Measurement means assigning numbers or other symbols to characteristics of objects according to certain pre-specified rules.

One-to-one correspondence between the numbers and the characteristics being measured.

The rules for assigning numbers should be standardized The rules for assigning numbers should be standardized and applied uniformly.

Rules must not change over objects or time.

1. Identity

2. Magnitude

3. Equal Interval

4. Absolute Zero

7 38

ScaleNominal Numbers

1 Assignedto Runners

Ordinal Rank Order1+2 of Winners

Interval Performance1+2+3 Rating on a

0 to 10 Scale

Ratio Time to Finish1+2+3+4 in Seconds

Thirdplace

Secondplace

Firstplace

8.2 9.1 9.6

15.2 14.1 13.4

Examples

Scale Basic Characteristics

Common Examples

Marketing Examples

Nominal Numbers identify & classify objects

Social Security nos., numbering of football players

Brand nos., store types

Percentages, mode

Chi-square, binomial test

Ordinal Nos. indicate the relative positions

Quality rankings, rankings of teams

Preference rankings, market

Percentile, median

Rank-order correlation,

Permissible Statistics Descriptive Inferential

relative positions of objects but not the magnitude of differences between them

rankings of teams in a tournament

rankings, market position, social class

median correlation, Friedman ANOVA

Ratio Zero point is fixed, ratios of scale values can be compared

Length, weight Age, sales, income, costs

Geometric mean, harmonic mean

Coefficient of variation

Interval Differences between objects

Temperature (Fahrenheit)

Attitudes, opinions, index

Range, mean, standard

Product-moment

Scales and Measurements :A scale is a technique to measure some thing. Scaling is used in ordering a series of items along sort of continuum. – they are methods of turning a series of qualitative facts into a quantitative series

Measurements are yardsticks – Measurement in research consists of assigning numbers to in research consists of assigning numbers to empirical events in compliance with a set of rules –Hence, measurement is a three part process(1) Selecting observable empirical events (2) Developing a set of mapping rules ie a scheme for assigning numbers (3) Applying mapping rule to each observation of that event. Example of studying people who attend a auto show

Different Scales :1. Nominal Scale : It is simply a system of

assigning number symbols to events in order to labelthem – example: assigning numbers to football players inorder to identify them – just for convenience – noquantitative value – can not come out with a meaningfulvalue – We use Mode as the measure of Central Tendency– eg. classifying the residents of a city according toreligious preferences.religious preferences.

2. Ordinal Scale : The lowest level of the ordered scale that is commonly used is the ordinal scale –This scale places events in order – Eg. Rank orders represent ordinal scales – a student’s rank in his graduation class involves the use of ordinal scale – these scales have no absolute values – all that we can say is that one person is higher or lower in rank on the scale –

Ram’s rank is 10 and Mohan’s is 40 – what do youconclude? – If a > b and b <c, then a>c – just mentionsgreater than or less than , without stating how muchgreater or less - the appropriate method of centraltendency is median

3. Interval Scale: It has the power of nominal andordinal scale plus one additional strength, the concept ofequality of intervals – eg. the interval between 1 and 2equality of intervals – eg. the interval between 1 and 2equals the difference between 2 and 3. In this case theintervals are adjusted in terms of some rule that hasbeen established as a basis for making the units equal –these scales can have an arbitrary zero – it lacks a truezero – The Fahrenheit scale is an example of an intervalscale – Mean is the appropriate measure of centraltendency

4.Ratio Scale : It incorporates all the powers of previous three Scales.

They have an absolute or true zero of measurement –Eg., measurement of physical dimensions like height,weight, distance and area- geometric mean orharmonic mean are the measures of central tendency

Sources of error in measurement :1. Respondent2. Situation2. Situation3. Measurer – behaviour, style and looks of investigator

may encourage or discourage certain replies from the respondent

4. Instrument – eg. use of complex words, ambiguous meaning etc.

http://cdn.information-management.com/media/assets/article/1023904/few_fig3.gif

http://star.gise.ntnu.edu.tw:8080/www/itemAnalysis/img006-2.gif

http://www.ams.sunysb.edu/~finchs/ams315/fall99/lectures/ams315l2/img020.gif

http://bistop.files.wordpress.com/2011/12/defined-name-assign.jpg

Rank order scaling questions allow a certain set of variables to be ranked based upon a specific attribute or characteristic.

http://www.questionpro.com/a/showArticle.do?articleID=survey-questions

“most important” to “least important,”

Ranking questions are best to use when all the choices listed should be ranked

according to a level of specification (e.g. level of importance).

If you have a question in which you need the respondents to indicate what items are the “most important” to “least important,”

then you can set up a ranking question (Waddington 2000).

http://s3.amazonaws.com/SurveyMonkeyFiles/SmartSurvey.pdf

the order of the values is what’s important and significant, but the significant, but the differences between each one is not really knowncannot quantify–how much better it is.

