Activity Questions 4 : Question 4 - Interval or Ordinal

[CG]

The correct answer indicated for the above question is Interval scale. However as per the associated lecture (Lecture 1.4 :Introduction and types of Data - Scales of measurement https://youtu.be/EVGVlzMuhIo) at 09:00 Prof. Usha Mohan clearly explains why such an example is to be considered as an Ordinal scale ( Since the difference between 1 and 3 may not be equal to the difference between 3 and 5).

Question 4 

Katheryn has recently read the booker prize winner “The Discomfort of Evening” by Marieke Lucas Rijneveld, and decided to rate this book on the Goodreads website. There she is asked to rate the book on a scale of 1 - 5. What kind of scale(s) of measurement is(are) being used here for rating?

• Interval scale 
• Ordinal scale 
• Ratio scale 
• Both interval and ratio scale 
• Both interval and ordinal scale

I am aware that this question has been raised on this forum quite a few times already, but the answers and explanations seem to be incongruous to the lecture.

Given below is the transcript from the lecture

08:55 Now, when we talk about ordinal scale, again I can code an ordinal scale of measurement. For example, in our earlier example my bad could have been coded as 1, my good can be coded as 2, and my excellent can be coded as 3. I could code them. There is an order in 1, 2, 3. But then one thing which I need to understand here is the distance between bad to good need not be the same as the distance between good and excellent. It is just an order, I know excellent is better than good, but I cannot say that excellent the difference between good and excellent is the same as the distance between good and bad. I have an order, but at this point of time I am not able to comment anything more about this order. So, when I go to interval scale of data, interval scale of data has all the properties of interval scale of data, but the interval between the values is expresses a fixed unit of measure. Remember, when I said bad, good and excellent, I said the difference between good and bad need not be the same as the difference between excellent and good. Whereas, when I have internal data I have an ordering, but in this case whenever I am ordering my data the interval between the values is expressed in units of a fixed unit of measure. When the differences expressed in a fixed unit of measure; so, if I have for example, it can I can find out the difference between any two values, ok.

[Rajaram Sahoo]

Even I have the same doubt. Kindly someone clarify it.

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[Anand Iyer]

Well, professor states that's it's the unit of measure is fixed.  Not the measurement as such.  As you say difference 1-3 and 3-5 is not same.  

But, the numbers used have the same interval.  1-2-3-4-5 have 5 divisions in the scale of measurement, which are equally separated from each other.

So, the answer is interval.

[CG]

Beg to differ - This explanation is not satisfactory. 

 - What is the fixed unit of measure for 1-2-3-4-5?

 - The example at 09:00 in Lecture 1.4 clearly alludes to this rating example and explains why it is to be considered ordinal scale.

 - The rating 1-2-3-4-5 cannot be added or subtracted as these are basically qualitative labels.

 - The diagram at 17:10 in Lecture 1.4 explicitly indicates that ranking/rating are to be considered as ordinal scale.

[goduma...@gmail.com]

Try to think like this, here in ratings they are actually tricky and changes with context of the data

 1) If it is Very Satisfactory, Satisfactory Not Satisfied  - It is ordinal (Here we can't perform averages It represents how may users are giving Satisfactory, very satisfactory or Not satisfied ) 

2) If it is coded Very satisfactory-1. Satisfactory 2, Not Satisfied -3 - it is also ordinal ( Here we can't perform averages, It just represents the same as above).

3) If it is just given as 1-5 rating  - it is interval (Here 2-1, 3-2 all are same measurements and also  here average of ratings making sense compare to other two above mentioned.

Hope this helps 

[CG]

Thank you for attempting to explain. However these ratings are indeed ordinal and not interval scale.

A simple search on google "is rating a categorical variable" will show beyond any doubt that this rating is ordinal scale

Some answers -

• Satisfaction ratings on a scale from 1 to 5. Although these are represented by numbers, they do not represent a count or true measurement. Such ratings are categorical.
• Opinion variables on a 1 to 5 or 1 to 10 scale are usually considered as ordinal categorical variables.

