I have become completely confused with regards to which variety of ANOVA I should be using to replicate some analysis. Beyond unfamiliarity with the test, I think this is due to trying to reconcile differing accounts of how the test has previously been performed with the data.
Whatever is the case, I just feel completely befuddled and would appreciate another pair of eyes and a clearer head chipping in.
The problem
Data
I have three sample sites - each a utility-scale solar power station. Around each I have 19 100m-wide rings extended outwards from their boundary. In each ring I have derived the average land surface temperature (LST). I have repeated this once a month for 24 months - one data per month per ring - with 12 months prior to construction, and 12 months after.
Hypothesis
Does the presence of a utility-scale solar installation affect land surface temperature nearby?
Data wrangling
The data are initially in a 'wide' table - with the first column Buffer (100-1900m), and the next 24 columns the monthly data.
I have used pivot_longer in R Studio to mutate this into a long table, then created additional columns for Month (by extracting a month number from the date), and TimePeriod (0 prior to construction, and 1 after construction).
My data table is therefore in the format:
Buffer LST Month TimePeriod
100 3.54 1 1
200 2.56 1 1
300 2.53 1 1
...
The analysis
Initially I used a two-way ANOVA with repeated measures, with dv = LST, wid = Month, and within = c(Buffer, TimePeriod).
Where:
- LST = surface temperature deviation (from an average) in C
- Month = 1-12
- Buffer = a value 100-1900 - one of 19 areas outward from the boundary of a solar power plant (each 100m wide)
- TimePeriod = a factor with a value of 1 or 2 corresponding to pre-/post-construction of a solar power plant.
Re-reading the original method, I'm not sure if I shouldn't be using a one-way ANOVA with repeated measures, where Month is the repeated measure and TimePeriod is the explanatory variable.
When I try and do this test, though, it doesn't work. I can't seem to group the data by Month in R, and if I can't do that there are obviously matching keys each month unless I incorporate Buffer as a variable.
I can't seem to get my head around which variables are which - and consequently can't work out the correct method. No matter how many examples I read online I can't get it to make sense and just seem to be making myself more confused.
Request for help
Can you help me get this straight? Which variable is which, and which test should I use?
Edit
To illustrate the 'rings' from which LST is derived.
Working in Google Earth Engine:
- Locate suitable aoi
- Draw geometry object to describe boundary of solar site. Draw additional geometry objects around surface features that might confound processing pipeline (e.g. topography, water, salt pans, golf courses)
- Generate 100m-wide rings (buffers) extending outwards from the boundary of the solar site.
- Create a mask using potentially confounding areas
- Create masked rings (this is the most extreme clipping of all sites due to the salt-pan and nearby solar-concentrator sites)
- Process Landsat 8 data to extract the average surface temperature in each masked ring.
Generated data:
dput(data)
structure(list(Buffer = c(100L, 200L, 300L, 400L, 500L, 600L,
700L, 800L, 900L, 1000L, 1100L, 1200L, 1300L, 1400L, 1500L, 1600L,
