# Chapter 9: Measurement and Scaling: Fundamentals and Comparative Scaling

## 18 terms

### Scaling

scales place the objects being measured along a continuum

### measurement

assigning numbers to characteristics of objects being measured according to predetermined rules

1. description
2. order
3. distance
4. origin

### Description (scale characteristic)

unique labels or descriptors that are used to desginate each value of the scale e.g. 1=female, 2=male; 1=unsatisfactory, 2=normal; every scale has description

### 3 criteria for measurement

1. One-to-one correspondence between the numbers
and the characteristics being measured.
2. The rules for assigning numbers should be
standardized and applied uniformly.
3. Rules must not change over objects or time.

### Order (scale characteristic)

the relative sizes or positions of the descriptors; greater than, less than; this is not in every scale e.g. male and female

### distance (scale characteristic)

abolute differences between the scale desciprtors are known and can be expressed in units; distance implies order but not necessarily the reverse

### origin (scale characterisitic)

the scale has a true zero point (what was your annual income, it could be zero) but if it has a moving scale it doesn't have the origin characterisitic

### Primary scales of measurement (4)

1. nomical scale
2. ordinal scale
3. interval scale
4. ratio scale
the level of complexity increases as you go down the list--respondenst find nominal easiest to use and ratio most complex

### nominal scale of measurement

1. uses numbers as labels or tags for identifying and classifying objects--a one to one correspondence exists between numbers and labels--this doesn't tell us which one is more popular than the other
2. classifcation puposes they serve as labels for clases or categories
3. they are mutually exclusive (no overlap) and collectively exhaustive (all objects fall into one of the classes)
4. e.g. social security number (higher one is no better than a lower one)
5. statistics to be used are percentage, mode, and chi-square

### ordinal scale of measurement

1. a ranking scales in which numbers assigned to objects indicate the relative extent to which some characteristic is possessed--but we don't know how much more and how less
2. greater than or less than
3. statistics can also include centiles and medians

### interval scale

1. numerically equal distances on the scale represent equal values in the characteristic being measured
2. 1= do not like at all, 2= neutral, 2= hated it
3. location of zero is arbitrary so you can't take ratios
4. the arithmetic mean and standard deviation can be taken here

### ratio scale of measurement

1. an interval scale with a set 0 point
following foods:
___ Carrots
___ Cupcakes
___ Fish
___ Mac 'n Cheese
100 Sum
2. height, weight, age
3. conversion formual is y=bx
4. all statistical measures can be used here

### 2 types of scaling techniques (3 for one and 2 for the other)

1. comparative scales
a) paired comparison
b) rank order
c) constant sum
2. noncomparative scales
a) continuous scale
b) itemized rating scales

### Comparatve scales--paired comparison

1. a respondent is presented with a pair of alternatives and asked to select one based on some criterion
2. ordinal in nature
3. no more than five brands being compared

### Comparative scales--rank order

1. respondents are presneted with severa lalternatives and asked to rank them according to some criterion
2. this is also ordinal data only

### comparative scales--constant sum scaling

1. respondents are asked to allocate a constant sum of units among several choices adding up to a final number
2. also ordinal data because the results are not generalizable to things outside of the study
3. some may allocate to much or too little so it needs to be adjusted

### noncompartive scales

objects are scaled independently of each other