# Variance in temperature across three sites - 2 way ANOVA?

Example data:

Temp      Site     Bleached  Year
20         A          Y      2001
25         A          Y      2004
20         A          Y      2008
25         A          Y      2011
32         A          N      2001
35         A          N      2004
32         A          N      2008
35         A          N      2011
46         B          Y      2001
23         B          Y      2004
46         B          Y      2008
23         B          Y      2011
23         B          N      2001
43         B          N      2004
23         B          N      2008
43         B          N      2011
33         C          Y      2001
23         C          Y      2004
33         C          Y      2008
23         C          Y      2011
32         C          N      2001
37         C          N      2004
32         C          N      2008
37         C          N      2011


I have made 3 line graphs of temperature across time where the mean temperature at each time for bleached / unbleached is plotted. I'd like to compare if the plots are significantly different in how much they vary within themselves. So for example, one graph has massive peaks and troughs, another is relatively stable. I'd like to analyse this statistically to say they are significantly different so I would think that as I'm analysing the variance in these data, an ANOVA should be used?

Could I use a two-way ANOVA for this, if normality is assumed?

I am using the following formula to input it into R, but I'm not worried about the R side of it. I know the formula looks at the interaction:

Site 1 ~ Site 2 * Site 3


But if I ignore that and just look at main effects, will a two-way ANOVA be appropriate or is there a better way to just look at differences minus interactions?

I missed quite an important edit the first time. I just want to compare how much each site varies within itself over time. I am looking at how variable temperature has an impact on predictability of bleaching / non-bleaching corals. Therefore I need to see if the variability is significant between the sites to make conclusions regarding the bleaching status.

• As it stands your formula does not match your question which is not quite clear either. Can you edit more details into your question? – mdewey Nov 11 '16 at 14:56
• Edited, hopefully clearer now. – MJ98 Nov 12 '16 at 15:07
• It is clearer, thank you, but one key element of the question is ambiguous: could you explain more precisely what a "difference in temperature variance from the mean across the site" might be? It sounds like you want to compare variances between groups, but (because that would be somewhat unusual) perhaps you really intend to compare means? And would "across the site" mean between sites or possibly between dates within sites? – whuber Nov 12 '16 at 15:20
• Sorry i missed quite an important edit the first time. I think that should be much clearer now. I just want to compare how much each site varies within itself over time. I am looking at how variable temperature has an impact on predictability of bleaching/non-bleaching corals. Therefore i need to see if the variability is significant between the sites to make conclusions regarding the bleaching status. Thanks – MJ98 Nov 12 '16 at 15:32

Bleached ~ temp.variance + Site