Video summary
The video introduces the four fundamental scales of measurement—nominal, ordinal, interval, and ratio—as essential concepts in research that determine which statistical analyses are valid for a given variable. Dr. Rashmi Singh explains that every data point collected, whether it be gender, income, or test scores, belongs to one of these specific scales, and this classification dictates the appropriate mathematical operations we can perform on them. Choosing an incorrect scale leads to meaningless results; for instance, calculating an average roll number yields a figure with no practical significance because numbers in that context are merely labels rather than quantities representing magnitude. The hierarchy established by Stevens in 1946 shows how each subsequent level builds upon the properties of the previous one: nominal scales provide only names or categories without any inherent order; ordinal scales add meaningful rank but lack equal distances between ranks, as seen in class grades where an 'A' is higher than a 'B', yet we cannot quantify exactly how much better.
Moving up the hierarchy, interval scales introduce equal intervals between values while still lacking a true zero point, meaning that ratios are not mathematically valid within this framework. Examples provided include temperature measured in Celsius or Fahrenheit and IQ scores; although 20 degrees is numerically twice as high as 10 degrees on an interval scale, it does not imply the object is actually twice as hot because zero here is arbitrary rather than representing a complete absence of heat. In contrast, ratio scales represent the most advanced level by possessing all previous properties plus a true zero that signifies the total absence of the quantity being measured. Variables such as age, height, weight, and exam marks fall into this category, where ratios are meaningful; for example, an 80-mark score is genuinely double a 40-mark score because both represent actual quantities received by the student, unlike temperature or IQ scores where zero does not mean "none."
The video concludes with critical warnings about common statistical mistakes that researchers frequently make when misidentifying these scales. A primary error discussed is treating Likert scale data (e.g., Strongly Agree to Disagree) as interval data; while convenient for analysis, such ordinal responses do not have equal gaps between points and should be analyzed using medians rather than means. Similarly, roll numbers or ID codes are often mistakenly treated as ratio data due to their numeric appearance, but they function purely as nominal labels with no mathematical value. Another significant misconception addressed is the belief that an IQ of 140 represents twice the intelligence of someone scoring 70; since IQ lacks a true zero, such proportional comparisons are invalid. The presenter emphasizes that before conducting any analysis, researchers must correctly identify their data's scale to ensure they apply valid statistics like mode for nominal data, median for ordinal data, and mean with standard deviation only when appropriate interval or ratio scales are used.
Read the full video transcript
Hello I welcome you all once again to my channel
Explore Education I am Doctor Rashmi
Singh Assistant Professor Department of
Education Asistanna Girls TOB College
University of Allahabad At this time I am
going to discuss with you a topic which is
Variant and I have discussed it earlier before but now it is
a new
advanced version of my previous video
that is Scales of Measurement. तो क्या
पढ़ेंगे हम इसमें? In this we will study Nominal
Ordinal Interval and Ratio Scale with
Everyday Examples. This is special in this.
देखिए, व्हाई शुड यू केयर अबाउट दिस?
स्केल्स ऑफ़ मेज़मेंट क्यों पढ़ रहे हैं?
एव्री वेरिएबल यू कलेक्ट इन रिसर्च। Be it
marks, gender, rank, income,
satisfaction rating, any variable
that we collect in research.
बिलोंग्स टू वन ऑफ़ फोर मेज़रमेंट स्केल्स।
वो इन्हीं में से किसी एक मेज़रमेंट स्केल
को बिलोंग करता है। This single choice
decides which statistics you are allowed
to compute and which are meaningless.
यही कि वो किस मेज़मेंट स्केल का है।
This will tell us which statistics we
can apply to it and which we cannot.
कैलकुलेट दी एवरेज ऑफ रोल नंबर्स
एंड द नंबर यू गेट इज़ रियल बट यूज़लेस। अगर
हमने क्या किया कि रोल नंबर हमारे पास है
और हमने क्या किया? If we take their average,
we will get some number but will
it have any meaning? That will be useless. दैट
इज़ व्हाट अ रॉन्ग स्केल डस टू अ होल
एनालिसिस। That's why if we choose the wrong scale,
our entire analysis will go wrong.