1700L, 1800L, 1900L), `15/01/2010` = c(0.580552675, 0.502427717,
0.424272426, 0.322662088, 0.276423067, 0.296410675, 0.300255406,
0.293503101, 0.221852835, 0.156474538, 0.155695066, 0.094020687,
0.087734787, 0.054501308, 0.032450673, 0.07752603, 0.044981296,
0.025642565, 0.028893467), `16/02/2010` = c(0.970746407, 0.908338611,
0.850354266, 0.724290238, 0.652515808, 0.548074344, 0.431608248,
0.305626873, 0.220168823, 0.321279759, 0.251755903, 0.171728052,
0.187491184, 0.141956002, 0.111823519, 0.15549293, 0.085887693,
0.020230238, 0.01256147), `20/03/2010` = c(1.627607407, 1.344880439,
1.115972847, 1.022763599, 1.023629255, 0.875259921, 0.768911951,
0.739025174, 0.689252542, 0.778222174, 0.683311682, 0.44018711,
0.48268724, 0.414392563, 0.460692024, 0.482097117, 0.235257584,
0.111643644, 0.084874091), `24/04/2011` = c(2.139468759, 1.97844065,
1.755013632, 1.547944727, 1.472394813, 1.365201053, 1.241123025,
1.130024888, 1.084274915, 1.13194737, 0.959184096, 0.743134896,
0.767854044, 0.706093082, 0.65185831, 0.622260835, 0.463780381,
0.227011499, 0.183078336), `07/05/2010` = c(1.902422481, 1.717518818,
1.660216773, 1.496388619, 1.401870845, 1.299025971, 1.155486691,
1.016700086, 1.02217537, 1.101631026, 0.870692549, 0.671948117,
0.748057897, 0.606251295, 0.621494879, 0.70676264, 0.45271351,
0.211009735, 0.089069586), `08/06/2010` = c(3.32007028, 3.186648108,
2.936677244, 2.644961785, 2.5073429, 2.467167746, 2.299195045,
2.075695529, 1.962051351, 1.878092876, 1.54267996, 1.323552333,
1.304628202, 1.162323339, 1.051259672, 0.884269577, 0.555640542,
0.359112194, 0.289248386), `13/07/2011` = c(1.673785717, 1.204228032,
1.105822441, 1.016173135, 1.042061594, 0.989341653, 0.901159817,
0.72302825, 0.665939195, 0.951083838, 0.669472768, 0.232645301,
0.363475069, 0.287011275, 0.326806226, 0.363444173, 0.212024406,
-0.029371312, 0.015562403), `11/08/2010` = c(2.736886567, 2.60539157,
2.469501584, 2.275886465, 2.09837318, 1.950031374, 1.821983277,
1.575978294, 1.486472168, 1.474843419, 1.288529464, 1.048647357,
0.924918731, 0.752713324, 0.665990131, 0.568233255, 0.509558561,
0.258469474, 0.115291942), `12/09/2010` = c(2.27466979, 2.032320987,
1.792664294, 1.527430512, 1.364542843, 1.168417468, 0.982597795,
0.798738224, 0.725485644, 0.835374787, 0.689866725, 0.412680956,
0.455946943, 0.412020544, 0.460535599, 0.43714151, 0.25975931,
0.129488195, 0.122330246), `17/10/2011` = c(0.987413345, 0.784724389,
0.784176687, 0.644814906, 0.629133012, 0.510671231, 0.430232302,
0.400574676, 0.424147592, 0.48291063, 0.372309613, 0.162324755,
0.234138215, 0.187219827, 0.177471, 0.214010818, 0.167027368,
0.087446525, 0.086473907), `15/11/2010` = c(0.903246924, 0.72172498,
0.620050579, 0.525618839, 0.476341845, 0.44011074, 0.471394944,
0.381367708, 0.407651659, 0.484202603, 0.39185362, 0.277105091,
0.294054245, 0.225477378, 0.258170655, 0.277554086, 0.160735717,
0.003292402, 0.041922402), `01/12/2010` = c(0.445461709, 0.367709462,
0.225302044, 0.110431575, 0.032934483, -0.026888269, -0.027638367,
-0.076156315, -0.089364579, -0.069446325, -0.086752955, -0.11515339,
-0.12853713, -0.086244552, -0.092839466, -0.002107235, -0.00117247,
0.00775231, 0.047308133), `18/01/2017` = c(-0.603685925, -0.4998813,
-0.461712479, -0.480862181, -0.44675639, -0.47646293, -0.445157252,
-0.378673096, -0.310299767, -0.298956311, -0.216420223, -0.122886169,
