measurement and scale 2014

Measurement And Scales

Qazi Subhan

Identify the four levels of measurement under which numbers generated through a survey can be classified.

Distinguish among attributes, behavioral variables, beliefs, and attitudes.

List and describe five methods for inferring people's attitudes.

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Discuss the various dimensions on which rating scales can vary.

Apply the formats of Likert, semantic-differential, and Stapel scales and discuss how data generated by these scales are analyzed and interpreted.

Define validity, reliability, and sensitivity of a scale.

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Measurement is “the assignment of numbers to observations [or responses] according to some set of rules”

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Reputation

Workplace Environment

Products andServices

Emotional Appeal

Financial Performance

Social Responsibility

Vision and Leadership

Emotional Appeal◦ Like ◦ Respect ◦ Trust

Workplace Environment◦ Well managed◦ Appealing workplace◦ Employee Talent

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Products and Services◦ Innovative◦ Strong brand◦ Quality◦ Value

Social Responsibility◦ Citizenship◦ Environmental stewardship◦ Ethics

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Vision and Leadership◦ Clear values◦ Strong leadership◦ Inspiring vision

Financial Performance◦ Growth prospects◦ Past results◦ Recognizes opportunities◦ Low risk

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Nominal

Ordinal Interval

Ratio

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Numbers forming a nominal scale are no more than labels used solely to identify different categories of responses

Example: What is the gender?◦ Male◦ Female

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Which one of the following media influences your purchasing decisions the most? ◦ Television ◦ Radio◦ Newspapers ◦ Magazines◦ Internet

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The mode is the most frequent category - only statistics applicable to nominal variable

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An ordinal scale is more powerful than a nominal scale in that the numbers possess the property of rank order

How long do you spend reading newspapers on a typical weekday?◦ Less than 5 minutes◦ 5 minutes to less than 15 minutes◦ 15 minutes to less than 30 minutes◦ 30 minutes or more

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The mode and the median are the most meaningful measures of central tendency for ordinal-scaled responses

Median – the category in which the middle value is called median when all responses are arranged from lowest to highest (or vice versa)

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In this case, the mode is category 1, and the median is category 2.

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Response Category Percentage of Respondents Checking Category

1 40

2 25

3 25

4 10

An interval scale has all the properties of an ordinal scale and the differences between the scale values can be meaningfully interpreted

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How likely are you to buy a new automobile within the next six months?

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(Please check the most appropriate category.) Will definitely not buy _____

(1)

Extremely unlikely _____

(2)Unlikely _____

(3)

Likely _____

(4)Extremely likely _____

(5)

Will definitely buy _____

(6)

Ratio scales possess all the properties of an interval scale and the ratios of numbers on these scales have meaningful interpretations

What is your annual income before taxes? $______

How far is your workplace from your home? _____ miles

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Attributes Behavior Beliefs Attitudes

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Attitudes are similar to beliefs, except that they also involve respondents’ evaluative judgments

For instance, do respondents feel print advertisements for cigarettes should be banned?

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A conceptual definition of attitude may be “a predisposition to respond favorably or unfavorably to a stimulus object”

An operational definition of attitude refers to a person’s attitude towards a particular retail store that may be measured as the total of the person’s expressed degree of agreement, on a 5-point, “strongly agree” to “strongly disagree” scale, with each of a set of 20 evaluative statements about various aspects of the retail store

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• Attitudes – Widely believed to be a key determinant of

behavior– Can only be inferred and cannot be directly

ascertained• Measures in which inferences are drawn

from – Observed evident behavior– Individual's reaction – Performance on objective tasks– Physiological reactions

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Observation of overt (Explicit) behavior is useful when other attitude measurement methods are inconvenient or infeasible

An observation study can be used to ascertain the attitudes of very young children toward a variety of toys

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Projective Techniques◦ The approach of analyzing reactions to partially

structured stimuli involves asking respondents to react to or describe in some fashion,

an incomplete, vague stimulus

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To evaluate performance on objective tasks, respondents are asked to complete an supposedly objective, well-defined task

The nature of their performance is then analyzed to infer their attitudes

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Monitoring physiological responses is based on the premise that a person's emotional reactions to a stimulus will be accompanied by corresponding involuntary physiological changes

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This method involves asking respondents relatively direct questions concerning attitudes toward whatever is of interest to the researcher.

The questions are typically in the form of rating scales on which respondents check off appropriate positions that best reflect their feelings

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A graphic rating scale presents a continuum, in the form of a straight line, along which a theoretically infinite number of ratings are possible

Example: Indicate your overall opinion about eBay by placing a mark at an appropriate position on the line below.

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VeryBad

VeryGood

Measurement scales that allow a respondent to register the degree (or amount) of a characteristic or attribute possessed by an object directly on the scale.

Six main types of rating scales:1. Category scale2. Semantic differential scale3. Stapel scale4. Likert scale (Summated ratings scale)5. Constant sum scale6. Graphic scale

A rating scale which the response options provided for a closed-ended question are labeled with specific verbal descriptions.

Example: Please rate car model A on each of the following dimensions:

Poor Fair Good V. good Excellent a) Durability [ ] [ ] [ ] [ ][ ]b) Fuel consumption [ ] [ ] [ ] [ ][ ]

Characteristics: Response options are still verbal descriptions. Response categories are usually ordered according to a

particular descriptive or evaluative dimension. Therefore scale has ordinal properties. However, researchers often assume that it possesses interval

properties => but this is only an assumption.** One special version is the Simple category scale.

• A category scale with only two response categories (or scale points) both of which are labeled.

Example: Please rate brand A on each of the following dimensions:

poor excellenta) Durability [ ] [ ]b) Fuel consumption [ ] [ ]

A rating scale in which bipolar adjectives are placed at both ends (or poles) of the scale, and response options are expressed as “semantic” space.

