# What statistical method should I use?

I want to show that a decision made by a group of people is more extreme than the same decision made individually.

I have the decisions of groups and individuals ranked in degrees of extremeness, but I don’t know what statistical method to use. I tried averaging the values, but the result was not good. How can I show that values of groups are more extreme?

You could compare standard devients. SD would shows the spread of values. A larger SD would show a larger spread of opinons.

What do you mean by the result of averaging not being good? I think folks could be more helpful if you described your experiment in more detail. How are you ranking extremeness? How is your data organized?

If the data doesn’t indicate what you want, you’re going to have a hard time getting it to do so.

That is why they are statistamagians

Logically, if it’s the same decision, it’s the same degree of extremity no matter who made it.

FWIW, I find your hypothesis unlikely – large number of people would usually follow a normal distribution when you add their results, which would be less extreme. You’ve probably heard how notoriously non-extreme comittees are.

I Concur with others, it’s impossible to give advice without more info. Please describe methodology and some sample results. It may be too late. I can’t quite put my finger on the quote, but asking statisticians to give you useful results after the tests have been run is like bringing a corpse into the morgue and asking for medical advice.

Do you mean: “I want to show that a decision about something made by a group of people is more extreme than the decision that would be made by individuals of the same group”?

You’ll first have to define how to determine the relative “extremeness” of two decisions. Good luck.

The only way for any individual view to be statistically more “extreme” than the group view is if, overall, the views of your sample population tend to fall in a distribution which allows for some individual view to deviate sufficiently from the view of mean “extremity”. Hence, you can only prove that either your sample population is comprised of individuals all sharing the same view, which negates relative extremity of any kind, or there is some distribution of views, in which case you will only prove the obvious: Not everyone is average. The way you have posed the hypothesis preculdes you from proving it, and hence it’s not a statistically or logically sound approach to characterizing individuals or a population.

Better find another idea.

Standard deviation worked. Thanks.

A friend of mine needed me to help her make some graphs in Excel. She gave me the data, but I don’t know how she collected them. The data were numbers from 1 to 9, where 5 was moderate and anything above or below was considered extreme.

If I understand the problem right, then standard deviation will give you an answer, but it won’t be what you want. Imagine:

Group decisions: 6 5 5 4 5 4 5 5 4 6 6 5
Individual decisions: 9 9 9 9 9 9 8 9 9 9 9

I think you would call the group decisions above less extreme than the individual decisions, but the SD is larger for the group decisions.

I don’t think you want an out-of-the-box algorithm. I think you just want to define what extreme means and ask what fraction of decisions made by groups/individuals meets that definition.

For example, if extreme means anything in the set [1,2,3,4,6,7,8,9], then my above data samples would show:

Group decisions: 6 out of 12 extreme = 50% (call this f[sub]G[/sub])
Individual decisions: 0 out of 11 extreme = 0% (call this f[sub]I[/sub])

The next step is the critical step: you must estimate the uncertainty on these fractions. Barring any number of complications which may or may not be present, the fractions f[sub]G[/sub] and f[sub]I[/sub] will follow a binomial distribution. Assuming you have lots of data, and your distributions are less, umm, weird than the ones I made up, you could use the data themselves to estimate the error.

If you have enough data to make your errors small enough, then you will now be able to address whether f[sub]G[/sub] is significantly greater than f[sub]I[/sub]. What might be a bit cleaner is to ask if the ratio r=f[sub]G[/sub]/f[sub]I[/sub] is inconsitent with 1 (and in which direction!) given the error on r (which comes from propagating the errors on f[sub]G[/sub] and f[sub]I[/sub].)

I’ve glossed over / left out some aspects which could be important, but this at least is (I think) closer to what you want (assuming I actually understand the problem in the first place. If I don’t, then my apologies for wasting everybody’s time .)

(And this just goes to show that actually getting a quantitative result from a set of data is way more involved than it might seem at first.)

I meant to add that I didn’t bother to explain the following:

because 1) it’ll be long, and 2) I’m hungry right now. If you are actually planning to do more analysis on the problem, I could flesh this out a bit more. (But I’m guessing you’ve moved on with life, though.)

Assuming the data is what Pasta was working with–decisions ranked 1-9, and 3-7 are not extreme–the thing to do is to test the hypothesis that [symbol]m[/symbol][sub]g[/sub] - [symbol]m[/symbol][sub]i[/sub] > 0, where [symbol]m[/symbol][sub]g[/sub] is the mean of the ratings of the group decisions, and [symbol]m[/symbol][sub]i[/sub] is the mean of the ratings of the individual decisions.

That’s a pretty standard test that’s covered in any first-year statistics book.

Using the means would answer whether the, well, mean group decision is more extreme than the mean individual decision, but I think the OP is after something different. I think the OP would claim that the following data have different "extremeness"es:

Group: 9 1 9 1 1 9 9 1 1 1 9 9
Individ: 4 5 5 6 6 5 4 4 6 6

but they have the same mean. I think the hypothesis the OP is trying to test is that the answer to the question “How often is a group decision ‘extreme’?” is higher than the answer to the question “How often is an individual decision ‘extreme’?” Dog80?

If I understand the data,
5 = perfectly moderate
4,6 = not as moderate
3,7 = a little nutty
2,8 = Will Ferrell doing a schtick
1,9 = Hitler

ergo, |decision rating - 5| = “Distance from 5” = extremeness.

So if a group average is 7.5, but those same people average 5.5 as individuals, you got something interesting.

Sounds about right Dog?

Ooops! Sorry! I was wrong

The range was 1 to 9 with 1 meaning “playing safe” and 9 “extremely risky”. I guess no need for std. dev. at all. Simply averaging the numbers would sufice.