Question

what is a measurement, how does it relate to statistics?

Answer 1

The word "measurement" in daily life, sound as we are measuring something like a piece of cloth or distance from earth to moon, but when we talk of this word in statistics, it comes up with a very broader use and is more appropriately termed scales of measurement. It refers to a way of defining and categorizing numbers and variables. Different scale of measurements possess certain properties which determines the appropriateness for using a particular statistical analyses.

There are 4 scales of measurement:

a) Nominal - Names doesn't mean anything. Just used as identifiers or names. For example, Coding 1 as keyboard, 2 as mouse and 3 as printer and saying 1 and 2 are input devices and 3 is an output device. It just represent category of data.

b) Ordinal - This is used to represent an ordered series of relationship. For example: If I say, How would you rate my answer from 1 to 10, from 1 being the best and 10 being the worst.

We can easily say that rating of 8 is better than that of 6 or 4, but we can't say that rating of 8 is two times good compared to 4. Also, we can't say that rating of 0 means absence of rating. Hence, there is an absence of absolute zero and ratios in this measure as in nominal.

c) Interval - It represents quantity and has equal units but doesn't consider zero as an absence of the thing. The best example is temperature where zero degree fahrenheit doesn't mean the absence of temperature.

d) Ratio - It is the most complete scale of measurement. It represents quantity ansd quality of units. For example, Weight. Weight of zero will mean the absence of weight, weight of 80kg is twice as heavy as 40kg, etc.

However, statistics refers to numerical facts collected systematically with a purpose.

Lets have a illustration of couple of examples used above....

How would you rate me on the scales of 1 to 10, 1 being the worst and 10 being the best. It is an example of ordinal scale. But after the ratings of 50 questions are received, I analysed it to find out that the average rating I have received is 9.2. It is a statistic.

Lets' jump back to temperature example. The temperature of NYC is 32degree C at this time. This is a measure of Interval scale. But the maximum temperature in this summers in India broke all records and touched 47degree C is a statistic.

A batting average in cricket is another example of statistic which reflects his ability to score runs.

What these examples have in common is that they are organising, describing and summarising a set of measurement.

And thats' how measurement is related to statistics.