linear (?) mixed models help?! - simple question from a simple mind

I have a stunningly simple data set and, unfortunately, an equally simple mind when it comes to stats. This is how my data are set up:

I asked people to sit small exams on different days of the week (Friday, Saturday, Sunday and Monday) and their performances in these tests have been calculated as a percentage. Some of them only sat the test on one day, others on more than one day and as such I have a data set that can neither be analysed with a paired nor independent samples test without cutting out data (and my sample size is small enough so that's a no go).

A mixed model is what I have been told I need and as my data are normally distributed am I correct in saying that a linear mixed model is the one to choose?

My study question is whether score is influenced by day of the week so I understand that I set up the model with 'score' as dependent variable, 'ID' as random effect and 'day' as fixed effect - please tell me if that is wrong!

So [1] can anyone point me in the direction of where to get a walkthrough for a LMM (or alternative test if that is incorrect), [2] tell me how to calculate the effect sizes, and [3] what exactly do you report from the wall of tables and figures that spews out of SPSS when it has completed the calculations?!

All help much appreciated!

PS - I have just attempted to tag this post and discovered there is a different between mixed-models and mixed-effects-models. I did not know that so if anyone can explain that also, that would also be swell.

• glmm.wikidot.com has quite a few worked examples to start you with. – usεr11852 says Reinstate Monic Dec 7 '13 at 0:04
• Mixed model is when you have both between-subjects and within-subjects factors (you may have heard of "split plot" ANOVA), which is not your case here. Mixed effects is what you are referring to. It's called mixed effects because you have two types of effects, fixed and random. – Patrick Coulombe Dec 7 '13 at 3:42
• Apologies, it looks like CV doesn't make this distinction between mixed models and mixed effects models. (I'm not sure why both tags are needed on CV then?) – Patrick Coulombe Dec 7 '13 at 3:46