal intervals between scale points.
Interval. Correct. GRE scores have the properties of identity, magnitude and equal intervals between scale points.
Ratio. Sorry, this is incorrect. GRE scores have the properties of identity, magnitude and equal intervals between scale points. They do not have a zero score; they range from 200 to 800.
Approximately Interval. We create GRE scores by combining responses across items. The items, however, are not rank or likert items.
Exercise #2
Children in elementary school are evaluated and classified as non-readers (0), beginning readers (1), grade level readers (2), and advanced readers (3). The classification is done in order to place them in reading groups.
Nominal. Sorry, this is incorrect. Reading levels are identified but they are also ordered by skill level.
Ordinal. Correct. The numbers identify and order the level of reading skill.
Interval. Sorry, this is incorrect. The reading level scores have the property of identity and magnitude/order but there is not equal distance between scale points.
Ratio. Sorry, this is incorrect. Even though the zero score may represent no reading skill (and thus is a true zero), the ratio scale of measurement requires both equal intervals and a true zero point.
Approximately Interval. Sorry, this is incorrect. This measurement is based on only one ordinal rating. Approximately interval scales require that multiple ordinal ratings are added together or averaged.
Exercise #3
During a clinical interview, survivors of a tornado are asked to state no or yes to whether they have experienced specific symptoms of Post-Traumatic Stress Disorder (PTSD) in the past week. The number 0 is assigned to no and the number 1 is assigned to yes.
Nominal. Correct. The numbers in this rating system identify the presence or absence of a symptom in the past week.
Ordinal. Sorry, this is not correct. The numbers in this rating system represent only the presence or absence of a symptom in the past week. They do not order the level of symptoms.
Interval. Sorry, this is not correct. This scale is simply classifying the presence or absence of a symptom in the past week. Scale points are not ordered and we do not have a fixed interval between no and yes.
Ratio. Sorry, this is not correct. Even though 0 represents the absence of a symptom in the past week, the ratio scale of measurement requires both equal intervals and a true zero point.
Approximately Interval. Sorry, this is incorrect. This measurement is based on only one nominal rating. Approximately interval scales require that multiple ordinal ratings are added together or averaged.
Exercise #4
Emory University wants to know which dormitories the students prefer. The administration counts the number of applications for each dorm. They assign a rank to each dorm based on the number of applications received.
Nominal. Sorry, this is incorrect. The dorms are identified in this number system but they are also ordered.
Ordinal. Correct. This ranking system has the properties of identity and magnitude.
Interval. Sorry, this is incorrect. This ranking system identifies and orders students preferences but the interval between each rank is not equal. It does not tell us how much each dorm is preferred (or not) over the others.
Ratio. Sorry, this is incorrect. This ranking system identifies and orders students preferences but the interval between each rank is not equal. It does not tell us how much each dorm is preferred (or not) over the others. There is also no true zero point on this scale.
Approximately Interval. Sorry, this is incorrect. This measurement is based on only one ordinal rating. Approximately interval scales require that multiple ordinal ratings are added together or averaged.
Exercise #5
During a clinical interview, survivors of a tornado are asked to state no or yes to whether they have experienced specific symptoms of Post-Traumatic Stress Disorder (PTSD) in the past week. The interviewer adds up the total number of yes responses.
Nominal. Sorry, this is incorrect. The yes/no responses to each symptom are measured on a nominal scale, but the total score counts of the number of yes responses.
Ordinal. Sorry, this is incorrect. The yes/no responses to each symptom are measured on a nominal scale, but the total score counts of the number of yes responses.
Interval. Sorry, this is incorrect. Counting the number of yes responses creates a scale with equal intervals between scale points, but it also has a true zero. A score of 0 means that the person interviewed stated that they did not experience any of the specific symptoms of PTSD in the past week.
Ratio. Correct. Counting the number of yes responses creates a scale with the properties of identity, magnitude, equal interval, and true zero. The 0 score is a true zero indicating that the person interviewed reported experiencing no symptoms of PTSD in the past week.
Approximately Interval. Sorry, this is incorrect. We are adding scores across items, but the original items are not measured on an ordinal scale. This scale is based on counting responses, which yields a scale with identity, magnitude, equal intervals and a true zero.
Exercise #6
A researcher wants to determine whether the circadian temperature cycle is less stable for older compared to middle aged adults. Body temperature in degrees Fahrenheit is measured every 15 minutes over a period of 3 days.
Nominal. Sorry, this is incorrect. Temperature identifies the volume of mercury on an equal interval scale. It has the properties of identity, magnitude and equal interval.
Ordinal. Sorry, this is incorrect. Temperature does have the property of magnitude (or order). It also measures the volume of mercury on an equal interval scale.
