First, I suggest you do a spaghetti plot of your data so i, at least can understand your experiment. I suggest that you probably want to know about tank temp difference over time. because the treatment temperatures are surely different.

Best, D. Booth

First, I suggest you do a spaghetti plot of your data so i, at least can understand your experiment. I suggest that you probably want to know about tank temp difference over time. because the treatment temperatures are surely different.

Best, D. Booth

Hello Shang-Hen,

It sounds to me as if you have two independent variables: treatment (2 levels), and occasion (14 levels). Treatment is a between-subjects factor, and occasion is a within-subjects (repeated measures) factor. So your design would be referred to as a one-between, one-within anova, a split-plot anova, or a "mixed" (old terminology use of the term, mixed) anova, depending on what source you consulted.

David Eugene Booth 's advice to inspect your data first is always a good idea.

Good luck with your work.

Yes, spaghetti plots suggested above is always a good idea.

Now about formal statistical tests.

Suppose you have two time series: x_t and y_t

Then delta_t=x_t-y_t

Your task is to see if mean(delta_t) is different from zero.

This series (delta_t) may contain auto correlations. Moreover, it may be non-stationary.

You need to apply ADF test. If delta_t is not an I(0) series, the conclusion is that yes, the temperature is different (high evidence for that).

If delta_t is likely to be (0), you need to describe in with an ARMA model with an intercept. You then need to detect if the intercept differs from 0 significantly. I think here you need standard methods for ARMA estimation.

If delta_t does not contain AR-terms, you can try t-test.

Also, I would recommend plotting delta_t instead of x_t and y_t.

P.S. For spaghetti plots please let me recommend our ePoster:

Poster A Visual Framework for Longitudinal and Panel Studies (with ...

Yes, David Eugene Booth 's advice to inspect your data first is always a good idea.

And just a personal choice, I prefer call "mixed" instead of split-plot anova because to me is confusing with split-plot design, but it is just me because I have an agronomical background and influenced by Fisher, that first propopsed the split-plot design in agricultural experiments.

Thank you for your advice, Dr. David Eugene Booth, Dr. David Morse Dr. Andrey Davydenko and Dr. Roberto Molteni , it really is a good idea. unfortunately, I haven't complete my formal experiment so far, so I can only provide the pre-test result.

In the experiment, I don't want any significant different between 2 treatment, please give me some suggestion, thank you very much.

If you plot delta_t as I described earlier, you'll see that delta_t is usually >0. Moreover, if you apply the Mann-Kendall test to delta_t, you'll probably see it has some trend.

So, yes, there's high evidence for the measurements being different.

In fact, from your plot you can see that the red line is usually a bit higher than the blue one.

Btw, to make your plots easier to read, you can use our framework presented here:

Poster A Visual Framework for Longitudinal and Panel Studies (with ...

In particular, instead of black filled circles it is better to use some shapes from 'xdPlotChars1' presented on the above ePoster. This is especially useful if you have many time series on the same plot: when filled shapes overlap, this harms readability.