We've data from a large ongoing project at a big science museum. We are showing people plates of food where we vary the plate shape (round or square; 0,1), food arrangement (polygonal or vertical arrangement; 0,1) and the number of items on the plate (3 scallops or 4). For each pair of plates+food, we ask the individual which they prefer. A person will only ever get trials where there are 3 vs 4 items on a plate. Below are our frequencies.

items,plate,arrangement,weight
3,1,1,249
3,1,0,177
3,0,1,282
3,0,0,184
4,1,1,243
4,1,0,297
4,0,1,185
4,0,0,281

I originally used loglinear analysis. I have a doubt though about this study. It feels as if some assumption has not been met. My question is: do you think this data is valid for such an analysis? Our criteria of only showing participants plates where there were 3 vs 4 items of food is bothersome.

For the curious, here is the loglinear model output (pdf).

We've data from a large ongoing project at a big science museum. We are showing people plates of food where we vary the plate shape (round or square; 0,1), food arrangement (polygonal or vertical arrangement; 0,1) and the number of items on the plate (3 scallops or 4). For each pair of plates+food, we ask the individual which they prefer. A person will only ever get trials where there are 3 vs 4 items on a plate. Below are our frequencies.

edit:

• I have added 'test' which details which item x plate x arrangement was tested with which other such grouping.
• where 'weight' is the number of times the people decided one grouping (item x plate x arrangement) was preferred over another in a given text.

items,plate,arrangement,test,weight

3,1,1,1,249

3,1,0,1,177

3,0,1,2,282

3,0,0,2,184

4,1,1,3,243

4,1,0,3,297

4,0,1,4,185

4,0,0,4,281

I originally used loglinear analysis. I have a doubt though about this study. It feels as if some assumption has not been met. My question is: do you think this data is valid for such an analysis? Our criteria of only showing participants plates where there were 3 vs 4 items of food is bothersome.

For the curious, here is the loglinear model output (pdf).

afraid I'm a newbie at stats.stackexchange.

we've data from a large ongoing project at a big science museum. We are showing people plates of food where we vary the plate shape (round or square; 0,1), food arrangement (polygonal or vertical arrangement; 0,1) and the number of items on the plate (3 scallops or 4). For each pair of plates+food, we ask the individual which they prefer. A person will only ever get trials where there are 3 vs 4 items on a plate. Below are our frequencies.

items,plate,arrangement,weight
3,1,1,249
3,1,0,177
3,0,1,282
3,0,0,184
4,1,1,243
4,1,0,297
4,0,1,185
4,0,0,281

I originally used loglinear analysis. I have a doubt though about this study. It feels as if some assumption has not been met. My question is, do you think this data is valid for such an analysis? Our criteria of only showing participants plates where there were 3 vs 4 items of food is bothersome.

For the curious, here is the loglinear model output (pdf).

With best wishes and many thanks, Andy.

We've data from a large ongoing project at a big science museum. We are showing people plates of food where we vary the plate shape (round or square; 0,1), food arrangement (polygonal or vertical arrangement; 0,1) and the number of items on the plate (3 scallops or 4). For each pair of plates+food, we ask the individual which they prefer. A person will only ever get trials where there are 3 vs 4 items on a plate. Below are our frequencies.

items,plate,arrangement,weight
3,1,1,249
3,1,0,177
3,0,1,282
3,0,0,184
4,1,1,243
4,1,0,297
4,0,1,185
4,0,0,281

I originally used loglinear analysis. I have a doubt though about this study. It feels as if some assumption has not been met. My question is: do you think this data is valid for such an analysis? Our criteria of only showing participants plates where there were 3 vs 4 items of food is bothersome.

For the curious, here is the loglinear model output (pdf).