To elaborate on Peter's point your options to identify systematic individual differences depend on the nature of your experimental design. If you have one data point per person you will find that any differences are perfectly aliased with the error term: you don't know whether someone scored better or worse because of systematic differences (they are genuinely better) or because of unknown/chance factors.

If you multiple observations per person and sufficient sample size you might be able to model individual differences (e.g., via a multilevel mode), but this is not a trivial matter.

You can also get further by making very strong assumptions about the nature of the errors (e.g., normality).

I think Jochen's original suggestion might be more useful in practice - identifying highly influential data points (e.g., by plotting or via a metric such as Cook's distance) and seeing whether your model is dominated by one or two very influential participants or data points.

Plot the data, look at "outliers". If you have some assumption about the underlying distribution you might find an "outlier test". Otherwise you can use bootstrapping to calculate the significance of the outlying values.

Thank you for your response. Will look into it.

Here, You can use Independent t-test to check the difference with same group. If your need to check more classification within group of men or women such like age-wise, education wise, etc., then you can use either one of these ANOVA/MANOVA/ANCOVA. It is fully depends on your purpose of study.

Good luck.  

Hi,

if you are testing auditory processing through a continous scale, and it is normally distributed, and you have enough number of participants {males and females: at least 35 per gender} then you can use the Independent sample t-test.

Dear Rangasamy and Muayyad,

how can the question ->"whether there were differences for some individuals across groups" be answered by ANOVA / t-test?

Dear Pasquale,

   I may not understand the question, but it doesn't appear entirely clear to me.

JW's solution is to effectively ask if each group (or the population) is normally distributed. Any cases that are "outliers" are worth considering as exceptions to your null effect. Obviously the p value depends on whether you actually do have knowledge of the population distribution for your auditory test... and the suggestion to bootstrap is practical but not always convincing.

I might be tempted to try to define (ideally theoretically) what a useful and important difference would look like. You can then compare this to the range from the lowest to highest scores and decide about the potential importance and coverage of your solution. If people fall within this range, no statistical approach is needed.

If people are more dispersed then this, then I would consider calculating the counter-null to see which is the largest group difference likely to be consistent with the actual data. This is not quite the statistical test you asked for, but the CI on the counter-null allows you place a reasonable limit on what effect could be present.

This does somewhat presume that the distributions within groups are somewhat continuous; if not you might consider comparing a finite mixture model against a simple normal (or other) distribution and using the resultant p value to address this. 

The answer to your question is that no statistical test is needed or even possible for this question.  But the answer to the question is always "yes".  That is, in any two (or more) groups of people (or other subjects) measured on hearing (or any other trait) there will be differences between some members of the groups.

The only exception would be if all subjects are the same.

Bruce,

"JW's solution is to effectively ask if each group (or the population) is normally distributed." - No. That was not meant. I don't care about the shape of the distribution. The purpose of plotting is just to get a visual impression of the distribution (of whatever shape it might be), to be able to recocnize if the values "clump" somwhere and if one can identify particular data points that are "clearly different" from the whole rest.

"he suggestion to bootstrap is practical but not always convincing." - Agreed :)

"I might be tempted to try to define (ideally theoretically) what a useful and important difference would look like. " - very very much agreed!!

It is really contingent on your Research Questions, and the unit of analysis, and the scales of measurement for your dependent measures. Book strapping is definitely an option.   Just exercise caution with T-test......you often have to run a number of t-tests that inflates your type 1 error....which you would have to correct with Bonferroni adjustment........any time you run excess stats test you can get an inflated Type 1 error....that's what it often prefer to use ANONA......MANOVA, if you have 2> DV most powerful and reduces type 1 but again contingent on your RQs.

You could test if there are other variables, such as age, interacting with sex to influence the results (so you need a multiple statistical model with interaction terms): for example you would possibly find differences between old males and old females. Othewise, the answer of Peter Flom is, in my opinion, the right answer, because statistical tests usually compare the average effect of the variables, not single individual differences! 

To elaborate on Peter's point your options to identify systematic individual differences depend on the nature of your experimental design. If you have one data point per person you will find that any differences are perfectly aliased with the error term: you don't know whether someone scored better or worse because of systematic differences (they are genuinely better) or because of unknown/chance factors.

If you multiple observations per person and sufficient sample size you might be able to model individual differences (e.g., via a multilevel mode), but this is not a trivial matter.

You can also get further by making very strong assumptions about the nature of the errors (e.g., normality).

I think Jochen's original suggestion might be more useful in practice - identifying highly influential data points (e.g., by plotting or via a metric such as Cook's distance) and seeing whether your model is dominated by one or two very influential participants or data points.