In each case, we know that a #4 is better than a #3 or #2, but we don’t know–and cannot quantify–how much better it is.

http://www.mymarketresearchmethods.com/types-of-data-nominal-ordinal-interval-ratio/

** pronounced 'lick-urt' with a short "i" sound

Rating type questions are used when surveying the frequency of something like behavior or attitude.

It is best to present the rating scale in a logical or consistent order.

Therefore, it makes sense to order the ranking or rating choices from low to high (e.g. Strongly Disagree to Strongly Agree

http://s3.amazonaw

s.com/SurveyM

onkeyFiles/SmartSurvey.pdf

(e.g. Strongly Disagree to Strongly Agree going from left to right).

http://s3.amazonaw

s.com/SurveyM

onkeyFiles/SmartSurvey.pdf

It is an interval scale because it is assumed to have equidistant (equal distance) points between each of the scale elements. This means that we can interpret differences in the distance along the scale. We contrast this to an ordinal scale where we can only this to an ordinal scale where we can only talk about differences in order, not differences in the degree of order.

When you are asked to rate your satisfaction with a piece of software on a 7 point scale, from Dissatisfied to Satisfied, you are using an interval scaleit is important that the space between each it is important that the space between each option, whether it's a number range or a feeling range, are equal.

scales asking about agreement strength, likelihood or satisfaction (i.e. very unsatisfied, unsatisfied, neither satisfied nor unsatisfied, satisfied, very satisfied).

Similar to ordinal, but the intervals between the values of the response options are evenly spaced

Can be used for any quantitative variable Measures variables that fall into logical ranges

Example: What was your undergraduate GPA upon graduation?a) 3.5-4.0 b) 3.0-3.49 c) 2.5-2.99 d) 2.0-2.49

http://www.virginia.edu/processsimplification/resources/survey_design.pdf

Interval scales show the order of things, but with equal intervals between the points on the scale.

Thus, the distance between scores of 50, 51, 52, 53 and so forth are all assumed to be the same 53 and so forth are all assumed to be the same all along the scale. Test scores are usually treated as interval scales in language research.

Scales based on Likert items are also commonly treated as interval scales in our (education/social research) field.

http://jalt.org/test/PDF/Brown34.pdf

Ratio scales differ from interval scales in that they have a zero value and points along the scale make sense as ratios. For example, a scale like age can be zero, and it makes sense to think of four years as twice as old as two yearsthink of four years as twice as old as two years

http://survey.cvent.com/blog/cvent-survey-blog/guide-to-the-five-types-of-survey-questions

When respondents are asked to tell us some physical measure, such as income, years of education, or how long their phone call was on hold, these are ratio scale questions. The data they provide have a true zero. (On an interval scale, a zero response option is simply arbitrary. Zero income, for example, is real.)

Frequently, we solicit ratio data with what appears to be an ordinal scale with response options presented in ranges, such as if we were to ask for the number of years of education the person had achieved, asking the respondent to check one of the following options: 1) 1 to 12 years, 2) high school degree, 3) associates degree, 4) bachelors degree, 5) graduate associates degree, 4) bachelors degree, 5) graduate degree. While the question looks ordinal, we could treat the data as ratio in our analysis.

Why present ranges? First, it's faster for the respondent to answer the question,

lowering respondent burden. Second, it's less invasive to ask someone to check an income

range, for example, then to ask them their annual income. Would you tell a stranger your income level? Probably not, but you might be willing to check a box that says your income is $50,000 to $75,000 per year.

http://www.greatbrook.com/survey_question.htm

http://www.mymarketresearchmethods.com/wp-content/uploads/2012/11/summary-of-data-types.png

Nominal: mode crosstabulation - with chi-square, etc. Ordinal: use non-parametric statistics, i.e. Median and mode, rank order

correlation, non-parametric analysis of varianceModelling techniques can also be used with ordinal data.

Interval: Interval scale data would use parametric statistical techniques:

http://efox.cox.smu.edu/m

ktg3342/dataanalysis.pdfhttp://w

ww

.csse.monash.edu.au/~

smarkham

/resources/scaling.htm

techniques: Mean and standard deviation

Correlation - rRegressionAnalysis of varianceFactor analysis

Cronbach analysis Plus a whole range of advanced multivariate and modelling

techniques

Ratio: variables which are ratio scaled include weights, lengths and times. virtually all statistical operations can be performed on ratio scales

http://efox.cox.smu.edu/m

ktg3342/dataanalysis.pdfhttp://w

ww

.csse.monash.edu.au/~

smarkham

/resources/scaling.htm

Matters in the slides are collected from various sources available in internet.