Example: Please rate car model A on each of the following dimensions:Durable ---:-X-:---:---:---:---:--- Not durableLow fuel consumption ---:---:---:---:---:-X-:--- High fuel consumption

Characteristics1. The scale has properties of an interval scale.2. Sometimes descriptive phrases are used instead of

bipolar adjectives, especially when it is difficult to get adjectives that are exact opposites

3. It is often used to construct an image profile.

A simplified version of the semantic differential scale in which a single adjective or descriptive phrase is used instead of bipolar adjectives.

Characteristics1. The scale measures both the direction and

intensity of the attribute simultaneously.2. It has properties similar to the semantic

differential.

Model A-3 -2 -1 Durable Car 1 2 3-3 -2 -1 Good Fuel Conaumption 1 2 3

A rating scale in which respondents divide a constant sum among different attributes of an object (usually to indicate the relative importance of each attribute).

Assumed to have ratio level properties.

Example: Divide 100 points among the following dimensions to indicate their level of importance to you when you purchase a car:

Durability Fuel Consumption Total 100

Any rating scale in which numbers rather than semantic space or verbal descriptions are used as response options.

Examples: Poor

Excellent Durability 1 2 3 4 5 6 7

Durable 1 2 3 4 5 6 7 N. Durable

Rating scales in which respondents rate an object on a graphic continuum, usually a straight line.

Modified versions are the ladder scale and happy face scale.

Characteristics1. The straight line scale has ratio level

properties.2. The ladder and happy face scales have

properties depending on the labeling option chosen – whether all response categories are labeled (ordinal properties) or only the scale end-points are labeled (interval properties).

A multiple item rating scale in which the degree of an attribute possessed by an object is determined by asking respondents to agree or disagree with a series of positive and/or negative statements describing the object.

Example:Totally

disagree Disagree Neutral AgreeTotally agree

a) Shopping takes much longer on the Internet [ ] [ ] [ ] [ ] [ ]b) It is a good thing that Saudi consumers have the opportunity to buy products through the [ ] [ ] [ ] [ ] [ ]c) Buying products over the Internet is not a sensible thing to do [ ] [ ] [ ] [ ] [ ]

Attitude toward buying from the Internet

The following procedure is used to analyze data from Likert scales:

1. First, weights are assigned to the responses options, e.g. Totally agree=1, Agree=2, etc

2. Then negatively-worded statements are reverse-coded (or reverse scored). E.g. a score of 2 for a negatively-worded statement with a 5-point response options is equivalent to a score of 4 on an equivalent positive statement.

3. Next, scores are summed across statements to arrive at a total (or summated) score.

4. Each respondent’s score can then be compared with the mean score or the scores of other respondents to determine his level of attitude, loyalty, or other construct that is being measured

Note that the response for each individual statement is expressed on a category scale.

Hard to attach a verbal explanation to response

Visual impact, easy for poor readers

Choose a visual picture 8. Graphic scale-picture response

No standard answers Visual impact, unlimited scale points

Choose a point on a continuum

7. Graphic scale

Endpoints are numerical, not verbal.

Easier to construct than semantic differential

Choose point on scale with 1 center adjective

6. Stapel scale

Difficult for respondents with low education levels

Scale approximates an interval measure

Divide a construct sum among response alternatives

5. Constant sum scale

Bipolar adjectives must be found, data may be ordinal, not interval

Easy to construct, norms exist for comparison, e.g. profile analysis

Choose points between bipolar adjectives on relative dimensions

4. Semantic differential and numerical scales

Hard to judge what a single score means

Easiest scale to construct Evaluate statements on a 5-point scale

3. Likert scale

Ambiguous items, few categories, only gross distinction.

Flexible, easy to respond Indicate a response category

2.Category scale

1. Simple attitude scaling

Disadvantages Advantages Subject must:Rating Scale

Characteristics Different Types of Rating Scales

1. Whether to use single or index measure.2. Whether to use a ranking, sorting, choice, or

rating scale.3. Whether to use monadic or comparative scale.

• Monadic rating scale is one in which respondents evaluate an object in isolation

• Comparative scale is one in which the object is evaluated in relation to other objects

• Construction and labeling is different for monadic and comparative scales

4. Whether to use category labels or not.5. If the decision is to use category labels, what

labels to use.

6. Number of response options (scale categories) to use, i.e whether to use 2, 3, 4, 5, etc response categories• In general, the larger the number of categories the

more sensitive the scale is; but also the more difficult it is for respondents to answer

7. Whether to use balanced or unbalanced scale.• A balanced scale has an equal number of points to the

left and right of a mid-point. An unbalanced scale has more response options on one side than the other

8. Whether the scale should force choice among the response categories, i.e should the scale contain a “neutral” or “don’t know” category.

Validity Content validity Construct validity Predictive validity

Reliability Test-retest reliability Split-half reliability

Sensitivity

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The validity of a scale is the extent to which it is a true reflection of the underlying variable it is attempting to measure

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Face validity or content validity is the extent to which the content of a measurement scale seems to tap all relevant facets of an issue that can influence respondents’ attitudes

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Construct Validity is the nature of the underlying variable or construct measured by the scale

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Predictive Validity refers to how well the attitude measure provided by the scale predicts some other variable or characteristic

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Reliability measures how consistent or stable the ratings generated by the scale are likely to be

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Test-Retest Reliability measures the stability of ratings over time and involves administering the scale to the same group of respondents at two different times

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Split-Half Reliability measures the degree of consistency across items within a scale and can only be assessed for multiple-item scales.

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Sensitivity focuses specifically on its ability to detect subtle differences in the attitudes being measured

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