I can definitely second MLwiN for multilevel modelling - and the online information course is excellent. Sorry, no help with R, but it does seem like a very steep learning curve to do ANYTHING!

Yeah I put these plots into my thesis too - though I ran LOTS of tests, so I ended up putting in an example of one that was pretty perfect in terms of normaliy and one that was not so great as illustrations.

The data are what the data are - you can't change it. I am wondering though if you can assume normality if the CLT applies - even if your actual data points are not normally distributed e.g in a t test as long as the underlying distribution is normal, and you have more than 30 observations then the CLT applies and you can assume normality. if you have less than 30 obs then it is best that the actual data points are normally distributed.I am not sure about time series data though so this may not be relevant. Also, it is multivariate normality that the test assumes?

I think that as long as you address what they say and explain why it doesn't work then as long as your explanation is justified and referenced then you can't do anything else.

Sounds a difficult situation. Are there any equivalent non-parametric tests you can do?

I know some people who wrote up their statistical tests even though assumptions were violated, but explained that there were violations and that care had to be taken in interpreting the results. Can you use robust standard errors so you don't need to assume normality/independence, depending on the test and the violations?

Alternatively, would it work if you outlined the more complex tests, talk about why they may not be reliable and then discuss your original analysis and contrast your results?

I think you might want to look into a repeated measures ANOVA, or you can possibly use regression and put in the time as a control variable. You may also be able to use robust standard errors for the ANOVA by applying a bootstrap to your data. The non-parametric anova is a kruskall-wallis. Not sure if you can do repeated measures on that in SPSS.

Andy Field's book (and the tons of hand outs he has on his website) will be really useful resources at this stage for more info on all the points I have made above. Take a bit of time and read it thoroughly and slowly as it is wordy but it really written for non stats people, just portion out time to read it - will make things less painful in the long run. The other book is the SPSS survival guide by Juile Pallant which is a bit less wordy - maybe start there and then read Field.

Good luck

I remember getting the song sung to me as a kid! What tests are you using? It sounds to me like your examiners think you might have violated assumptions of independence. In this case the multilevel models could still work - it is quite an emerging technique outwith education - but I do know it can be applied in the sciences. Have a good weekend and try not to stress too much - you really are so close!

Hey,
Just the final push now! My thesis was quite stats heavy too - but I haven't used minitab. Let me know if I can help. If you are using educational data, accounting for nesting seems to me to suggest using multilevel models - is that what your internal suggests? If so, it is quite hard-core at first, but is easy enough to get your head around the basics. I can recommend you some resources. If they haven't mentioned multilevel modeling then I don't want to scare you - I am sure they would have said if that was what they intended. Message if I can be of any use.