Can such ratings ever be ordinal? 

For the given number of options to the user (1-5) it is to be considered as ordinal scale. 

[Sauro, Jeff. 2011. "Should you care if your rating scale data is interval or ordinal ?." MeasuringU. June 1. Accessed 2020-10-11.]

The rating system in the question is similar to the 7 point Single Ease Question (SEQ) rating mentioned in the article linked above. This is considered to be ordinal scale. However the same article mentions a Subjective Mental Effort Questionnaire (SMEQ) rating which is interval scale because it provides thousands of response options to the user.

I hope someone from the course team pitches in at this point to acknowledge and rectify the error or provide a correct explanation for the said rating being ordinal scale.

[Agatha Chatterjee]

Yes I agree to your point, a simple google search says that any kind of rating is an ordinal scale.

There is a FAQ posted for this same question mentioning that this kind of rating 1-5 is to be considered as interval as there is a difference of 1 between each of these ratings.

But the point is the interval of 1 does not correspond to the true measurement as you have mentioned. It can also be considered as coded value for some value like satisfactory and poor.

Can someone take this question up on the zoom call maybe?

[CG]

Take for example Rank of students in a class based on total marks. Is Rank ordinal scale or interval scale?

Each rank is linked to and justified by the total marks of a student relative to the total marks of each of the other students in a given class population.

Rank represented by 1-50 or 1-1000 or 1-x is a ordinal scale since the difference between 1st and second rank is not necessarily the same as the difference between third and fourth rank and so on...

Perception from different people cannot be easily represented by a number like age or marks.

Now in the case of the goodreads website rating system for books:

- Is my rating of 4 for a given book the same as someone else's rating of 4 for the same book ?

- If I change my rating from 4 to 5 after some reflection, would it be the same quantum increment as changing a rating from 1 to 2 ?

- Is there a consensus among all the people using the GoodReads rating system for books about what each numerical rating signifies ?

https://transplantportation.com/2011/11/07/the-uselessness-of-likert-scales-in-rating-books/

I still fail to understand why the Goodreads Book Rating is considered an interval scale in this course while similar rating scales are widely considered ordinal scale. 

[Agatha Chatterjee]

A Goodreads book rating system can be considered an interval scale when it is exclusively mentioned that the ratings are at an equal interval.

In this case the interval being 1.

[CG]

There is no explicit mention of "equal interval" or any statement that implies this in the question which would be essential in assuming or concluding that it is an interval scale. 

[palani...@gmail.com]

The below links may help us to understand this question.

"This is a preferred scale in statistics because you can assign a numerical value to any arbitrary assessment, such as feelings and sentiments."

 https://www.questionpro.com/blog/interval-scale/

"Another type of interval scale is a rating scale. With rating scales it is usually assumed that the distances between the single expressions of evaluation (score) are equal. There is however no natural zero point. Thus, we can calculate an average of a rating scale. However, it is not possible to make the statement that the score 8 (on a scale of 1 to 11) is twice as high as the score 4. "

https://www.statista.com/statistics-glossary/definition/320/interval_scale/#:~:text=Another%20type%20of%20interval%20scale,average%20of%20a%20rating%20scale.

"Strictly speaking, most rating scales are ordinal scales. The intervals between the individual steps are not always the same size. It is not unusual in statistics, however, to define these rating scales as interval scales anyway. Same-sized intervals between individual steps are assumed; therefore a mean is sometimes defined for rating scales as well.  "

https://www.statista.com/statistics-glossary/definition/366/rating_scale/

Thanks!

On Sunday, October 11, 2020 at 7:02:55 PM UTC+5:30, CG wrote:

[CG]

As it is mentioned most rating scales are ordinal - This is the norm. ("Strictly speaking, most rating scales are ordinal scales")

Sometimes these rating scales are defined as interval scales - This is the exception. ("It is not unusual in statistics, however, to define these rating scales as interval scales anyway.")

