# Data Analysis for ranking data?

I want to compare three types of designs(A, B and C). After showing the images of three designs to each user, I have asked the user to rate/rank these 3 designs as Best, Worst and Average.

Users response were: A-Worst, B-Average, C-Best and so on. For data analysis, when user rated a design as best, I gave a score of 3, for an average- score of 2, and for worst- score of 1.

I asked each user 5 questions (criteria) to rank these designs. So data collected would look like as follows: How should I analyse this data (which test/procedure I should use)?

Does usage of ANOVA valid here?

Also, I would like to use Tukey's pair wise comparison along with ANOVA to find any significant difference among the means.

I will be thankful for the responses.

• stats.meta.stackexchange.com/a/3181 – Kodiologist Sep 11 '17 at 18:37
• Your example seems unrelated to your description, which indicates the data could be represented as a table with one column for each design, one row for each subject and question, and values of just "1", "2", or "3" in each row. What do the numbers you have shown mean? Would they be the sums of your numeric codes? If so, then these aren't actually your data--they are a digest of them--and you should consider analyzing the raw data before performing any such summations. For the purpose of asking this question you at least need to explain what you want to learn from the data! – whuber Sep 11 '17 at 18:52
• There are 30 subjects mentioned under column 'Sub'. These numbers are just serial numbers or subject IDs. Under A, B or C is rating score of for each design which I want to compare. I want to know which is better. e.g. Sub1 rated C as best (high score based on the 5 questions). Hope this explanation will be helping. – Tony Sep 12 '17 at 16:28

## 1 Answer

By adding up the ranks you have implicitly stated that they are interval level, rather than ordinal. This is not technically right (although it is very commonly done). But, once you've done that, you can use ANOVA as you would on any other data set.