I would try the test for parallel lines using interaction regression variables. See Ott and Longnecker's Intro to Stat Methods for the details. Best, David PS most design of experiments books cover this too

yes I think interaction regression variables are the best suit you

I don't know the background beyond what you have explained, so forgive me if there is an unmentioned reason. You mention expenditure so perhaps a test more directly related to this would be useful? I would need to understand a lot more about the exact question you need to answer. A non-exhaustive list of questions:

Do differences in the temperature range matter? (test for equal variances)?

Do differences in periodicity matter? (test frequencies)

Does an offset matter? (test difference in means)

Does it matter if two rooms are equally variable but shifted in time? (cross correlation)

If it is expenditure, surely you need to estimate total heating load time based on temperature rises, taking into account the effect of external diurnal fluctuations.

one way Anova

I should have been more clear, I am not analyzing cooling loads in this study and energy expenditure, just temperature. I would say that temperature range differences are relevant. I don't really think periodicity matters, it is more of a matter of was room A generally cooler than room B over the time period. Hmm not exactly sure about James' other questions. I don't have access to HVAC data, and am only analyzing temperature data. Basically I am just wanting to find out, do green roofs help lower the temperatures of the rooms below them? I am just looking at the temperature trends over the time period, and ultimately want to conclude if it can be confidently said that room A (with green roof) was cooler than room B (without green roof) over the time period. Of course I need much more types of data to conclude whether it was actually the green roof that caused this temperature difference, but that is for the discussion section of the report. I attached an image of type of graph I am working with.

Thank you all for the thoughtful and insightful responses!

Simple: Take a time period (say 4 hours) and find an average temperature (or minimum/maximum, or range, or median). Do this for green roof and non-green roof. This is a t-test, or if there are several roof materials then something like Tukey's test.

More complex: The shape of the lines in your figure are different. So try accumulating heat units within a time period. You could try different time intervals, 2, 4, 6, 12, or 24 hour periods. In some fields like entomology, a concept of growing degree days is studied where insect life cycles are estimated using accumulated thermal units.

There is a problem if all you have is room A and room B. There is no replication. You need several structures of each roof type. Depending on how the experiment is run, you might think of running the experiment once, then changing the roof type on all buildings. Rerun experiment. Test if there is a building by roof interaction.

Well, the data certainly doesn't form a line graph. This graph looks like a time series with slightly downward trend. There is clearly some periodicity to take into account, maybe two types. Under these conditions I would build two separate predictive time series models for each color roof. Then I would look at cross correlation as a way to compare the two models. For me this would require serious time with an advanced time series book. A good way to start might be to first build the two models and then look at how they are correlated. Googling some of these things might get you started I am clearly out of my depth. Best regards, David

The questions that Prof Beattie raised are clearly important. A good book to look at might be Hamilton, Time Series. Another is J. Keith Ord, Time Series

Best of luck, DEB

Hi everyone, thank you all for the answers! This has given me a lot to reevaluate with my study. Also David, thank you for helping me clear up the type of graph I am working with! I looked into it, and yes, this is definitely a time series! With that being said, it looks like an ideal test for my data will be the repeated measures ANOVA. I think that with this test I will be able to analyze variation between each group. Is anyone familiar with this test? Though I am not sure if it is really statistical difference I am looking for, since I want to know if each group was either significantly warmer or cooler than the others.

Thanks!

Lino, If you go that way check out Longitudinal models. Marie Davidian at North Carolina State Univ. Has an excellent set of teaching notes you can download from her website. See Stat Dept NCSU. If you go the time series route you want to ask how different are the series from the different color roofs. I suspect ways exist but I don't know them. Good Luck, David PS Here is the link for the website.

http://www.stat.ncsu.edu/people/davidian/courses/st790/notes.html

Lino, and discussants,

There is certainly a time series structure in the data, but I think it is largely irrelevant, and should just be regarded as an underlying variation with time (due to variation in outdoors temperature, sunshine, etc). Try to keep it simple! The 24 hours periodicity motivates working with averages over 24 hours, that is daily values. (Possibly at a later stage changed to 12 hours averages, if difference between daytime and nighttime is of interest to investigate.)

Some days are warmer than others, but judging from the diagram, this day to day effect is essentially the same on all curves (plot to check!). Thus, when comparing curves (groups, rooms), the daily average differences between curves are hopefully independent of the temperature level (check by plotting differences against temperature level). This appears to lead basically to a two-way ANOVA structure. A very simple repeated measures situation, if you prefer. If difference between rooms depends on (average) temperature level, this might be interesting per se.

This structure is certainly not perfect, but perhaps good enough, at least to draw conclusions for your next experiment.

Lino, interesting data, I hope my understanding of your situation is good enough to be relevant.

Hello all, thank you for the very insightful suggestions! David and Rolf, understanding my data as a time series really helped me make sense of all my data and potential conclusions. I also put the data for each day as one average temp. for each day, which made working with graphs a lot faster and more digestible. I have made a choice for the statistical test, and went with a one-way ANOVA, with the Tukey-HSD post-hoc test. This was, I can see if there was an overal statistically significant difference between rooms, and then to see how each room compared to the other individually (ex. roomA-roomB (P0.05), roomB-roomC (P

I had a lot of thinking to do about the purpose of my research and the most appropriate statistical test, and chose a one-way ANOVA, and the post-hoc Tukey-HSD test. My reasoning for this test is that each room will be compared to each other room, with each day serving as a different category. The Tukey-HSD serves to find whether the difference in temperature between two rooms is significant. 

While I have heard that regressions might be more appropriate than ANOVA for this type of time series data, I am not really looking for a trend, just difference. For instance, if this were looking at something like climate change, I would be interested in the trend, to see if the globe is warming, and by what degree. Since my data was just recorded over a few weeks during the summer, I don't expect any type of trend upward or downward. However, I am interested in the difference in temperature between rooms. For this reason, I felt that I should use the x-axis (day) as categorical. As far as whether the temperature was taken during the day or night, I just took the average temperature for each day, so one single average temperature for each day.

A confusing aspect I keep coming across is whether my variables (rooms) are independent of each other, or dependent on one another. They are separate rooms, but in the same building, so I am not completely sure. As for whether or not the x-axis is dependent or independent, I would think that time throughout each room would be dependent, because temperature is being recorded in the same room every day. 

The results from the Tukey-HSD test came back with some pretty straight forward results, telling me which room differences where significant, so for now I am thinking this should do.

Do you think this sounds ok?