The ability to calculate mean/average on a set of numbers does not indicate that 1-5 is an interval scale.

"Equal intervals" must be explicitly mentioned to safely assume that it is an interval scale and go ahead and calculate the mean/average.

[goduma...@gmail.com]

Based on the performance of the student , you should give marks to a student from 1-5 same here also in rating 1-5 means same it is just a value as context is not defined. I think this example clears your doubt.

Hope this helps you

On Sunday, October 11, 2020 at 7:02:55 PM UTC+5:30, CG wrote:

[DHARMA TEJA GODUMALA]

See you are always checking the examples( like good-3,avg-2,bad 1)of defined terms where averages doesn't make sense and you are confusing. Look at not defined terms where averages makes sense like in our context if possible. 

Mean is not defined for ordinal scale.It is defined for Interval scale only.

Here as I said above giving marks from 1-5 to a student is same as giving rating it is just a value.

Hope it helps

And this is as for as my understanding that on interval scale based on my research.

we will wait for the final response from the Discussion team as they are also little confused about this query yet.

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[Jai Hanani]

Any update on this yet?

[palani...@gmail.com]

The ability to calculate mean/average on a set of numbers does not indicate that 1-5 is an interval scale.

As mentioned by Dharma, unless it is a numerical code/tag for some attribute, (eg., Good - 3, bad - 2, worst-1`), mean/average can be taken for exact numerical values with equal interval depending on the context.

Also, except few variables like Gender, many variable can be measured at different levels. There is no fixed norm for many variables. Everything depends on the context and the purpose of the survey.

Here GoodReads scale must be interval as the average rating for  each book can be used for their internal purpose (like in sales/marketing).

On Sunday, October 11, 2020 at 7:02:55 PM UTC+5:30, CG wrote:

[Jai Hanani]

Interesting Discussion on Interval vs Ordinal Scale for Ratings.

[Jai Hanani]

and this.

[CG]

Rating is an Individual opinion and has no real measure 

In order to compare with something that has a real measure, let us consider an example of marks scored by students in a class. 

Now instead of grading students A-B-C-D-E-F, we can do it like 1-2-3-4-5-6.

Grade/Rating | Marks scored

1 (90-100]

2 (80-90]

3 (70-80]

4 (60-70]

5 (50-60]

6 [0-50]

Now every student has a numerical grade or rating. For the purposes of sales and marketing or whatever other reason if the school decides to calculate the average grade/rating of students, that does not make the Grade/Rating of the students an Interval scale. 

Just by virtue of the range of values that is captured or represented by each Grade/Rating, the difference between two separate Grades/Ratings cannot be considered or assumed to be equal. And the distance between 1-2 or 3-4 is not known. 

Since, by definition, the Interval scale has equal distances between values, it would not be correct to call this an Interval scale.

[Antony]

Rating scale can be considered an interval scale only when equidistance between steps is *assumed*, followed by the assumption that every user who puts in a rating is aware of this "scale". 

Its ideal that objective questions are not left for reader's interpretation and provides enough information which directs to an agreeable answer. Quite a few chicken or egg trivia spread across most assignments. 

On Sunday, October 11, 2020 at 7:02:55 PM UTC+5:30, CG wrote:

[palani...@gmail.com]

Agree that. 

Ambiguity exists in W1A2 - Q4 too since only 3 rows are mentioned as Cases.. 

9 AM, 9:30 AM, 10 AM are cases; time, temperature, and relative humidity are variables.

On Sunday, October 11, 2020 at 7:02:55 PM UTC+5:30, CG wrote:

[CG]

In activity questions 4 for week 1 question 4, the correct answer as per the system is that a rating on goodreads of 1-2-3-4-5 is on interval scale. Now 1-2-3-4-5 is implicitly coded to denote bad-poor-neutral-good-great in order.