-0.150782556, -0.136289643, -0.154670754, -0.079275892, -0.011842791,
-0.009469936, -0.022468661), `22/02/2018` = c(-1.124681463, -0.801306336,
-0.755583247, -0.740326501, -0.668324266, -0.689888268, -0.669552645,
-0.651560906, -0.577414836, -0.467275485, -0.487228815, -0.409886962,
-0.339771295, -0.287868452, -0.234320675, -0.165150807, -0.120599508,
-0.061993602, -0.016360896), `07/03/2017` = c(1.329852307, 1.521997519,
1.522106108, 1.400016254, 1.338277656, 1.224286792, 1.130104983,
0.956249083, 0.908992192, 0.931772828, 0.806931434, 0.584368236,
0.49521751, 0.413895491, 0.451224297, 0.445326963, 0.216153288,
0.09338156, 0.087259489), `11/04/2018` = c(1.13671915, 1.271315292,
1.196803329, 1.060659471, 0.952872701, 0.809563336, 0.714209605,
0.54478728, 0.519822384, 0.632381179, 0.478456984, 0.251899601,
0.278961934, 0.264918062, 0.359475174, 0.434851799, 0.25797282,
0.115218938, 0.072084668), `13/05/2018` = c(1.725072693, 1.832845518,
1.723416198, 1.567146116, 1.48656916, 1.385401332, 1.292099523,
1.10273938, 0.992515988, 1.090988341, 0.905774546, 0.573138388,
0.628058313, 0.600917424, 0.765747186, 0.804390958, 0.468728651,
0.219101582, 0.165915934), `11/06/2017` = c(-0.479335831, -0.314947809,
-0.264819184, -0.251703507, -0.137968968, -0.059339841, -0.073599131,
-0.19171072, -0.129989925, 0.072601877, 0.050119742, -0.096187105,
0.023082622, 0.100666227, 0.267515091, 0.424105329, 0.226430498,
0.017793336, 0.029264774), `13/07/2017` = c(1.788870991, 1.964130171,
1.868023031, 1.683639109, 1.591554741, 1.505087822, 1.411819622,
1.202865437, 1.12775115, 1.180889497, 1.015211991, 0.71164468,
0.698152287, 0.648626148, 0.704817323, 0.733601897, 0.482795278,
0.224762541, 0.157508633), `14/08/2017` = c(0.641000659, 0.803521865,
0.829508933, 0.749577188, 0.715266444, 0.60777392, 0.523682821,
0.39903637, 0.374236154, 0.5373327, 0.368061386, 0.167257017,
0.244832382, 0.238687289, 0.355596645, 0.421776592, 0.165438239,
0.061793892, 0.064796355), `15/09/2017` = c(1.980544532, 2.035384652,
1.959463004, 1.821066338, 1.732695208, 1.639481006, 1.544433362,
1.35466796, 1.340717639, 1.443343258, 1.263020735, 0.91330116,
0.833106684, 0.727635541, 0.783767958, 0.775874298, 0.46740165,
0.238773239, 0.175371937), `17/10/2017` = c(-0.243510898, 0.401164034,
-0.053037472, -0.270425909, -0.585057603, -1.181875975, -1.403380965,
-1.226971005, -1.299582453, -1.591256404, -1.461596763, -0.954695328,
-0.986725894, -0.848527732, -0.83831278, -0.674072473, -0.36912586,
-0.1668887, -0.06190761), `18/11/2017` = c(0.417556054, 0.587617646,
0.605567495, 0.50148853, 0.442361194, 0.35698149, 0.343588132,
0.277403781, 0.307254095, 0.364764256, 0.29872284, 0.212383583,
0.195995796, 0.169475825, 0.180584641, 0.217495988, 0.176084307,
0.07891974, 0.042541297), `04/12/2017` = c(-0.531951698, -0.227923203,
-0.134122336, -0.134927573, -0.130396791, -0.173586594, -0.159608649,
-0.126192771, -0.097069894, -0.110894672, -0.130800036, -0.039673738,
-0.044150392, -0.048348765, -0.105812518, -0.136823811, -0.08622897,
-0.015346085, -0.006710123)), class = "data.frame", row.names = c(NA,
-19L))
Processed data for ANOVA (as described above):
str(data_long)
tibble [456 x 4] (S3: tbl_df/tbl/data.frame)
$ Buffer : int [1:456] 100 100 100 100 100 100 100 100 100 100 ...
$ LST : num [1:456] 0.581 0.971 1.628 2.139 1.902 ...
$ Month : num [1:456] 1 2 3 4 5 6 7 8 9 10 ...
$ TimePeriod: num [1:456] 1 1 1 1 1 1 1 1 1 1 ...
