Date: Sun, 25 Sep 2011 15:00:44 -0400 Gene Maguin "SPSSX(r) Discussion" Gene Maguin Re: 2 x (2) design with binary-->continuous within-subject variable <1316920405699-4837785.post@n5.nabble.com> text/plain; charset="us-ascii"

I don't know how to analyze this but I'm curious about the study design. How did the design work? Do you present them with a scenario but vary the outcome likelihood information such that in one condition you say 'likelihood of success is x' and in the other condition you say the 'likelihood of success is 'y out of 100' where y=100*x. And while x varies over persons, x and y/100 are the same for both of a person's trials? The person then makes a yes/no decision?

If so, it would seem like the null hypothesis is that the two plotx of proportion of yeses by likelihood of success should be coincident or, more correctly, be not different.

Gene Maguin

-----Original Message----- From: SPSSX(r) Discussion [mailto:SPSSX-L@LISTSERV.UGA.EDU] On Behalf Of ac11ca Sent: Saturday, September 24, 2011 11:13 PM To: SPSSX-L@LISTSERV.UGA.EDU Subject: 2 x (2) design with binary-->continuous within-subject variable

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.