It sounds like you are looking for a seasonal model.
For example, you might use a linear regression model with ARIMA as the error term as you can do with the arima function in R.
Tableau doesn't have any sort of seasonal model yet.
A linear trend through your data will give you an insignificant p-value if there is no significant slope.
However, in 7.0, we have added t-tests for the significance of each term in the regression in addition to the f-test which gives you the p-value for the line. With 7.0, you would see that your intercept term has a significant p-value.
But, I recommend adding reference lines instead. You could add a reference line for the average and another for a confidence band at the 95% level. This gives you the information you would get from a constant model. You could also add the standard deviation band and show your students how the confidence band changes width as either the number of observations or the standard deviation of the observations changes.
With regards to ANOVA, Tableau currently only has multi-factor ANOVA for regressions. This is used to test the significance of categorical variables in the trend line model when you use them to partition your data.
If you are using a 7.0 beta, I have five workbooks that I use for teaching statistics with Tableau.
A couple of them use references lines as I described above and another shows how to use trend line ANOVA feature to select the correct categorical variable to use in your model.
I've attached a couple just in case.
Remember, you need the 7.0 beta to view the workbooks.
good luck, Scott
That's fantastic - thanks for the help and advice
The materials from the Tableau Customer conference 2011 (TCC11) Session presentations are now online.
Here is the link to a zip of the powerpoint and all the demos for my Statistics session: