Comparisons with Negative Numbers

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GREtaker

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Hi! I'm trying to compare a list of averages that includes some negative numbers. The negatives especially are throwing me. The numbers listed are:

Issue 1: 149
Issue 2: 143
Issue 3: 139
Issue 4: 50
Issue 5: -1
Issue 6: -72

They are pros v. cons for six different issues. (In Issues 5 and 6, there were more complaints than good things.)

I think I can do the comparison BACKWARDS correctly with the positive bases. For example, I can say:
People are 2.48 times less likely to support addressing Issue 3 (139) than Issue 4 (50). I did that by dividing 139 by 50. BUT, I'm doing it backwards.

We're supposed to figure out what people are most likely to want to change and state the finding in the form:
Students are _____ times more likely to want to address _______ than ________.

The most popular item should be the final blank, so it becomes:
Students are ______ times more likely to want to address _______ than Issue 1.

All five problems will be:
Students are ______ times more likely to want to address Issue 2 than Issue 1.
Students are ______ times more likely to want to address Issue 3 than Issue 1.
Students are ______ times more likely to want to address Issue 4 than Issue 1.
Students are ______ times more likely to want to address Issue 5 than Issue 1.
Students are ______ times more likely to want to address Issue 6 than Issue 1. (Issue 6 had the most complaints, so it's what people most want to see fixed. I know this will be the highest figure. The negative really confuses me though.)

How do I do this?
 
Last edited:
How are these numbers computed? Do you know the raw data behind them?
 
JeffM said:
How are these numbers computed? Do you know the raw data behind them?
Click to expand...

Yes. It was a survey I did of my school. I chose six issues, then asked people if they thought we were doing a good job or bad job about each one. People could choose both or not answer at all. The idea is that if people think we're doing a bad job, it's an issue that needs to be addressed. I took the number of people who said we were doing a good job and subtracted the number of people who thought we were doing a bad job on each issue.

So, for Issue 1: 193 people said we were doing a good job. 44 people said we were doing a bad job. So I combined them for 149. For Issue 6: 68 people said we were doing a good job. 140 people said we were doing a bad job. So I combined them for -72. Etc.

(Also, this might not be statistics. I thought it was, but maybe it's algebra? I might have posted in the wrong place - sorry!)
 
The way that you have constructed your index is inconsistent with the question you have been asked to answer.

There are probably quite a few ways to construct such an index. An index is just a way to summarize data in a comprehensible form.

Here is a very simple way

For this question, ignore the favorable answers. Take the issue with the smallest NON-ZERO number of unfavorable responses and divide the number of unfavorable response on each issue by that number and multiply all those numbers by 100. You can see at glance the answer to the question of how many times more students think an issue needs to be addressed than the issue that anyone at all thinks needs to be addressed. Moreover that question can be addressed for any pair of issues with unfavorable responses simply by taking ratios of the index.
 
Okay. Thank you. Is there a way to weigh in the positive responses after doing that?

Here are all the numbers:

Issue 1: 193 Good, 44 Bad
Issue 2: 191 Good, 48 Bad
Issue 3: 169 Good, 30 Bad
Issue 4: 135 Good, 85 Bad
Issue 5: 105 Good, 106 Bad
Issue 6: 68 Good, 140 Bad

Following your instructions:

Issue 1: 193 Good, 44 Bad = 1.7
Issue 2: 191 Good, 48 Bad = 1.6
Issue 3: 169 Good, 30 Bad = 1
Issue 4: 135 Good, 85 Bad = 2.8
Issue 5: 105 Good, 106 Bad = 3.5
Issue 6: 68 Good, 140 Bad = 4.7

That makes Issue 3 look like the best thing. But, when I average good and bad, Issue 3 is the third best thing. I want people's "good" votes to count for something. I think maybe I made my survey too complicated by letting people vote for both good and bad if they wanted too. I figured the "good" votes would basically "downvote" the bad votes and vice versa.
 
First, and way most important, things like averages and index numbers lose information. Their purpose is to simplify masses of data so that it is comprehensible and easily communicable. But when you simplify, some information is necessarily lost. So the “best” DESCRIPTIVE statistic depends on what questions are relevant. This is the primary reason that we usually describe data in terms of several different descriptive statistics. That way we can answer more questions than we can from a single statistic. So one thing you could do is calculate the index numbers for the “good” answers. You now have double the information. You can easily compare goods with goods and bands with bands. (By the way, it makes little mathematical difference, but it is usual to multiply the numbers by 100 and round to whole numbers.)

Second, it literally has been five decades since I studied survey design, which is more about human psychology than mathematics and is not a static field. There may be better answers than I am able to give you. A standard way to design a survey like yours is to use a 10 point scale with 1 meaning horrible up to 5 meaning almost acceptable and 6 meaning barely acceptable and 10 meaning excellent. The reason for this is that setting up a simple good/bad dichotomy frequently leads to poor answers because people cannot express any complexity of feeling with such a restricted range of choice. “Do you want to marry X or murder X“ is not a question likely to generate meaningful answers; most people you want neither to marry nor murder. For a less extreme example, suppose 169 people think issue 3 is barely ok and 30 think issue 3 is horrible. If that was true, you could make a lot of people happy by addressing issue 3 even though filtering the information through a good/bad filter suggests ignoring it. Reliable answers to meaningful questions lead to better decisions, but the data determine what questions can be answered reliably. Make sense?

Third, (and this is after decades of personally having made decisions from imperfect data), you have to make do with the data you have even though you know it is not nearly as good as you might wish. Here is another way to turn your raw data into a useful tool for analysis and communication. First calculate the percentage of good versus bad for each response. You had different numbers of responses, but percentages will standardize the number of responses. Present that. If you want to further summarize into a single number for each issue, divide the number of goods into the number of bads, divide all six ratios by the lowest ratio, and multiply all six quotients by 100. That will give you an index of relative degree of unhappiness.
 
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