# Help with ambiguity (and misunderstanding+confusion) in ANOVA choice

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.

1. Locate suitable aoi
2. 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)
3. Generate 100m-wide rings (buffers) extending outwards from the boundary of the solar site.
4. Create a mask using potentially confounding areas
5. Create masked rings (this is the most extreme clipping of all sites due to the salt-pan and nearby solar-concentrator sites)
6. 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,
-1.461596763, 0.29872284, -0.130800036, 0.094020687, 0.171728052,
0.44018711, 0.743134896, 0.671948117, 1.323552333, 0.232645301,
1.048647357, 0.412680956, 0.162324755, 0.277105091, -0.11515339,
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))

• Can you share the entire dataset? I'm having a tough time understanding the setup of the rings Commented Jan 5, 2022 at 16:23
• Sure - I'll edit the main question. Commented Jan 7, 2022 at 8:42

Reading Datanovia's guide on Anova with repeated measures I think my ANOVA should be specified as follows:

• Dependent variable is LST
• Sample/case ID is Buffer (100-1900)
• Within-subjects variables are Month (1-12) and TimePeriod (0/1) (before/after constuction)

i.e. This is a "two-way repeated measures ANOVA used to evaluate simultaneously the effect of two within-subject factors on a continuous outcome variable."

Specifying the ANOVA in this way:

> res.aov <- anova_test(
+   data = LST_Weather_dataset, dv = LST, wid = Buffer,
+   within = c(Month, TimePeriod),
+   effect.size = "ges",
+   detailed = TRUE,
+ )
> get_anova_table(res.aov, correction = "auto")
ANOVA Table (type III tests)

Effect  DFn   DFd     SSn    SSd      F        p p<.05   ges
1      (Intercept) 1.00 18.00 127.992 42.944 53.647 8.41e-07     * 0.585
2            Month 1.28 23.05  96.549 23.787 73.061 2.43e-09     * 0.516
3       TimePeriod 1.00 18.00  20.290  7.912 46.163 2.31e-06     * 0.183
4 Month:TimePeriod 1.53 27.58  46.699 15.970 52.634 3.08e-09     * 0.340


Could someone confirm this is correct?