My doubt is a basic one. However, I still havent found what i am looking for...

All the inferential statistics textbooks and tutorials I have consulted so far give examples in which each subject gives only one response in each level of the independent variable. So I am unclear about the correct procedures in cases in which each subject of a group is given more than one trial at each level of the independent variable.
(I have sometimes seen the expression "pooling across subjects" but I have never undesrtood it (i am not an english speaker, as you probably can see))

For example,
"I want to measure the reponse time of 5 subjects in a certain task in two different conditions, A and B. Then, each of the 5 subjects is given 40 trials in condition A and 40 trials in condition B. A paired t-test is performed to determine the statistical significance of the difference between the conditions A and B".

What is the correct way to calculate the means to be compared?
1.Should I analyse each subject separately?
2.Should I first calculate the mean response time of each subject and then calculate the mean of these means in each condition such that i can compare the two means using the t-test (n=5)?
3.Should I calculate the mean of the 200 (5 x 40) values in each condition and then compare the two means(n=200)? (Is that "pooling across subjects"?)

No reply...

As a beginner i am just wondering if my question is senseless or maybe too obvious.

If so, please let me know.

Thanks...

Hi Daniel,

Does each of the 40 trials in each condition contain a single item, like a word, behavior, situation? For example, I know it's common in psycholinguistics that subjects will see the same 40 words in each of 2 conditions, for a total of 80 trials.

Or is each trial just a replication of the exact same situation?

If it's the former, the traditional way to approach this is to average across the 40 trials in each condition (pooling across trials) so that each person has 2 values--one in each condition. Then run a paired t-test.

Depending on the purpose of your research and the amount of variability among trials, you might be able to use this approach. The problem with it, though, is it ignores the variability among the trial items. But if you're hoping to publish and if there is a lot of intertrial variation, you probably won't be able to. Instead, you'll have to use a mixed model with crossed random effects. I can give you more info on that, if that's the case. If you're familiar with mixed models, it's not too difficult.

If the trials are just replicates, then it's not quite the same, because beyond order, there's no reason to think that trial 10 for one subject would be more similar to trial 10 for another. You will still have to run a mixed model, because there will still be variability among the trials.

Karen

Dear Karen,
thank you for the reply.

-Presently, I am not involved in any research activity. So i prefered to give an as-simple-as-possible example.

-I am not certain i actually understand the difference between the two possibilities you mention. Is that the the same as the difference between the following two instances (based on the example given in the first post)?

1. Condition I: words; Condition II: nonwords. (We have two sets of 40 different stimuli corresponding to each condition).
2. Condition I: a sound increasing in pitch; Condition 2: a sound decreasing in pitch. (The same sound is presented on each trial within each condition).

If so, I hadn't considered such difference. I thought both cases would be treated as equivalent since the value of the independent variable is the same within one level.

-I know what linear mixed models are but I have never used them. Let me see if I got the point:

Based on your replay I can conclude that it can be acceptable (but not ideal), for example, the simple procedure of making a table in SPSS with 5 lines (subjects) and two columns (conditions A and B) and then run a paired t-test. Each cell would contain the average across 40 trials, hence I would be ignoring the variability among trials within each subject.

A better (more rigorous) choice would be to use mixed models becouse I have two levels: the level of the individual trials and the level of the subjects. That sounds very interesting. I could make a table in SPSS with 200 rows and 3 columns ("subject", "condition" and "response time") and run a mixed model. This way the intertrial variability would be taken into account.
But I still dont understand why "crossed random effects". I can identify only one random effect (subjects).:o

Thank you very much for your help. I greatly appreciate it.

Daniel.

Dear Karen,
thank you for the reply.

-Presently, I am not involved in any research activity. So i prefered to give an as-simple-as-possible example.

-I am not certain i actually understand the difference between the two possibilities you mention. Is that the the same as the difference between the following two instances (based on the example given in the first post)?

1. Condition I: words; Condition II: nonwords. (We have two sets of 40 different stimuli corresponding to each condition).
2. Condition I: a sound increasing in pitch; Condition 2: a sound decreasing in pitch. (The same sound is presented on each trial within each condition).

If so, I hadn't considered such difference. I thought both cases would be treated as equivalent since the value of the independent variable is the same within one level.

These are equivalent. :) What I mean was--let's use your example 2--in the case of pure replication you use the exact same sound increasing in pitch 40 times. You literally play a copy of the same stimulus over and over--ma, ma, ma.

In the case of different stimuli, you would have 40 different sounds--ma, ri, lu, whatever--each of which increase in pitch. So every subject gets all 40 stimuli, but these 40 stimuli are a sample of all sound stimuli that rise in pitch.

-I know what linear mixed models are but I have never used them. Let me see if I got the point:

Based on your replay I can conclude that it can be acceptable (but not ideal), for example, the simple procedure of making a table in SPSS with 5 lines (subjects) and two columns (conditions A and B) and then run a paired t-test. Each cell would contain the average across 40 trials, hence I would be ignoring the variability among trials within each subject.

A better (more rigorous) choice would be to use mixed models becouse I have two levels: the level of the individual trials and the level of the subjects. That sounds very interesting. I could make a table in SPSS with 200 rows and 3 columns ("subject", "condition" and "response time") and run a mixed model. This way the intertrial variability would be taken into account.
But I still dont understand why "crossed random effects". I can identify only one random effect (subjects).:o

Thank you very much for your help. I greatly appreciate it.

Daniel.

The other random effect is stimuli. The idea is those 40 stimuli weren't chosen because you want to compare the reaction time of "ma" to "ri." (I am totally making up these stimuli!). You just chose 40 that work from the world of all possible sounds that rise in pitch.

The two random factors are crossed if every subject gets every stimuli. It's weird to think about because you could think of trials nested in subjects, as you are correctly doing. But trials are also nested in stimuli. The same stimulus, say "ma" has 5 trials (for the 5 subjects). If people, for some reason, always have faster response times to "ma" than to "ri" then there will be similarities in the response times to the stimuli.

It's kind of weird to think about, I admit.

Here are a few resources:

http://www.analysisfactor.com/statchat/?p=187
http://psych.unl.edu/psycrs/945/index.html -- go to week 5.

The first is a quick article, the second is more in depth.

Karen

Nice! I can see! Time to study it hard.
Then I can conclude that in a case in which the 40 sounds are replications of the exact same sound (ex. :40 rising-pitch ma vs. 40 decreasing-pitch ma), the number of random effects is one.

Thank you SO much and best wishes!