dput(data_long)
structure(list(Buffer = c(100L, 100L, 100L, 100L, 100L, 100L,
100L, 100L, 100L, 100L, 100L, 100L, 100L, 100L, 100L, 100L, 100L,
100L, 100L, 100L, 100L, 100L, 100L, 100L, 200L, 200L, 200L, 200L,
200L, 200L, 200L, 200L, 200L, 200L, 200L, 200L, 200L, 200L, 200L,
200L, 200L, 200L, 200L, 200L, 200L, 200L, 200L, 200L, 300L, 300L,
300L, 300L, 300L, 300L, 300L, 300L, 300L, 300L, 300L, 300L, 300L,
300L, 300L, 300L, 300L, 300L, 300L, 300L, 300L, 300L, 300L, 300L,
400L, 400L, 400L, 400L, 400L, 400L, 400L, 400L, 400L, 400L, 400L,
400L, 400L, 400L, 400L, 400L, 400L, 400L, 400L, 400L, 400L, 400L,
400L, 400L, 500L, 500L, 500L, 500L, 500L, 500L, 500L, 500L, 500L,
500L, 500L, 500L, 500L, 500L, 500L, 500L, 500L, 500L, 500L, 500L,
500L, 500L, 500L, 500L, 600L, 600L, 600L, 600L, 600L, 600L, 600L,
600L, 600L, 600L, 600L, 600L, 600L, 600L, 600L, 600L, 600L, 600L,
600L, 600L, 600L, 600L, 600L, 600L, 700L, 700L, 700L, 700L, 700L,
700L, 700L, 700L, 700L, 700L, 700L, 700L, 700L, 700L, 700L, 700L,
700L, 700L, 700L, 700L, 700L, 700L, 700L, 700L, 800L, 800L, 800L,
800L, 800L, 800L, 800L, 800L, 800L, 800L, 800L, 800L, 800L, 800L,
800L, 800L, 800L, 800L, 800L, 800L, 800L, 800L, 800L, 800L, 900L,
900L, 900L, 900L, 900L, 900L, 900L, 900L, 900L, 900L, 900L, 900L,
900L, 900L, 900L, 900L, 900L, 900L, 900L, 900L, 900L, 900L, 900L,
900L, 1000L, 1000L, 1000L, 1000L, 1000L, 1000L, 1000L, 1000L,
1000L, 1000L, 1000L, 1000L, 1000L, 1000L, 1000L, 1000L, 1000L,
1000L, 1000L, 1000L, 1000L, 1000L, 1000L, 1000L, 1100L, 1100L,
1100L, 1100L, 1100L, 1100L, 1100L, 1100L, 1100L, 1100L, 1100L,
1100L, 1100L, 1100L, 1100L, 1100L, 1100L, 1100L, 1100L, 1100L,
1100L, 1100L, 1100L, 1100L, 1200L, 1200L, 1200L, 1200L, 1200L,
1200L, 1200L, 1200L, 1200L, 1200L, 1200L, 1200L, 1200L, 1200L,
1200L, 1200L, 1200L, 1200L, 1200L, 1200L, 1200L, 1200L, 1200L,
1200L, 1300L, 1300L, 1300L, 1300L, 1300L, 1300L, 1300L, 1300L,
1300L, 1300L, 1300L, 1300L, 1300L, 1300L, 1300L, 1300L, 1300L,
1300L, 1300L, 1300L, 1300L, 1300L, 1300L, 1300L, 1400L, 1400L,
1400L, 1400L, 1400L, 1400L, 1400L, 1400L, 1400L, 1400L, 1400L,
1400L, 1400L, 1400L, 1400L, 1400L, 1400L, 1400L, 1400L, 1400L,
1400L, 1400L, 1400L, 1400L, 1500L, 1500L, 1500L, 1500L, 1500L,
1500L, 1500L, 1500L, 1500L, 1500L, 1500L, 1500L, 1500L, 1500L,
1500L, 1500L, 1500L, 1500L, 1500L, 1500L, 1500L, 1500L, 1500L,
1500L, 1600L, 1600L, 1600L, 1600L, 1600L, 1600L, 1600L, 1600L,
1600L, 1600L, 1600L, 1600L, 1600L, 1600L, 1600L, 1600L, 1600L,
1600L, 1600L, 1600L, 1600L, 1600L, 1600L, 1600L, 1700L, 1700L,
1700L, 1700L, 1700L, 1700L, 1700L, 1700L, 1700L, 1700L, 1700L,
1700L, 1700L, 1700L, 1700L, 1700L, 1700L, 1700L, 1700L, 1700L,
1700L, 1700L, 1700L, 1700L, 1800L, 1800L, 1800L, 1800L, 1800L,
1800L, 1800L, 1800L, 1800L, 1800L, 1800L, 1800L, 1800L, 1800L,
1800L, 1800L, 1800L, 1800L, 1800L, 1800L, 1800L, 1800L, 1800L,
1800L, 1900L, 1900L, 1900L, 1900L, 1900L, 1900L, 1900L, 1900L,
1900L, 1900L, 1900L, 1900L, 1900L, 1900L, 1900L, 1900L, 1900L,
1900L, 1900L, 1900L, 1900L, 1900L, 1900L, 1900L), LST = c(0.580552675,
0.970746407, 1.627607407, 2.139468759, 1.902422481, 3.32007028,
1.673785717, 2.736886567, 2.27466979, 0.987413345, 0.903246924,
0.445461709, -0.603685925, -1.124681463, 1.329852307, 1.13671915,
1.725072693, -0.479335831, 1.788870991, 0.641000659, 1.980544532,
