# Word choice for a comparison of different amounts

I'm currently struggling to clearly state the following situation:

Background: Let's assume I have two newspaper articles A and B. Let's say I want to count how often a specific word (for instance bird) occurs in A and in B. For instance, the word bird appears 5 times in article A, but only 3 times in article B. I'm trying to express that bird occurs 3 times in both (so at a minimum of 3 times in each article) and that bird appears 2 times (2=5-3) more in article A than in article B. Let's assume that bird is only a special case and that I'm actually looking for animal names and want to count the number of word occurences for different words as well. I intentionally don't want to refer to the articles A and B by name, because bird may be more frequent in article A, but dog might appear more often in article B.

My current wording is:

For each animal, we count how often it occurs in both articles and how often it occurs more in one article than in the other.

Questions:

1. Does ''how often it occurs in both articles'' really mean that it occurs individually in article A and in article B? Or can this wording be confused with in total, like summing up the occurances in both articles?
2. Is there a better way to express ''how often it occurs more in one article than in the other''. I dislike ''occurs more'' and ''than in the other''. Does anyone have an alternative formulation for this sentence?

I hope my question fits on this site as word choice and usage. I doesn't seem to fit to Writers.SE.

Edit based on the comments: Sorry, I was unable to properly explain the context. I do have a machine learning background and I was trying to generalize a bag-of-words model in my explanation. I do have a fixed vocabulary of words and try to count their appearances in two different articles. It is possible that a word from the vocabulary doesn't occur in any of the two articles. Try to think of the for each animal as an iteration over all words in the vocabulary.

• I would say, "how many times", or "the number of occurrences", or "the number of instances" for each, etc. Commented Feb 5, 2016 at 14:47
• Do you actually count animals that only occur in one article but not the other? What about the (almost infinite number of) animals that don't occur in either article? Perhaps you'd be better saying For each animal that occurs in both articles, we count how often it occurs more in one than the other. Commented Feb 5, 2016 at 14:47
• @FumbleFingers: It might be possible that an animal might be mentioned in one article but not in the other. It is also possible that it is mentioned in both articles. Commented Feb 5, 2016 at 14:50
• That's implicit in your original text, but you haven't answered my question. Do you have an exhaustive list of all possible animals, some of which may not appear in either article - and will therefore be reported as having equal occurrence counts (total "zero" for each article). Or are you going through each article looking for animals, and only then comparing the occurrence counts for that animal in each article? That dictates whether in my suggested rephrasing you say that occurs in both articles, or that occurs in either article. Commented Feb 5, 2016 at 14:57
• Really you are simply reporting the minimum frequency for the two articles and the difference between min and max. “For each listed animal, the minimum frequncy of occurrence in the two articles is reported along with the delta between the minimum and the maximum.
– Jim
Commented Feb 5, 2016 at 16:04

Since the context is machine learning, there is a well known discipline that goes by its abbreviation, tf-idf.

tf–idf, short for term frequency–inverse document frequency, is a numerical statistic that is intended to reflect how important a word is to a document in a collection or corpus. Wikipedia

Perhaps one could borrow these terms:

• term
• term frequency
• document
• inverse document frequency

So the sentence could become:

For each term, we determine term frequency in both documents and compare inverse document frequency.

The inverse document frequency may work better than a sheer word count, because bird appearing 5 times in a document has more import if the the document is 50 words long and less import if the document is 5000 words long.

(I realize that this is a new direction from the OP's question, but the machine learning context puts a different slant on the terms used.)

Does "how often it occurs in both articles" really mean that it occurs individually in article A and in article B? Or can this wording be confused with in total, like summing up the occurances in both articles?

It can be interpreted either way, though I'd favour the sum.

Is there a better way to express ''how often it occurs more in one article than in the other''. I dislike ''occurs more'' and ''than in the other''. Does anyone have an alternative formulation for this sentence?

Try this:

For each animal, we count the number of times it appears in each article and report the difference together with the smaller number.

"For each animal, we count how often it occurs in both articles and how often it occurs more in one article than in the other."

"How often it occurs in both articles" is asking for a sum (i. e., 8 times).

"How often it occurs more in one article than in the other" is ambiguous.

As an less ambiguous alternative, how about,

For each animal, we count how many times the name of the animal was used in each article, and then we determine the difference, if any, between the number of times the word was used in the first article and the number of times the word was used in the second article.

These two tasks could be separated, of course, and should be if your audience is young students learning how to read and recognize words. Otherwise, the reason to determine the difference may become lost.

You could say

We examine [or count] the common incidence of the use of the animal's name between the articles as well as the differential incidence.

Collins defines incidence as

degree, extent, or frequency of occurrence; amount

a high incidence of death from pneumonia

1. Yes, if you write both articles that could be interpreted as meaning the total appearances in both articles combined - better to say each article.

2. Rather than how often it appears in one article more than another, you could say the difference in number of appearances between the two articles.

Taken together, with a little editing, that gives the following:

We count how often each animal appears in each of the two articles and, where an animal appears in both, we record the difference between the two.

If you wanted to make it even more concise, you could just go with this:

We count how often each animal appears in each of the two articles and, where an animal appears in both, we record the difference.

Having said all that, rather that avoiding technical terms, you should maybe just adopt one and stick with it - once defined or explained as required, you can use it throughout the entire article. I think Jim's frequency is best; certainly, that is what you're measuring.