So what turns out is that the scale of a
variable decides the statistics you're
allowed to use on it, not the other way around.
It is the scale of the variable that determines
which statistics will be applied and which
we can apply. Correct? तो फोर
स्केल्स में हर बार इनेशन जो है वो
इंक्रीस होती जाती रहती है। मतलब
हायरार्किकल और ये किसने दिया है?
स्टीवेंस ने 1946 में दिया। ईच लेवल कीप्स
एव्री प्रॉपर्टी ऑफ़ द वन बिफोर इट एंड
इट्स वन मोर। जो ईच लेवल है वो नीचे वाले
की प्रॉपर्टी रखता है और उसमें एक जुड़
जाता है। जैसे देखिए यहां से चलते हैं
नॉमिनल सबसे नीचे वाला निम्नतम है स्केल।
इसमें केवल नाम या लेबल होते हैं। ऑर्डिनल
नाम और लेबल तो होंगे लेकिन ऑर्डर जो होगा
वो मीनिंगफुल होगा। इंटरवल नाम भी होगा,
मीनिंगफुल ऑर्डर भी होगा और इक्वल
इंटरवल्स होंगे। And the ratio will also have a name
, an order, an interval, and
a true zero. जैसे समझिए नॉमिनल
मतलब सिर्फ नाम है। अब नाम ऊपर नीचे कहीं
भी है किसी भी ऑर्डर में उससे क्या फर्क
पड़ता है? जब तक अल्फाबेटिकली की बात
नहीं। जैसे जेंडर तो जेंडर मेल फीमेल
लिखिए या फीमेल मेल लिखिए। Blood grows,
right? There is no hierarchy in this. लेकिन
ऑर्डिनल में एक मीनिंगफुल ऑर्डर ऑर्डर है। For
example, instead of class rank first, second, third,
you will write it as first, second, third only.
थ्री टू वन नहीं लिखेंगे। Isn't it? There
are grades. Only A, B, C will do. CBA will not
work.
Interval interval means equal intervals
like temperature, like IQ score
after 10, 20, 30, 40 is equal interval and there is
true zero in ratio, like
temperature in IQ score and there is no true zero in IQ score, it
means 0 degree
centigrade does not mean that there is
no temperature there, it is
assumed that 0 degree and below 0 degree is
minus and above it is plus but
marks age and height have true zero. That
means zero means zero marks, which
means that you have actually
not got any marks. ऐज जीरो मतलब आप पैदा हुए
हैं अभी जस्ट या पैदा नहीं हुए हैं। हाइट
जीरो मतलब कोई कोई हाइट नहीं है।
is null. लेकिन टेंपरेचर में ये शून्य जो है वो
एब्सोल्यूट जीरो नहीं है। 0 degree
centigrade means there
is no temperature there. It's not like that. टेंपरेचर तो है ना
कोई ना कोई। We have assumed the standard value
here to be zero, plus above zero and
minus below zero. Ok? Each scale down this
list can do everything given above. It can plus more.
Meaning it is saying that as we go down, the
nominal is automatically added to the ordinal.
इंटरवल में ऑर्डिनल और नॉमिनल जुड़ा हुआ
है। In ratio, interval, ordinal, nominal are all
connected. You have to pay attention to this.
Let's start with nominal scales:
variables that only name and label categories
in which we only name or label.
There is no order. There is no order here. There is
no ranking. There is
no numeric meaning. Isn't it? There is a
property category of . Only. There is no
group, no order among them.
Equal to not equal to is the only comparison
possible. The only comparison you can make is whether
this is equal to that or not equal to that.
Any numbers used are labels, not
quantities. You can use any number you want to use as a label. For
example,
in education research, if we talk about nominal scale,
such as gender male female or other, blood
group A B A B O, subject stream science
arts commerce. There is no order in this, whether
Science comes first or Arts comes first. These are
just names, roll number, teacher ID code,
class rank. But class rank has a
meaningful order, so it will be
ordinal instead of nominal. Now coming
to ordinal, there are variables with meaning. Meaning, when
order is added to nominal, it becomes ordinal.
