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# Statistica measurements, questionnaire types, and sampling

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Differentiate among the four type of measurement scales, and tell me the type of information.

the advantage and disadvantages of open-ended questions and closed ended questions.

Distinguish among a systematic sample, a cluster sample, and a stratified sample. Give example of each.

Explain how the determination of sample size is a financial, statistical, and managerial issue.

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#### Solution Preview

Differentiate among the four types of measurement scales, and tell me the type of information.

Currently, the most common types of measurement scales, namely nominal, ordinal, interval and ratio.

Nominal
Nominal comes from the Latin root nomen meaning name. Nomenclature, nominative, and nominee are related words (Andrews University).
Examples
Changing Minds.Org and Dwikat (2011) gave us these examples of nominal data:
"Employee ID numbers, eye color, sex (male, female), the number pinned on a sports person, a set of countries."

Ordinal
Blacksacademy (2001) defines ordinal data as "measures of physical quantities that can be ranked. For example, the variable X could measure the number of days individuals have been subject to a special diet; the variable Y could measure the position of those individuals in a race. Here, it is meaningful to ask how does the position of an individual, that is his rank, in terms of values of X correlate with his position, or rank, in terms of Y".
Examples
The first, third and fifth person in a race. (Changing Minds.org)
Pay bands in an organization, as denoted by A, B, C and D. (Changing Minds.org)

Interval
Schwarz (2010) defines interval data as "ordered, constant scale, but no natural zero".
UNESCO suggested that "interval data cannot be multiplied or divided".
Examples
My level of happiness, rated from 1 to 10. (Changing Minds.org)
Temperature, in degrees Fahrenheit. (Schwarz, 2010)

Ratio
Schwarz (2010) identified Ratio as "continuous positive measurements on a nonlinear scale".
"A typical example is the growth of bacterial population (say, with a growth function AeBt.). In this model, equal time intervals multiply the population by the same ratio. (Hence, the name ratio - scale)". (Schwarz,2010)
"Ratio data can be multiplied and divided because not only is the difference between 1 and 2 the same as between 3 and 4, but also that 4 is twice as much as 2." (Changing Minds.org)
Example (Changing Minds.org)
A person's weight
The number of pizzas I can eat before fainting

The advantage and disadvantages of open-ended questions and closed ended questions.

Colorado State University (2011) cites the advantages of open-ended questions:
"1. Open-ended questions allow respondents to include more information, including feelings, attitudes and understanding of the subject. This allows researchers to better access the respondents' true feelings on an issue. Closed-ended questions, because of the simplicity and limit of the answers, may not offer the respondents choices that actually reflect their real feelings. Closed-ended questions also do not allow the respondent to explain that they do not understand the question or do not have an opinion on the issue.

2. Open-ended questions cut down on two types of response error; respondents are not likely to forget the answers they have to choose from if they are given the chance to respond freely, and open-ended questions simply do not allow ...

#### Solution Summary

This solution differentiates and gives examples of the four type of measurement scales. It also identifies the advantages and disadvantages of open-ended questions and closed ended questions. Systematic sample, a cluster sample, and a stratified sample were also discussed and examples of each were given.

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