Introduction (Science, Statistics and Measurement Scales) : Part -1

   Hello friends, This is my first article on my blog. From this article, I am going to start from the very basic of Statistics to the achievable highest level and will explain each and every concepts of Statistics using R and python. There will be some intoductory articles that will help you in understanding the concepts frequently used in Statistics. This is Part - 1 of introdcutory articles. Now, it's time to dive into the article 😊 

Aim of Article

• Definition of Science

• Definition of Statistics

• Concept of Measurement Scales

• Nominal Scale

• Ordinal Scale

• Interval Scale

• Ratio Scale

What is Science

   The following is the very basic definition of Science and I think that you have already read it in your intermediate class -

A well – organized , structured and systematic study of any subject is known as Science.

  

  There are several branches of Science and they are commonly divided into four major groups as follows –

• Formal Science : Mathematical Science(Mathematics & Statistics), Computer Science etc. 
• Natural Science : Physical Science, Chemical Science, Life Science
• Social Science : History , Geography , Poilitics etc. 
• Applied Science : Applied Mathematics , Applied Statistics , Applied Physics 

 

If you are interested to know about the above mentioned sciences in details, read here. 

What is Statistics

Statistics is a mathematical science pertaining to the Collection, Presentation, Analysis and Interpretation of data. OR, Statistics is science of data ,i.e., well – organized and systematic study of data is known as Statistics.

Now question arises – What is data ?

In Statistics, Any information available on an individual (or group of individuals) is known as data. 

           For Example : 

• If I measure my (an individual) weight, say 62 kg , then it is weight information available on an individual (me)  and hence is a data. 
• If I measure the average weight of students of a class (group of individuals), say 52 kg, then it is weight information available on a group of individuals (students of a class). 

Note – 

• Here it must be noted that individual may be anything (living or non – living). For Example – we can collect data on the performance (in terms of production per day) of a particular machine.
• In second example, I have used a term average height. If you know the meaning of this term then it is fine, otherwise, just leave it here. I'll explain you in upcoming articles.

Next question arises – How many types of data in statistics ? 

Well, I'll give the answer but to get better understanding of types of data, you must understand a new concept which is Measurement Scales used in Statistics.

What are Measurement Scales

Generally, when one hears the term measurement, they may think in terms of measuring the length of something (say, a rod) or measuring a quantity of something. This represents a limited use of term measurement. 

In Statistics, the term measurement is used more broadly and is more appropriately termed as measurement scales. Measurement scales refer to ways in which data are defined and classified. Each measurement scale has certain properties which in turn determines the appropriateness for use of certain graphical and numerical statistical tools.

For Example – If I have data on ordinal scale, it suggests the use of Bar or Pie chart to represent the given categorical data.

Note – In the above example, I have used certain new terms like – 

• Ordinal scale – One of the types of measurement scales (will be discussed later). 
• Bar or Pie chart – Graphical tools of statistics (will be discussed later). 
• Categorical data – Data which represents a category like male or female (sex of a person ) etc. 

Now, I am going to discuss about different types of measurement scales.

There are four types of measurement scales as follows – 

• Nominal Scale
• Ordinal Scale 
• Interval Scale
• Ratio Scale 

1. Nominal Scale

It is a measurement scale in which data, available on a characteristic, are used only to identify any individual (or group of individuals) by means of identifiers, names,  categories  or  numbers (that have no value (other than differentiating individuals) at all, that means these numbers are not eligible for mathematical operations, like addition, substraction, multiplication or division)

For Example – Suppose in your classroom , there are two students whose data are given in the following table –

All the data available in the above table are in Nominal measurement scale. Why ? 

Because all the information (data) available on characteristics (Sr. No., Name, Gender, Mobile No) in the above table are used,  only to identify an individual (person). 

Moreover, Sr. No. and Mobile No. are representing numbers but that have no value at all. These numbers are not eligible for any mathematical operations. Addition, substraction or any other mathematical operations on two mobile numbers or serial numbers is meaningless.

2. Ordinal Scale

It is a measurement scale in which data, available on a characteristic, can be sorted/ordered from lowest (or highest) to highest (or lowest). Moreover, such data also identify any individual (or group of individuals) by means of  identifiers, names, categories or numbers (that have no value (other than differentiating individuals) at all, that means these numbers are not eligible for mathematical operations, like addition, substraction, multiplication or division)

For Example – Suppose in your classroom , there are three students whose data are given in the following table –

The data available in second column of the above table are in ordinal scale. Why ? 

Because these data (First (1), Second (2), Third (3)) can be sorted/ordered as follows – 

First (1) > Second (2) > Third (3)

Moreover, the data (First (1), Second (2), Third (3)) in second column of the above table identifies Ram, Sita and Lakshman respectively. 

Also, the rank data (1, 2, 3) are numbers but that have no value at all. These numbers are not eligible for any mathematical operations. Addition, substraction or any other mathematical operations on two ranks is meaningless.