Interval. Correct. Temperature has the properties of identity, magnitude, and equal interval.
Ratio. Sorry, this is incorrect. Temperature has the properties of identity, magnitude, and equal interval. The zero point on the Fahrenheit scale is arbitrary, thus there is no true zero point.
Approximately Interval. Sorry, this is incorrect. Temperature is measured once during each interval. No summary score was created.
Exercise #7
All new clients in a mental health clinic are given a symptoms checklist that asks them to report how often they experienced each symptom in the past week. They assign a frequency rating to each symptom (0 not at all, 1 sometimes, 2 often, 3 almost all the time).
Nominal. Sorry, this is incorrect. Each number identifies a frequency level but the levels are ordered.
Ordinal. Correct. This rating scale has the property of identity and order. Each number identifies a frequency level on an ordered scale.
Interval. Sorry, this is incorrect. Each number identifies a frequency level on an ordered scale, but the interval between scale points is not equal.
Ratio. Sorry, this is incorrect. Even though 0 represents the absence of a symptom in the past week, the ratio scale of measurement requires both equal intervals and a true zero point. The distance between points on this scale is not equal.
Approximately Interval. Sorry, this is incorrect. This measurement is based on only one ordinal rating. Approximately interval scales require that multiple ordinal ratings are added together or averaged.
Exercise #8
.Subjects are asked to sit at a computer screen. In 30-second intervals, a picture of a wrench is flashed on the screen. The picture may appear anywhere on the screen. Sometimes the wrench has an open end (curved) and sometimes the wrench is a closed hexagon. Subjects are asked to press the Y key on a computer keyboard if the wrench is open and the N key if it is closed. The total score is the number of correct responses.
Nominal. Sorry, this is incorrect. Each trial is measured on a nominal scale of correct or incorrect. However, adding together the correct responses to yield a total number of correct responses results in a count scale with properties of identity, magnitude, equal interval and true zero.
Ordinal. Sorry, this is incorrect. The total score will tell us who has high and low scores, but it will also tell us how many were correct.
Interval. Sorry, this is incorrect. The total score has the properties of identity, magnitude and equal interval. A 0 score, though, is a true or meaningful zero because it tells us that, across trials, none of the responses were correct.
Ratio. Correct. This scale has all of the properties of the abstract number system identity, magnitude, equal interval and true zero.
Approximately Interval. Sorry, this is incorrect. We are adding scores across items, but the original items are not measured on an ordinal scale. This scale is based on counting responses, which yields a scale with identity, magnitude, equal intervals and a true zero.
Exercise #9
All new clients in a mental health clinic are given a symptoms checklist that asks them to report how often they experienced each symptom in the past week. They assign a frequency rating to each symptom (0 not at all, 1 sometimes, 2 often, 3 almost all the time). Responses across all items are averaged to yield an overall symptom score.
Nominal. Sorry, this is incorrect. The overall score identifies average frequencies. The scale also has properties of magnitude. Distances between scale points are treated as interval.
Ordinal. Sorry, this is incorrect. The individual items are likert ratings, which are ordinal. Averaging scores across items yields a scale with properties of identity and magnitude. Distances between scale points are treated as equal.
Interval. Sorry, this is incorrect. The individual items are likert ratings, which are ordinal. Averaging scores across items yields a scale with properties of identity and magnitude. Distances between scale points are only treated as equal; they are not technically equal.
Ratio. Sorry, this is incorrect. The individual items are likert ratings, which are ordinal. Averaging scores across items yields a scale with properties of identity and magnitude. Distances between scale points are treated as equal. There is no true zero point.
Approximately Interval. Correct. The individual items are likert ratings, which are ordinal. Averaging scores across items yields a scale with properties of identity and magnitude. Distances between scale points are treated as equal
Exercise #10
Interviewers ask research subjects to describe in some detail their relationships with important people in their lives. Using established criteria, raters review these personal descriptions and assign a dominant attachment category (Secure - 1, Preoccupied - 2, Fearful - 3, Dismissing - 4).
Nominal. Correct. The numbers on this rating scale name the dominant attachment style. This scale only has the numerical property of identity.
Ordinal. Sorry, this is incorrect. The numbers in this rating system only identify the attachment style. There is no inherent order in the styles.
Interval. Sorry, this is incorrect. This scale is simply classifying the dominant attachment style. Scale points are not ordered and we do not have a fixed interval between the styles.
Ratio. Sorry, this is incorrect. There is no 0 score on this scale.
Approximately Interval. Sorry, this is incorrect. This measurement is based on only one nominal rating. Approximately interval scales require that multiple ordinal ratings are added together or averaged.