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Context

I have 25 men and 25 women as participants, and they did exactly the same thing: Each of them heard an attractive dialogue and they had to choose between a photo of a woman in red and a woman in green. Then each of them heard an unattractive dialogue and they chose again between the red and the green shirt.

My hypothesis is that men are attracted to women in red in contrast to women. So, I 've got gender (2levels:0=male, 1=female), attraction (1=yes, 0=no) and trials/colour (0=green, 1=red)

I am interested in showing that the colour (red) predicts attraction as far as men are concerned and that there are gender differences! Men are much more attracted to it.

Questions

  • Should I use a test which combine all of them or a test that combine first the attraction and colour for men, then the attraction and colour for women and then the gender differences?

I've been told to run a pearson's correlation (one for men and one for women) but I think that it demands interval data.I was also told to use the chi- square test but it's not for participants who parrticipated in the same experimental conditions.

  • What about repeated measures logistic regression? If so, can you give me some advice how to process my data? Any suggestions?

P.S. I really appreciate everyone who answered my previous posts here and here, they helped me to go one step further!

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If we can assume that the men and women were selected randomly, your design is a special case of completely randomized design (CRD) with 2 treatments. As you mention, repeated-measures, I must remark that if gender is assumed to be a block, then it models correlation (and repeated measures is a way of imposing correlation). If you treat gender as a block, then the design will be a randomized complete block design (RCB) with 1 treatment. You can still test the effects of gender, but the tests will be conservative.

In summary:

  • Response: attraction (0 or 1)
  • Treatment 1: gender (male or female)
  • Treatment 2: color (green or red)

If the analysis is CRD, then you model gender and color as fixed effects and attraction as response.

If the analysis is RCB, then you model gender as a block (random effect), color as fixed effect, and attraction as response.

Irrespective or RCB or CRD, your responses are binomial (Bernoulli, 0 or 1). Therefore the solition boils down to fitting a GLMM with a logit-link.

As you are interested in the relationship between men and color, you might want to include the interaction of color and gender in the model. This will be in the case of CRD. Once you have the model fit, you can use the following contrast to see if men are attracted to red than women:

$$H_0: g_mc_r-g_fc_r=0$$ $$H_a: g_mc_r-g_fc_r\neq0$$

Unfortunately, ANOVA (or GLMM) can't give you a one sided test, that is, $g_mc_r-g_fc_r>0$ (although I have seen people do it).

I am aware that SPSS can fit GLMM, but not sure how. I will let someone else give the exact SPSS instructions.

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  • $\begingroup$ Perhaps it deserves its own question, but do you mind elaborating on the statement in regards to the RCB "You can still test the effects of gender, but the tests will be conservative." $\endgroup$ – Andy W Jul 8 '11 at 14:55
  • $\begingroup$ @Andy This is a good question. Unfortunately, a lot of people don't bother about it. A good discussion is on page 108 of Statistical Design by Dr. Casella. In short, blocking pays off only when the block-effects are significant. Thus, if we are in a situation where the blocks can be chosen, it makes sense to choose them as disparate as possible. Blocking is a form of modeling correlation structure. Testing for a random term to be some fixed number doesn't make sense (even though it can be done.). The anova test-statistic is approx. F, hence conservative. Proper way is to use mixed-models. $\endgroup$ – suncoolsu Jul 9 '11 at 11:49
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Generalized Mixed is available in latest version of SPSS. But Olga might prefer easier ways. So, as I understand, there are 3 variables in the data: gender (values male vs female), attractive dialogue (values red vs green), unattractive dialogue (values red vs green). To check hypothesis that males endorse red more often than green hearing dialogue one just performs gender X colour chi-square test (probably 2 times, once for attractive dialogue, once for unattractive). Because the table is 2x2 it's equivalent to Pearson r. To check hypothesis that the attractive dialogue envokes more red responses than the unattractive one, McNemar's test is suitable. The tests are found in SPSS Crosstabs procedure.

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Just run a contingency table, and then a logistic regression. contingency table: color x gender and color vs dialogue.

Then, logistic regression

color = a + b*gender + c*dialogue + d*dialogue *gender

the interaction term will test your hipothesis that the main efect of gender isn't affected by dialogue. However, be awere that interpreting interactions terms in logistic regressions are tricky:

Ai, Chunrong / Norton, Edward (2003): Interaction terms in logit and probit models, Economic Letters 80, p. 123–129

Last, but not least, I don't think you have a nested model, but a non-nested model. In any case, since the groups are small, It won't help you to model it as a multilevel model. So, just run a simple logistic regression.

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The main criterion on which test or further handling is appropriate depends on the level of measurement. As you've pointed out, your data are nominal. To every level there are allowed operations e.g. nominal: $=, \ne$, on ordinal: $\lt, \le, \gt, \ge$ and so on.

Hence the only thing to describe nominal data is by showing equality to one category. I would suggest that you just count if more male or female are attracted to it in contrast to which are don't.

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  • $\begingroup$ p.s.: you should also specify the main group of people for whom your thesis is appropriate because to conclude from 25 men on all men isn't really representive. Just be more specific: All men on your workplace or your town or something like that. $\endgroup$ – beyeran Jul 8 '11 at 7:37

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