Friday, August 30, 2013

Scales for measurement of variables

Scales for measurement of variables
To measure is to assess, quantify, analyze or appraise. It is to discover the extent, dimensions, capacity and quantity of any physical object.
Educational research deals mainly with ideas. “How sound is an idea” is parallel to assessing “how well you like a song, a painting or personality of your manager”. While physical objects are measured directly, ideas or concepts are measured with the help of an operational definition. Four scales are used to measure any object or to quantify any concept or idea or properties. These are discussed as follows:
It is just a label having no intrinsic value or quality. It cannot be used in grading or ranking, There are no overlaps and nominal scale are mutually exclusive. One can be either Muslim or non-Muslim, not both at the same time as it requires an item to be placed in one and only one class. It is used for counting or cross-tabulation.
Hair could be black or grey, blood can be A, B, O or AB. In cricket, there is left arm or right arm spinners.
It is used for obtaining personal data and is usually exhaustive to include all categories or segmentation.
It used for ranking, rating or grading. It can show best to worst status or first to last preference. But distance between two ordinal scales is not the same. Income level of poor, middle and rich class are like less than Rs.10,000, between Rs.11,000 to Rs.50,000 and 51,000 and above. The distances are 10,000, 39,000 and infinitive respectively.

It is evident that ordinal scale can rank some items in an order like less than or more but not “how much more”
It is more powerful than nominal and ordinal as it not only orders or ranks or rates but also shows exact distances in between. But it does not start from zero. If there is zero like zero temperature is not natural but arbitrary as 0 degree does not mean any temperature. Likewise, year 0 in a forecast is the end of construction year.
This scale is used in addition or subtraction of scale value to calculate mean, range, variance, standard deviation, correlation and regression.
Difference between interval and ordinal scale:
Ordinal scale only ranks but does not measure difference between the two ranks like “satisfactory” and “not-satisfactory”. Interval scale not only ranks but also gives exact distance between them by assigning a value. Difference in temperature of 20 degree and 40 degree is 20 but 40 is not double hot than 20.
This scale can perform all functions. It can show all mathematical and geographical indicators. It is useful when exact figures are required in objective matters are required.
If a person is drawing a salary of Rs.20, 000 and another Rs.40,000, it can be said that the latter is getting double the salary of the former.

Classification but no order, distance or origin 
Classification but order but no distance or unique origin
Classification, ordered and distance but no unique origin
Classification, order, distance and unique origin
Determining of equality
Determination of greater or lesser value
Determination of equality of intervals or differences
Determination of equality of ratios
Only Label 
Ranks, Rating and Grade 
equal grouping 
Weight, height 
Gender (male, female)
Doneness of meat, (well, medium well, medium rare, rare)
temperature in degrees
Age in years
Frequency Distribution
Addition/subtraction but no multiplication or division
All functions
Black & While
personality measure
Can say no measurable value like zero sales 
Levels, one-star & 4-star
Mean, range, variance, standard deviation 
Annual Income