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waeggles
10-03-2011, 01:12 PM
Hello,

I have been working with higher level statistics for so long that I have started to forget rudimentary techniques...
I have a sample of 350 individuals and I ask them to indicate their agreement with a set of emotions after a certain event (on a likert scale, like so:
Did you feel:
Happy 1 2 3 4 5 6 7
Sad 1 2 3 4 5 6 7
Annoyed 1 2 3 4 5 6 7
Excited 1 2 3 4 5 6 7

I then create composite variables: Positive emotions (Happy+Excited), Negative Emotions (Sad+Annoyed). If I want to make a statement about whether in general the sample felt more positive emotions than negative, i.e. Mean_Positive > Mean_negative. What would I use for significance testing? Paired t-test???

Thanks,

J

noetsi
10-03-2011, 01:30 PM
The problem with using a paired t is that you have to be able to generate a mean to test. Some argue that this is not valid with Likert data which is ordinal in nature (although composite values limit that problem). In other words you have to conclude that the data above reasonably allows a mean. Usually when you do paired t-test you are testing if the the same unit changed over time or from one state to another. I don't think you are doing either here, you are simply looking at whether the overall mean is negative or positive. There is nothing to compare it to to determine if its statistically signficant.

If you had another population, perhaps generated in different research or some theorized mean agreed on in the literature you could do a one sample t-test (where you would be comparing your values to that other mean). Or you could state substantively that the effect size was large enough and in the right direction to matter (this would not be a statistical test, it would be an interpretation of the result based on the literature, your own opinion, or past results in related areas).

waeggles
10-03-2011, 02:03 PM
The problem with using a paired t is that you have to be able to generate a mean to test. Some argue that this is not valid with Likert data which is ordinal in nature (although composite values limit that problem). In other words you have to conclude that the data above reasonably allows a mean. Usually when you do paired t-test you are testing if the the same unit changed over time or from one state to another. I don't think you are doing either here, you are simply looking at whether the overall mean is negative or positive. There is nothing to compare it to to determine if its statistically signficant.

If you had another population, perhaps generated in different research or some theorized mean agreed on in the literature you could do a one sample t-test (where you would be comparing your values to that other mean). Or you could state substantively that the effect size was large enough and in the right direction to matter (this would not be a statistical test, it would be an interpretation of the result based on the literature, your own opinion, or past results in related areas).

Thank you very much for the help. Sorry if I was unclear. What I want to test is whether the sample experienced greater positive emotions than negative ones. So, I want to test whether the Composite score for positive emotions is significantly higher than the negative composite.

noetsi
10-03-2011, 02:51 PM
No that was clear. I just don't think a paired t-test will do that. Normally with such a test you are comparing the individuals on one dimension (usually after some time period, intervention etc). For example people on weight before and after a diet. The same measure (weight) is having a mean calculated at two different times (or before and after an intervention if you prefer). In your example you are trying to compare means on two different measures to see which measure is larger for them - and I have not seen paired t tests used that way (or described that way in the literature).

But I could well be wrong. Others may clarify this better.

Jake
10-03-2011, 04:08 PM
I don't see a problem, I think the description just makes it sound a little odd. Testing the difference described by the OP simply amounts to testing whether the difference score [(happy + excited) - (sad + annoyed)], or equivalently, [happy + excited - sad - annoyed], differs from 0. The OP frames this as testing the difference between two different measures, but in practical terms it is equivalent to testing whether a single composite measure differs from an a priori value of 0. It's not fundamentally different from testing whether [posttest - pretest] differs from 0. There are more optimal ways to ask both sets of questions but that discussion is perhaps for another thread.

noetsi
10-03-2011, 04:32 PM
That makes sense to me:) I thought of it as comparing two totally different measures not the difference between two related measures. To me Jake's comments suggest one unified measure with happy plus excited reflecting the positive half of the scale and sad plus annoyed the negative half.