The dictionary meaning of the noun "rating" is a classification or ranking of someone or something based on a comparative assessment of their quality, standard, or performance. So when you ask some one to rate a book or an app for example you are asking to classify it in buckets that denote bad-poor-neutral-good-great. Going strictly by definition, this has to be considered ordinal scale as the distance between good and poor or 1 and 2 is not the distance between neutral and good or 3 and 4.  In a rating 1-2-3-4-5 have an implicit meaning and denotation - It is clearly qualitative. 

If the word "scoring" was used could things be different?

Now the justification being provided to justify the correctness of interval scale for 1-2-3-4-5 rating is that some people assume that the company (Goodreads / Google / Apple / Amazon) is taking these numbers and calculating the mean to give a rating to the book so it must be interval scale. 

[Antony]

In real world, there is definitely a use case to judge the user's "mood" or "feelings". But its not practical to have a universal scale to define "feelings", since there are far too many variables. I would think that rating scale is probably a widely accepted/acknowledged case of "data dredging" where numbers are presented as statistically significant but could have hidden risks due to inconsistent interpretation of data ( or numbers). 

This is probably done due to the fact that there is no other way to come up with KPI's such as average rating. Though the average rating by text book definition may sound incorrect, it gives some confidence when sample size is large (4.1 avg rating from 1000 users gives better confidence that the book might be good as compared to 4.3 avg rating from 5 users.)

Coming to this question, I feel this is a candidate for a subjective question or a class room discussion. This is bit all over the place if you try to think it through  and try to merge the real world and text book concepts.

If this question was to repeat itself in qualifier exam, you are in a catch 22 situation where you need to decide between what you believe to be correct and what you know is the expected answer. With any luck, by the time you decide the page wouldn't have gotten timed out without saving the already submitted answers.

On Sunday, October 11, 2020 at 7:02:55 PM UTC+5:30, CG wrote:

[_Music_ Viking]

Can someone from the course support team provide an update on this?

Thank you

[Prerna Sahu]

the rating being the countable and numerical value comes under interval scale of measurement. if instead of 1-5 rating there would be good,bad,very good,average ratings than this would come under ordinal(categorical datatype). lastly, interval and ratio comes under numerical datatype.

On Sunday, October 11, 2020 at 7:02:55 PM UTC+5:30, CG wrote:

[Nikita Kumari]

Hello all,

We will give you an update regarding this problem in 1-2 days. All of your doubts are genuine. Sorry for the delay.

Thank you

Nikita

Statistics course support team

[Jai Hanani]

So, I have reached to some sort of an understanding regarding ratings. Here it goes: 

If the user was asked to rate from 1-5 with '1' representing 'Bad' and '5' representing 'Excellent', then the data becomes Discrete Numerical. Because, data collected at the source is numerical.

If the user was asked to rate from 'Excellent-Bad' with 'Excellent' representing '5' on 5-pointer scale and  'Bad' representing '1', then the data becomes Ordinal Categorical. Because of the same reason stated above.

The trick is to find out what is representing what, which is primary and which is secondary. Is 'Excellent-Bad' primary or '1-5'? If it's 'Excellent-Bad' then '1-5' is in helper role. If it's '1-5', then 'Excellent-Bad' is in helper role. We don't care about helper roles.

[satya takkellapati]

I've been a Goodreads user for a while. If you're precisely referring to goodreads they actually equate their scales with

1 star= did not like it

2 star= it was ok

3 star= liked it

4 star= really liked it

5 star= it was amazing

Now if you take this into consideration wouldn't it be ordinal?

[CG]

These codes are explained at https://www.jzacharypike.com/blog/2015/04/one-reason-why-amazons-reviews-are-higher-than-goodreads/

Now even if it were not explicitly codified and denoted (this would make for clumsy UI), these meanings are implicitly attached to and connoted by the 1-2-3-4-5 rating system. 

Hovering over a star with the mouse pointer will show what each star denotes. Goodreads also provides a neat histogram based on the frequency distribution of the ratings and the total number of ratings per book.