Quant analytics: define and differentiate between nominal, ordinal, interval and ratio scale clearly with examples.

i am very confused about these measurement scales.

==i want quick reply of my question.

==Google to the rescue…http://www.usablestats.com/lessons/noirhttp://en.wikipedia.org/wiki/Level_of_measurementhttp://www.statisticalanalysisconsulting.com/nominal-ordinal-interval-ratio-stevens-typology-and-some-problems-with-it/ and 1000s more…

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===There are a variety of naming conventions for numbers representing mathematicians, philoshopers and computer language. But the concepts are aligned. Here is my explanation from an engineering view.

Nominal (name) has no quantitative relation. In a rock collection, there is the first rock you got, then the second, third, etc. But, the numbers are just names and do not represent any quantity related to properties of the rock. The names could have well been “A”, “B”, “C”, or “alpha”, “beta”, “gamma”. We name trial runs in randomized sequence. The “1” in the name “Trial 1” has no relevance to the flow rate, the impact, the difficulty, the benefit etc.

Ordinal (order) means sequence or rank. A runner comes in 1st place, or 2nd, or 3rd, etc. in a race. Here the number is a measure of placement, or goodness, or desirability, and relates to some property of the event. Or property of an item (largest, second largest, … brightest, second brightest, …) . Ordinal numbers reveal order. But they do not indicate a relative or proportional quantification of the property. First and second may be nearly tied, and far ahead of third. Alternately, first may be far ahead of second and third. Ranking does not indicate relative relationship.

Integers are the counting numbers, the whole numbers, the indications of the number of whole items. They can only have integer values. They can only have values that exist at intervals of unity.

Integers are a type of interval number. But the interval could be half or quarters or 16ths. The Westminister Clock chimes on the quarter hour. Its interval is 1/4-hr. Or is it 15-min? Either way the time interval is not unity. In bit representation of computer storage, an 8-bit storage location might be 00101101. The discrete interval is 1-bit. But representing a display range of 0 to 100% the 2^8 possible numbers in an 8-bit storage have a 1-bit discretization interval which represents a (100%-0%)/2^8 = 0.390625% interval. Observing such a number display, you would see all reported values as multiples of the 0.390625% interval. I call this discretization error or uncertainty. Look at a table of viscosity or table of t-statistic critical values, and you will find that the table does not report infinite numbers for each entry. It may report one decimal digit inwhich case the discretization interval is 0.1. Or 4 decimal digits, in which case the discretization interval is 0.0001.

We often imagine that properties of space, time, mass, temperature, are continuous. That the property can be divided into infinitisimal intervals. Real Numbers permit having infinite decimal places. The ratio of 1 to 3 is 0.3333333… But on an atomic view, mass is not continuous. If you want to increase the amount of water in a glass, the smallest increment you can add is one molecule of water. Effectively, on a large engineering scale the continuum view seems valid, and we consider the measurements of peroperties to be real numbers or continuum, with the interval effectively zero

From a mathematics view, real numbers are rational (ratio) and can be represented by a ratio of integers, or irrational and cannot be represented by a ratio of integers. When the decimal part has a repeated pattern the number is rational. If there is no repeated pattern (sqrt of 2, Pi, e, gamma, etc.) the real number with infinite decimal digits is irrational.

Real numbers (rational or irrational) and interval numbers (which includes integers) are directly related to the property of the event or item (time, mass, weight, intensity, value, etc.). As a result real and interval numbers have a ratio or proportional property. If the numerical representation of one event is twice in magnitude as the numerical representation of the other, then the one event has twice the magintude, impact, value, of the other. Real and interval numbers preserve this ratio or proportional relation, making them useful.

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