-0.243510898, 0.417556054, -0.531951698, 0.502427717, 0.908338611,
1.344880439, 1.97844065, 1.717518818, 3.186648108, 1.204228032,
2.60539157, 2.032320987, 0.784724389, 0.72172498, 0.367709462,
-0.4998813, -0.801306336, 1.521997519, 1.271315292, 1.832845518,
-0.314947809, 1.964130171, 0.803521865, 2.035384652, 0.401164034,
0.587617646, -0.227923203, 0.424272426, 0.850354266, 1.115972847,
1.755013632, 1.660216773, 2.936677244, 1.105822441, 2.469501584,
1.792664294, 0.784176687, 0.620050579, 0.225302044, -0.461712479,
-0.755583247, 1.522106108, 1.196803329, 1.723416198, -0.264819184,
1.868023031, 0.829508933, 1.959463004, -0.053037472, 0.605567495,
-0.134122336, 0.322662088, 0.724290238, 1.022763599, 1.547944727,
1.496388619, 2.644961785, 1.016173135, 2.275886465, 1.527430512,
0.644814906, 0.525618839, 0.110431575, -0.480862181, -0.740326501,
1.400016254, 1.060659471, 1.567146116, -0.251703507, 1.683639109,
0.749577188, 1.821066338, -0.270425909, 0.50148853, -0.134927573,
0.276423067, 0.652515808, 1.023629255, 1.472394813, 1.401870845,
2.5073429, 1.042061594, 2.09837318, 1.364542843, 0.629133012,
0.476341845, 0.032934483, -0.44675639, -0.668324266, 1.338277656,
0.952872701, 1.48656916, -0.137968968, 1.591554741, 0.715266444,
1.732695208, -0.585057603, 0.442361194, -0.130396791, 0.296410675,
0.548074344, 0.875259921, 1.365201053, 1.299025971, 2.467167746,
0.989341653, 1.950031374, 1.168417468, 0.510671231, 0.44011074,
-0.026888269, -0.47646293, -0.689888268, 1.224286792, 0.809563336,
1.385401332, -0.059339841, 1.505087822, 0.60777392, 1.639481006,
-1.181875975, 0.35698149, -0.173586594, 0.300255406, 0.431608248,
0.768911951, 1.241123025, 1.155486691, 2.299195045, 0.901159817,
1.821983277, 0.982597795, 0.430232302, 0.471394944, -0.027638367,
-0.445157252, -0.669552645, 1.130104983, 0.714209605, 1.292099523,
-0.073599131, 1.411819622, 0.523682821, 1.544433362, -1.403380965,
0.343588132, -0.159608649, 0.293503101, 0.305626873, 0.739025174,
1.130024888, 1.016700086, 2.075695529, 0.72302825, 1.575978294,
0.798738224, 0.400574676, 0.381367708, -0.076156315, -0.378673096,
-0.651560906, 0.956249083, 0.54478728, 1.10273938, -0.19171072,
1.202865437, 0.39903637, 1.35466796, -1.226971005, 0.277403781,
-0.126192771, 0.221852835, 0.220168823, 0.689252542, 1.084274915,
1.02217537, 1.962051351, 0.665939195, 1.486472168, 0.725485644,
0.424147592, 0.407651659, -0.089364579, -0.310299767, -0.577414836,
0.908992192, 0.519822384, 0.992515988, -0.129989925, 1.12775115,
0.374236154, 1.340717639, -1.299582453, 0.307254095, -0.097069894,
0.156474538, 0.321279759, 0.778222174, 1.13194737, 1.101631026,
1.878092876, 0.951083838, 1.474843419, 0.835374787, 0.48291063,
0.484202603, -0.069446325, -0.298956311, -0.467275485, 0.931772828,
0.632381179, 1.090988341, 0.072601877, 1.180889497, 0.5373327,
1.443343258, -1.591256404, 0.364764256, -0.110894672, 0.155695066,
0.251755903, 0.683311682, 0.959184096, 0.870692549, 1.54267996,
0.669472768, 1.288529464, 0.689866725, 0.372309613, 0.39185362,
-0.086752955, -0.216420223, -0.487228815, 0.806931434, 0.478456984,
0.905774546, 0.050119742, 1.015211991, 0.368061386, 1.263020735,
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0.44018711, 0.743134896, 0.671948117, 1.323552333, 0.232645301,
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