Now the order is meaningful, but the
position between them is not equal.
Like sometimes it happens that there is a
difference of 105 marks between the first and second,
but there is a difference of 10 marks between the second and third, so they are
not equal,
but even then, one will be first, the other will be second, the other will be
third. That means, there is an order,
but the interval between the orders is not equal. The
same thing is there in grades, in the Likerd scale,
Strongly Disagree, Strongly Agree,
Socioeconomic Status, Low, Middle, High. So, there is an order in these, that is,
they are nominal
and there is an order between them. And the order has
one meaning; you cannot change that meaning,
like categories can be. Run high to
low order is meaningful but distance between ranks is
not, the distance between them is
not equal in the sense but there is an order, first
and second may be closer than second and
third, that is what I was telling you but not this
scale, now what is not in this is nominal not
ordinal ratio like marks out
of 100 that between 70 and 80 is measurable
so that is ratio not ordinal but like
you can find the ratio of marks between 80 and 70 then
this ratio scale will come, it will
not come ordinal means
what is the scale next to this, ratio sorry interval so
nominal ordinal interval ratio means that
in interval there will be names also, that means there will be rank. There will be
order between the ranks and there will
also be distance between the orders.
Variables with equal meaning have full intervals between
values, but the zero point is
arbitrarily not a true absence of the
quantity. This is saying that there is a variable here
also. There is also an interval between them. The interval
is also equal. But
we have accepted the zero point. That does not mean
that zero does not mean that quantity.
Ok? Like zero is just a reference point.
Ratios are not meaningful here.
Like meaning 20° centigrade is not twice as
hot as 10° centigrade. This does
not mean that 20°C is twice as hot as 10°
C. We are under a delusion.
If we think so then we should
know it right. So if we look at education research,
temperature in Celsius or
Fahrenheit. This will come in interval scale.
IQ scale scores will come in interval scale. The
calendar year will come. Standardized
test scores will be available. That means these are their names only.
Meaning there is some order, some label, there
is nominal as well as ordinal between them, there
is order as well, the distance between the orders is
also equal but zero here
we have accepted it as arbitrary, I think zero does
not mean that there is no intelligence, right, age is
near but if the age is zero then it is
actual zero, it means there is
no age, so what will it be, it will be a ratio, it will
not be an interval, now go ahead, ratio
score scale is the most complete scale, it has
everything, there is name as well, there is order as well, there is rank
after rank, there is order after order, there is
interval as well and there is zero in the interval also.
Meaning None of the Quantity Exists. Meaning there will be
a place, a point
where that magnitude will not be there. So ratios and
differences both make sense here. Like what happened to the
properties? Has everything
interval has plus a true zero as well.
Zero genuinely makes none. If zero
mark means that no mark has been
received. And here the ratio
is meaningful. That means 80 marks
is really double 40 marks. That means double of 40 marks is
80 marks. But
double of 10 degree centigrade is not 20 degree centigrade.
Know this. So if we
look at the example in education research, marks obtained are
based on age, height and weight and age is also double. The
height also doubles. Years of
Teaching Experience. Number of books read,
family income, all these things will happen. Ok?
Correct? Now look at all four side by side.
Nominal Ordinal Interval Ratio.
Look at this, identity, nominal, gender, class,
rank, temperature but also ratio, that is, all four will come
in identity, it is
not nominal in order, it cannot be ranked, hence it is ordinal, it is interval as well as
ratio, equal
intervals means see like this, these four are your
scale of measurement and these are their
qualities, so in identity, category differs,
order can be ranked,
gaps are measurable in equal intervals.
True zero means zero.
Nun. Now he is telling gender that there is
identity in gender but there is no order. There
is no equal interval. There is no true zero.
Class rank has identity and order
but no equal interval. There
is no true zero. Temperature has identity,
order, equal interval but it does
not have true zero. And here in Marx there is
identity, order, equal
intervals and true zero. He will do it like this.
