Date: Sat, 24 Sep 2011 20:13:25 -0700 ac11ca "SPSSX(r) Discussion" ac11ca 2 x (2) design with binary-->continuous within-subject variable text/plain; charset=us-ascii

Hi there,

I am hoping that you might be able to help me analyse some data from a decision-making experiment I ran recently.

I have a 2 x (2) design where the within-subjects measure variable changes from a binary response (i.e., 0,1) to a continuous response (i.e., 0-100). I realise that this is very odd, but it is central to my current research question: Are people more like to prefer a risky gamble over a safe gamble if the choice is presented as a single play or the accumalted sum of 100 plays?

My data looks like this in SPSS (Note: Format = between-subjects categorical IV [coded 1,2] and Plays = within-subjects categorial IV [coded 1,2], and Choice = DV that is half the time binary [0,1] and half the time continuous[0-100]):

ID Format Plays Choice 1 1 1 0.00 1 1 2 0.15 1 2 1 1.00 1 2 2 0.78 . . . . 93 1 1 0.00 93 1 2 0.01 93 2 1 1.00 93 2 2 0.97

I started by analysing my data with a mixed ANOVA and found an interaction, which is what I was hypothesising. Of course, one of the assumptions of the ANOVA is that the data are normally distributed, which they clearly are not with my binary response data.

To get around this problem I conducted a repeated measures logistical regression using the SPSS Generalised Estimating Equations function (GEE) under a binary model type. However, the GEE method accepts only one distribution for my within-subjects variable: binomial or scale responses. If I chose scale, then I am just running an ANOVA (I think!). If chose binomial, then I have to convert the continuous DV to a binary DV (and cut all 50/50 responses), which basically undermines the motivation of the experiment and eliminates crucial differences.

Thus, I think that I must use the original mixed ANOVA analysis and produce some hand-waving sort of justifcation. I was wondering if anyone might be able to help me with this justification. For example, what is the impact of having a binary DV in the middle of a mixed ANOVA and is it really so bad?

Thanks for any help that you might be able to provide. If anyone wants to see the data, feel free to email me at ac11ca[at]hotmail[dot]com.