3. Interval Scale

It is a measurement scale in which data, available on a characteristic, can be equally spaced  that means a difference of one unit has the same meaning for all data values.  

Moreover, This scale has no absolute/true zero, that means, zero does not indicate the absence of characteristic of an individual (or group of individuals). 

Also, such data can be sorted and also identify any individual (or group of individuals) by means of numbers only and these numbers are eligible for addition and substraction only, and not eligible for comparison that means multiplication or division of data values is meaningless.

For Example – Suppose we have data on two different laboratory in respect of temperature (in celsius ) as follows –

The data available in the third column of the above table are in Interval measurement scale. Why ?

Because 

• These temperature data (20 degree, 40 degree) in celcius can be evenly spaced because - "The difference between 20 degree and 21 degree is same as the difference between 40 degree and 41 degree. The difference is of 1 degree." This indicates that a difference of one unit has the same meaning for all data values. 

• Further, if I consider that the temperature of Lab-1 is 0 degree Celsius, then does it mean that the temperature (characteristic of Lab) is absent in Lab-1 ? No, because there is still the presence of temperature in Lab-1 that is 0 degree Celsius and hence, no absolute/true zero in this case. 

• Moreover, temperature data (20 degree, 40 degree) in celcius can be sorted (20 < 40), indentifies Lab-1 and Lab-2 respectively, and are eligible for addition and substraction only. We may calculate temperature difference but can't calculate how many times a lab temperature is than the other ? Actually, this question is meaningless in the sense that 40 degree celcius is not two times as hot as 20 degree celcius. Hence, comparison of temperature data in celcius can not be done.

So temperature (in Celsius) is an example of Interval Scale.

Note : 

• Interval scale data may take negative values. Example : - 5 degree celcius temperature

• But test score data (negative marking not allowed) are interval scale data but do not take negative values. On the other hand, test score data (negative marking allowed) are also interval scale data but take negative values.

Test score data are interval scale data. Why ? Because true zero does not exist in this case, that means zero score does not indicate that student/examinee has complete lack of score. "Student has scored zero". Moreover, all other properties like equal spacing, sorting, identifying an individual, eligibility for addition or substraction holds. But comparison can not be done, why ? Suppose Ram and Shyam has scored 40 and 80 marks in a test respectively. Does it mean that Shyam's mark is two times as good as Ram's mark ? No, the statement would make no sense at all. That's why comparison of two test scores can not be done. All that can be said is that Shyam scored more than Ram in the test and how much ? The answer is 40 marks (It can be said because addition or substraction of marks holds, i.e., 80 - 40 = 40).

4. Ratio Scale

It is a measurement scale in which data, available on a characteristic, can be compared that means ratio of any two data values is meaningful and equally spaced that means a difference of one unit has the same meaning for all data values.

Moreover, This scale has absolute/true zero, that means, zero indicates the absence of characteristic of an individual (or group of individuals). 

Also, such data can be sorted and also identify any individual (or group of individuals) by means of numbers only and these numbers are eligible for addition, substraction, multiplication or division.

 

For Example – Suppose in your classroom, data on the weight of two chair is as follows - 

 

The data available in the second column of the above table is in Ratio measurement scale. Why ?

Because 

• These weight data (80, 40) can be compared as - "80 kg is two times as heavy as 40 kg." It means, There is meaning to the ratio of 80 to 40.

• These weight data (80, 40) can be evenly spaced because - "The difference between 40 kg and 41 kg is same as the difference between 80 kg and 81 kg. The difference is of 1 kg." This indicates that a difference of one unit has the same meaning for all data values. 

• Further, if  I consider that the weight of chair - 2 is 0 kg, this indicates that chair is weightless, that means, the weight characteristic of chair is absent and hence, there is absolute/true zero in this case.

• Moreover, Weight data (80, 40) can be sorted (40 < 80), indentifies Chair-1 and Chair-2 respectively, and are eligible for mathematical operations. We may calculate Total weight, Weight difference, How many times heavy a chair is than the other ?

 

So weight is an example of Ratio Scale.

Note : Ratio scale data never take negative values, that's why lowest possible value for ratio scale data is zero.

Trick : Comparison of data values can be done if and only if absolute/true zero exists.

I have a question for you. Suppose you have data on Temperature (in Kelvin), then what is its measurement sacle ? Give answer in comment box with logical argument. Well, I'll give you its explanation in upcoming articles, till then try to find out its answer and logic both 😁

That's all about measurement scales in this article.  

So, I want to stop here in this article. In next article we'll discuss some more concepts that are frequently used in Statistics. Till then, Good Bye !

Happy Learning ! 😊

If you find any mistake or have any suggestions,  just let me know using Suggestion Form given below (for mobile users) or in sidebar (for laptop users). Thank you in Advance ! 😊

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