Meaning class rank will come in gender nominal scale. It will
come in ordinal, temperature will
come in interval and marks will come in ratio.
Ok? Now look at the most
important thing, which is the statistical skill you
can use? What is the central tendency
you can report in nominal? Just the
mode and frequency or percentage.
What are the typical inferential tests? Kai
Square. What can I put in the bus ordinal
? You can use median, percentile
and in inferential you can use Mann Vitani u and
Spearman's rho.
You can also calculate the mean in interval. You
can calculate the standard deviation. And typical
inferential tests may involve the p test.
ANOVA may be applied. Pierceness may seem R.
And we can find the mean in the ratio.
Can remove SD. We
can calculate the coefficient of variation. and
All of the Above in the Inferential Test. Meaning all this will definitely
happen. Plus the geometric mean too
because here zero means zero. Ok?
So how to identify a scale in three
questions? Does the variable have a meaningful
order? If there is no order then it will be nominal.
All are the gaps between values
equal and measurable. If the gaps between them
are equal and you can measure. If yes then it is
fine, if not then it will be ordinal. And is there
a true zero. If not, there will be an interval. If yes then there will be a
ratio. In this way you
can understand which variable will
go in which scale. Common Mistakes
Treating Liked Items as Interval Data.
What do we do? Linked items are
considered interval data. Like Strongly Agree
Five Responses Assume Equal Gaps It
in Points Technically it's ordinal data.
But the linked item which comes in the scale of
strongly agree, agree, disagree is actually
ordinal data. There
is no interval. We consider the roll number and ID code as
ratio data. Whereas what
is that? There is an interval. Ok? They look numeric
but they are just nominal. You have a roll number,
right? That is nominal. There is no ordinal either. There
is no ratio either. We
consider it as a ratio. There is no ratio. Computing
a Mean for Ranked Data. What we do is find the
mean of the rank data. You ca
n't average class ranks meaninglessly; use the
median for ordinal data instead. He is saying that do
not take the mean of ordinal data. Find the median. And
what do we do? They often make this mistake.
We think that someone with an IQ of 140 is
double the IQ of someone with 70. But we forget
that this is an interval scale variable.
Not the ratio. Unless the ratio is known,
we cannot find its proportion.
IQ is interval not ratio. There is no true
zero. So ratios don't hold. That means, as
long as we have only age, height, weight and
marks, the meaning of zero in them will be
zero, only then the ratio will be calculated.
Understand it like this. Ratio is the
highest scale of measurement and nominal
ordinal interval all three have
qualifications, categories and space
specificity in it. So we should not make these common mistakes
that students make.
Likert items are not to be treated as interval data.
Roll number and ID code are
not to be considered as ratio data. The mean of the rank data is not to be
calculated. And IQ doesn't have to be doubled and halved.
Because this is an interval, not a ratio.
Ok? So what are the takeaways? Nominal
means just name like gender, blood group,
subject, stream. Only counting is done in this.
Its Only Counts and Mode Makes
Sense. In this only counting can be known
and it can be known who is there how many times. Nothing else will happen
in it. There is
order in the ordinal but the gaps are uneven.
Like rank has been done, grade has been done, liquid
rating has been done. So here we will find the median
, not the mean. There are
equal gaps in the interval but there is no true zero.
Like temperature, IQ, here mean can be
calculated but ratio should not be
calculated. And the ratio also has equal gaps
and a true zero. Like
marks, age, height. So every
statistic will be applied here. So remember the
scale of your data decides which
statistics are valid. Always identify it
before you analyze. This means that the
scale of your data will determine which
statistics you will apply. You will have to identify it first
before analyzing it. Ok? So this happened. This was a very
important topic. And I Have Covered It
Again because this one is definitely
better than the last one. But there must be something better in the previous one too.
When it was made,
I must have covered a lot of things before making it.
But this is definitely more
advanced than that. I have covered a lot of things.
Ok? So in your educational measurement
and evaluation, these are the scales of
measurement. So I have done it for you. So go
through it and understand your understanding
about scales of measurement. Ok? So thank
you for watching and happy learning.