I want to conduct an contrast analysis to confirm a hypothesis but am confused by the SPSS output and unsure wheather I chose the correct test. It would be great if someone could help me with this.
My hypothesis is that the means of 3 groups differ significantly and that group 1 has the highes mean, group 2 the second highes mean and group 3 the lowest mean (mean 1 > 2 > 3). Therefore, I conducted an ANOVA and tested for polynomial contrasts. The output of the ANOVA showed that all means differ significantly from each other and that there is a significant linear trend (as predicted) AND a significant quadratic trend. How is it even possible to have a linear and a quadratic trend at the same time?
Plus, looking at the means, it is clear that group 1 has indeed the highest mean, but group 2 has the lowest and group 3 is in the middle. So I'd naturally reject my hypothesis, but why does SPSS find a significant linear trend without there being one? Or did I chose the wrong test, if so, how do I test my hypothesis correctly?
My sample size is fairly large (4400 participants, almost equally distributed on the three groups) if that makes any difference.
I hope someone can help me out with this, I'll be gratful for any suggestions!