Test for frequency data of related sample

[sharmachetan]

Hello, I was wondering if someone can please help me know what type of test i should apply on my frequency data. Here is situation:

I have frequency data of 45 consumers, obtained through five answer boxes for 7 samples. Consumers were asked to taste the sample and write their response about taste in the five boxes below. Their response were categorized into 4 categories, like Abstract taste for 1st answer box = 350, abstract taste for 2nd answer box = 250 and so on.

So now i want to compare abstract response from answer one to answer two and so on, so what kind of test i should use. I was thinking of chi-square test of association, but i think this test presumed independent sample to different answer boxes. What other tests could be use?

I added image also for insight.

[ballardw]

Before deciding on a test what are the questions that you want answered from the test?

What does "first response" mean as shown? Did each respondent answer the same question multiple times? If so then some hint about how that "first' is collected would be helpful. If first and second mean different items tasted/sniffed/ what ever evaluation then your really don't have much of a "first" it is just a category like "product 1" "product 2" and so one.

Since you only have 45 "consumers" then how do you get "frequency" in the 400 range?

[sharmachetan]

@ballardw Thanks for the prompt help. 

Here is more information: I provided 45 consumers a sample set of 7 candies and they have to taste each candy (randomly provided). So 45 consumers would taste each candy and then answer a question which has 5 open-ended boxes. So suppose i am a consumer and have a sample M&M and i would describe it in five open-ended boxes. Then i classified responses as if they are abstract or appearance based, and so on. So my question is that if i want to compare the number of responses, say abstract ones, across samples, are different from the number of responses (abstract) obtained from second box or third or fourth or five.Or in other words, this pattern is independent of samples. 

[ballardw]

Your first step would be to associate the exact product with the measurements. So that way you can compare "M&M" to "Hot Tamales" (or whatever the others are). Your presentation of the items in a random order is a way to help control response order bias but you don't want to compare "First" scores at all. You  want the products.

Then a chi-square with product as one dimension and "taste" would tell you if there is a difference in the distribution taste ratings between the products.Or appearance, or what you presented.

5 choices and 45 samples (customers) may result in a number of warnings about number of cells with expected responses < 5 and that chi-square is possibly inappropriate.

What exactly do you mean by "open ended boxes"? Were responses words like "ack" "good" "too sweet"? If so and you imposed as scale on those then you may only be testing your scale not the products.

You may have to provide some example data so we can actually see what you have.

[sharmachetan]

So, @ballardw 

Please find below an attached image of open-ended question. Responses were very diverse, yes, some people used "ack" or "yuck" and many more. So what i did, I counted them and classified them if they are based on appearance of the product or texture or aroma or if they are abstract in nature, like "good".

So now I am interpreting it that there are more abstract and appearance words in first response box, so we should avoid this box for future testing. But how i can statistically say that number of abstract words was significantly higher than others so we should avoid it for future. May be this new graph would help you understand my problem better.

  

[sharmachetan]

@ballardw ???

[ballardw]

Data, not pictures of some summary. The structure of a data set can limit what can be done and sometimes getting into a different structure is needed.

Research questions to answer. Not "compare numbers" but something like "which response is more frequent" or "is the distribution of x different between category y values" or "is the mean value of z different that/ equal to/ greater than / less than <something> between categories" or are you testing the respondent against some hypothetical distribution of responses? Something like that. Without a fairly well defined question  a specific type of test is hard to recommend, or determine which types of test might even be relative. 

With a response like "yuck" how to know to code that to "flavor" and not "aroma" or "appearance"?

I have absolutely no feeling what "abstract" could mean in any context of "potatoes".

For all I can see from your stuff a respondent might have 5 "abstract" or "appearance" responses for a product.

Whether every response had exactly 5 answers matters as well. And are you trying to determine a "rank" with the 1st, 2nd, etc?

I just cannot tell what you are looking for.

[sharmachetan]

@ballardw Thanks for the response. I attached sample data file.

1. With regard to responses, yes every respondent provided 5 answers. No exception. I didn't get what do you mean by rank?

2. With regard to categorization, "yuck" was just an example, but I think one can categorize words used by respondents, though to some extent, into categories.

3. Regarding questions, I thought of these would be appropriate:

a) the distribution of abstract, or say texture responses is different between "response boxes" 

b) the frequency of abstract response is highest in first response box