# Stats question

1. Jul 20, 2004

### lunchblaze

i've got a stats issue that i'd love some ruling on if anyone cares to help..

i've got a population of hospital patients with a diagnosis of anemia admitted in 2004 - n=191

the rate at which these 191 catch the flu while in stay is 39% (or 75 of them)

during that same time (2004) 90 of these anemia patients were given a special drug.

these 90 pats caught the flu while in stay at a rate of 23% (or 21 of them)

now, my contention is that i can only say that there was a 16% improvement related to the taking of the special drug (or 39%-23% = 16%)

a friend of mine says that there is a 41% improvement because of the "percent change in" method (or 39%-23% = 16% then 16%/39% = 41%)

i say you cannot do this since it is not the same population that has changed, and there is not two time periods over which you are measuring change
i.e. town x's # of crimes in 2003 was 75, in 2004 it was 21, thus town x's crime rate has had a 72% (not 41%) reduction from 2003 to 2004 (or (75-21)/75 = .72)

any help would be appreciated,

edit to say: i titled this "stats question" even though i know that for anyone with a working knowledge of statistical analysis this is extremely simple.

danke!

Last edited: Jul 20, 2004
2. Jul 20, 2004

### AKG

I would say there's a 16% improvement. 16% means 16 in 100. Originally, 75 or 191 people got the flu, so 39 in 100 got sick. Now, if 21 in 90 get sick, we extrapolate to say that 23 in 100 get sick. In a hundered people, 16 fewer people get sick, I would say that's a 16% improvement. The percent difference in the two sickness rates may be 41% relative to the original sickness rate, but I think 16% is a more telling number. It's strange because you're dealing with percents.

If we had 5 apples, then added 3 to have 8 apples, then the improvement would be 3 apples, or 60%. We're dealing with apples here. In your example, the quantity itself is perent. In this example, it's fair to say both that the improvement was 3 apples or 60%. In your example, it's strange because of the "units" so it almost seems fair to say that the improvement is 16% and 41%. Actually I might say this:

Actual improvement: 16%
Relative improvement, or percentage improvement: 41%

3. Jul 21, 2004

### lunchblaze

thanks for the response!

i like your approach of breaking it down in to the meaning of percent. we always throw around percentage figures but sometimes forget exactly what it's conveying.

i think the real question to ask is:

given the two rates of becoming sick for these two groups, at what rate would we expect the whole population of patients to become sick were we to have given them all the special drug, as opposed to just 90 of them - 16% less than without the drug, or 41% less than without the drug?

this way, only one answer can be correct.

to answer this question do you think you'd go with 16% or 41%?

thanks.

Last edited: Jul 21, 2004
4. Jul 21, 2004

### NateTG

The question you need to ask with percentanges is always going to be percentage of what.

For example, let's say that I have 5 apples, and then increase that by 5 apples, the result is 10 apples.

If I want to make the increase look small, I say:
"The increase was 50% of the total"
If I want to make it look big I say:
"There was a 100% increase"

Both of these are correct.

So, in your case, you have:
"There was a 41% change in the infection rate."
Which refers to the change in the rate as a fraction of the rate, and
"There was a 16% change in the infection rate"
Which refers to the absolute change in the rate of infection.

Because the language is ambiguous, they are both correct.

If you add units, it becomes clear that the are different:
"There was a change of 41% of the rate of infection in the rate of infection"
and
"There as a change of 16 of 100 patients in the rate of infection"

Similaly, when asking the question, you should specify the units that you want to have the answer in, for example, "What is the change in infection rate in patients per 100?"

5. Jul 21, 2004

### lunchblaze

i agree that the language can make it unclear what is actually being asked.

do you think that the question

"given the two rates of becoming sick for these two groups, at what rate would we expect the whole population of patients to become sick were we to have given them all the special drug, as opposed to just 90 of them - 16% less than without the drug, or 41% less than without the drug?"

is still ambiguous enough to allow for both answers to be correct?

6. Jul 22, 2004

### NateTG

No, but it's hard to read.

7. Jul 22, 2004

### lunchblaze

given all that is known, if we give all anemia patients the drug next year, what's the best guess as to the rate they'll get the flu?

thanks.

8. Jul 24, 2004

### AKG

lunchblaze

In response to post #7, I think you know the answer to that to be 23%. As to your other question, whether both 16% and 41% are acceptable due to the amibguity of the question, I would say yes. Well, I'll tell you what I think, then you can judge:

If we have 10 apples, and you gain two more, then are asked what the "improvement" or increase in apples is, is it right to say that you gained, 2 apples? Is it right to say you gained 20 percent? If both of these are okay, then both 16% and 41% are okay. In the first example, the "units" were apples. In your example, the units are percentages themselves, which makes it strange, but not wrong. So as long as you'd accept 2 apples and 20%, I would think you should accept both 16% and 41%. In an answer to a school question, I might write both answers and explain what each one is (because the "units" are confusing). Of course, the 16% tells you the actual number of additional people in 100 that will not get sick due to the treatment, and the 41% tells you, as a ratio, how much better the treatment is compared to no treatment; it tells you that 41% of the people who would be sick will actually be healthy. In different ways, both numbers tell you the improvement, I suppose you simply have to be clear as to how you're measuring improvement (is it overall number of people that will not get sick, or is it the percentage of people that are healthy that would otherwise have been sick?)

9. Jul 28, 2004

### lunchblaze

true enough - the gain is 20%.

however, it's so simplified as to not really be applicable to my example. all it does is verify the procedure of arriving at "percent change in" by dividing the difference between the old number and the new number by the old number. this of course is obviously fine to do (same as my crime rate example showed).

the problem i think lies in the fact that in my example, a statement about the efficacy of the anti-flu drug needs to be made (perhaps i didn't make that clear in my OP sry) - i.e. - "if we spend the money to give everyone the drug next year, how much better will it be for patients?"

i think my problem with it is that one is a population and the other is a sample (pop = anemia pats, sample = anemia pats with drug) even if not random. it seems to me that statistics doesn't provide for sample traits being subtracted from population traits to arrive at some percentage of change (albeit a valid mathematical operation in and of itself) and suggest that the 41% number is useful to make inferences.

does this seem sound or am i confusing/being confused more? hehe.

Last edited: Jul 28, 2004