How can rating have interval scale?

[swapna gavhane]

Question number 4 in Graded assignment, can any one explain to me why rating has interval scale of measurement instead of ordinal.

Over the internet and over many standard books and presentations of university courses it is clearly stated that rating is ordinal (with a reason). Here are some links for reference 

http://homepage.stat.uiowa.edu/~rdecook/stat1010/notes/Section_2.1_2.2_data_types_and_errors.pdf

here in slide number 11 it is clearly written, "Watching two 2-star** movies isn’t the same as watching one 4-star**** movie (the math not relevant here)."

kindly reply.

[Vedansh Gupta]

Hello,

It depends on the context in which it is used. Am attaching a screenshot from the question:

It is written that the rating of the app is the arithmetic mean of all user ratings.

For example.

User 1 , user 2 , user 3 rated app 1 as 4,3 and 2 and the average rating of app 1 was (4 + 3+ 2)/3 = 3

Notice that taking average is only possible if it represents a numerical data. If the rating given by user represents a categorical data (ordinal), then no mathematical operations are possible and average rating of app cannot be calculated. Hence, it is not a categorical data. Since true zero is missing, it follows interval scale.

In short, it depends on the context used.

[swapna gavhane]

i can have a counter argument where, if we have 4 different ratings for a product like,

1) poor

2) good

3) very good

4) excellent 

and then vectorization of above ratings will give us, values 1,2,3,4 and then we can take average of those ratings, but does that mean anything? 

also for further reference kindly have a look at 

1) Rating Scale https://en.wikipedia.org/wiki/Rating_scale

     also it is clearly mentioned that,  "Attitude and opinion scales are usually ordinal".

2) likert Scale https://en.wikipedia.org/wiki/Likert_scale 

3) a blog piece https://measuringu.com/mean-ordinal/

     It states that some people do take mean of ordinal scale, doesn't make the scale interval

4) https://stats.stackexchange.com/questions/67551/calculate-mean-of-ordinal-variable

      can you read the 3rd and first response 

So in our context can we ask a user rating a movie 4 likes the move 4 times more than who rates the move 1? again if it follows the arithmetic then does it mean if we Watch the movie whose rating is 1 for 4 times will that be equivalent to watching the movie whose rating is 4 one time. << if 1+1=2 arithmetic is true then the above statement should also be TRUE.

[CG]

Hi,

Please see this topic Activity Questions 4 : Question 4 - Interval or Ordinal where this issue has been discussed in great detail. We analyse why activity question regarding the Goodreads rating should be considered ordinal and not interval. There has been no response from the course team for over a week regarding this.

Goodreads actually explicitly codifies

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

Goodreads also possibly calculates arithmetic mean of all ratings and displays the rating of a book.

This conundrum remains unanswered so far. 

The Google ratings question is directly related to this. 

* The justification provided by many as to why it is an interval scale is actually a post-hoc fallacy : Because Google is calculating arithmetic mean, it must be true that the ratings are on interval scale OR  because Goodreads is calculating arithmetic mean, it must be true that the ratings are on interval scale.

[Rajoshi Seth]

I agree. It depends on the user's perspective: a difference between a rating of "1" and "2" may not be the same as the difference between a "4" and "5".

Additionally, the "arithmetic mean" argument doesn't make sense on an individual level. The question doesn't specify otherwise, emphasizing ambiguity.

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[uday sai]

As we can perform numerical operations we are coming to a conclusion that rating of an app is numerical.
but here we aren't having any units for that avg . so is it right to say it is numerical?

On Tuesday, October 20, 2020 at 12:59:52 AM UTC+5:30 Vedansh Gupta wrote: