style="font-size:15px;"> 8 D
Module Quiz
These questions are designed to touch on the most crucial concepts of the module.
1 Expand and solve the following expressions if X1 = 10; X2 = 5; Y1 = 3; Y2 = 2Σ(X + Y) =Σ(X2 + Y2) =Σ(X + Y)2 =Σ(2X + 3Y) =3Σ(X + 3Y) =
2 Complete the following chart:
3 Solve for X in the following equations:X + 15 = 252X + 3 = 96X − 7 = 41
4 You are interested in studying the mating habits of the remaining 4,000 chimpanzees in the wild. However, you are unable to find all 4,000 chimps and so you observe 200. In this example, how many chimps are in the population, in the sample, and in a case?
5 According to the conventions of the social sciences, what is the solution: 9.87532 + 10.78672?
Quiz Answers
1 201382184590
2
3 X = 10X = 3X = 8X = 108.50X = 0.10
4 The 4,000 chimpanzees are a population and the 200 are a sample, and 1 chimp would be a case.
5 20.66
Module 2 Measurement Scales
Learning Objectives
Define a scale of measurement
Classify data according to their scale of measurement
Distinguish between discrete and continuous variables
Establish real limits for continuously scored data
Module Summary
Statistics are used to investigate variables. Just as there are different types of variables (age, height, gender, occupation, etc.), there are different scales in which variables can be measured. Measurement refers to the value that is assigned to a specific trait. The meaning that you assign to a certain measurement depends on the scale of measurement that was used. In statistics, there are four types of scales of measurement: nominal, ordinal, interval, and ratio.
A nominal scale is one that is divided into distinct categories. Additionally, the categories are not ranked; one category is not higher or lower than the next. Favorite color would be an example of a nominal scale. My favorite color is blue, whereas yours may be red. Personal opinion aside, my preference for blue is no better or worse than your preference for red.
An ordinal scale is one that ranks cases in order, but the precise difference between two cases is unknown. For example, you might classify one person as attractive and another as gorgeous. You know from these descriptors that gorgeous is above attractive, but you cannot be certain of the exact amount of improvement from one rank to the next.
An interval scale is similar to an ordinal scale in that individuals are ranked in order, but in contrast to an ordinal scale, the precise difference between individuals is known. There is, however, no true zero. A true zero means that it is possible to have a complete absence of the variable being measured. For example, the Fahrenheit temperature scale is an interval scale. When comparing 36 degrees and 12 degrees, you can be certain that there is a 24-degree difference between the two temperatures. You cannot, however, ever have no Fahrenheit temperature. Most measures of mental ability or traits (intelligence, extraversion, etc.) also are interval scale.
A ratio scale is similar to an interval scale but possesses a true zero. Again, a true zero means it is possible to have a complete absence of the variable being measured. The amount of money in your wallet is a ratio scale. This is because it is possible for you to have no money, regardless of the amount of money that you actually do have.
Variables can also be considered either continuous or discrete. Continuous variables have values that can fall anywhere on the scale, including between two adjacent values. An example of a continuous variable would be time (as specified by minutes and seconds). You could have a value 1 min and 3 s. In comparison, discrete variables have values that cannot fall between adjacent values. An example of a discrete variable would be the number of students in your class, because there cannot be less than a full student, or a fraction of a student.
Continuous variables are defined by their real limits. A real limit is defined as ±0.5 of the score’s unit. This makes each score contiguous with the next score. Thus, for a score of 10, when the scores are scaled in units of 1, the upper real limit would be 10.5 and the lower real limit would be 9.5. For a score of 10 when scores are scaled in units of 5, the upper real limit would be 12.5 and the lower real limit would be 7.5. Note that an observed score will never fall at the real limit.
True/False Questions
1 The scale of measurement for the favorite animals of your classmates would be a nominal scale.
2 In an interval scale, there is an equal amount of distance between adjacent ranks and there is a true zero.
3 You are attending a swim competition and notice that the swimmers are ranked by their time. Their ranking is an ordinal scale.
4 (Refer to Question 3.) The ranking through the use of their time is an interval scale.
5 Flavors of ice cream would be a discrete and ordinal scale.
6 The number of trumpet players in an orchestra is a discrete variable.
7 The distance that you can throw a football is a discrete variable.
8 For a scale of 4 when scores are in single units, the real limits are 3 and 5.
True/False Answers
1 True
2 False
3 True
4 False
5 False
6 True
7 False
8 False
Short-Answer Questions
1 What scale of measurement best classifies the following?Number of calories in a candy barColors in a bouquet of flowersElevation in reference to sea level
2 What is the highest scale of measurement for the following?Number of available TV channelsNumber of pets you can ownResponses to a questionnaire that ranges from −5 to 5
3 What is a nominal scale?
4 What are the limitations of a nominal scale?
5 What is the difference between an interval and a ratio scale?
6 What
