NeuroAnalyzer tutorials: Statistics (1)

Load data:

using NeuroAnalyzer
using NeuroStats
using Plots
eeg = load("files/eeg.hdf");
e10 = epoch(eeg, ep_len=10)

[ Info: Loaded: EEG (24 × 308480 × 1; 1204.996 s)

NeuroAnalyzer.NEURO(NeuroAnalyzer.HEADER(Dict{Symbol, Any}(:weight => -1, :id => "", :middle_name => "", :height => -1, :head_circumference => -1, :handedness => "", :last_name => "528004  SIT 52, 20220831-122227-{d589f756-53fc-4f1b-915d-6e3b8c1560ad}", :first_name => ""), Dict{Symbol, Any}(:epoch_id => "length_10s", :channel_type => ["eeg", "eeg", "eeg", "eeg", "eeg", "eeg", "eeg", "eeg", "eeg", "eeg"  …  "eeg", "eeg", "ref", "ref", "eeg", "eeg", "eeg", "eog", "eog", "ecg"], :label => ["Fp1", "Fp2", "F3", "F4", "C3", "C4", "P3", "P4", "O1", "O2"  …  "T5", "T6", "A1", "A2", "Fz", "Cz", "Pz", "EOG1", "EOG2", "ECG"], :prefiltering => ["HP:0,18Hz LP:104,0Hz", "HP:0,18Hz LP:104,0Hz", "HP:0,18Hz LP:104,0Hz", "HP:0,18Hz LP:104,0Hz", "HP:0,18Hz LP:104,0Hz", "HP:0,18Hz LP:104,0Hz", "HP:0,18Hz LP:104,0Hz", "HP:0,18Hz LP:104,0Hz", "HP:0,18Hz LP:104,0Hz", "HP:0,18Hz LP:104,0Hz"  …  "HP:0,18Hz LP:104,0Hz", "HP:0,18Hz LP:104,0Hz", "HP:0,18Hz LP:104,0Hz", "HP:0,18Hz LP:104,0Hz", "HP:0,18Hz LP:104,0Hz", "HP:0,18Hz LP:104,0Hz", "HP:0,18Hz LP:104,0Hz", "HP:0,18Hz LP:104,0Hz", "HP:0,18Hz LP:104,0Hz", "HP:0,18Hz LP:104,0Hz"], :gain => [0.17935713740749218, 0.17935713740749218, 0.17935713740749218, 0.17935713740749218, 0.17935713740749218, 0.17935713740749218, 0.17935713740749218, 0.17935713740749218, 0.17935713740749218, 0.17935713740749218  …  0.17935713740749218, 0.17935713740749218, 0.17935713740749218, 0.17935713740749218, 0.17935713740749218, 0.17935713740749218, 0.17935713740749218, 0.17935713740749218, 0.17935713740749218, 0.17935713740749218], :data_type => "eeg", :recording_notes => "", :recording_date => "31.08.22", :sampling_rate => 256, :file_type => "EDF"…), Dict(:name => "", :design => "", :notes => "")), [0.0, 0.004, 0.008, 0.012, 0.016, 0.02, 0.023, 0.027, 0.031, 0.035  …  1199.961, 1199.965, 1199.969, 1199.973, 1199.977, 1199.98, 1199.984, 1199.988, 1199.992, 1199.996], [0.0, 0.004, 0.008, 0.012, 0.016, 0.02, 0.023, 0.027, 0.031, 0.035  …  9.961, 9.965, 9.969, 9.973, 9.977, 9.98, 9.984, 9.988, 9.992, 9.996], [0.06299352498755795 98.63512726760528 … 41.64779361459051 40.27715442572031; 0.11655563660927726 -53.828853350413745 … 345.96748535110487 347.7616741828556; … ; -0.022184604323419066 127.03733086748798 … 42.55039163342602 44.143978691184884; -0.055585528301492104 530.00037195304 … -179.54843878264597 -97.67507694089335;;; 40.58017280035072 38.69000241338162 … -7.037891014697759 -7.6384338583029905; 344.18870568332585 339.2435612554108 … -2.1636004350702924 -1.243066521339322; … ; 48.60829031932775 41.434311602707794 … 0.22361559170736633 5.107585048673709; -61.66159371531367 -60.51281779857858 … -25.091166799203215 -12.149362788293596;;; -7.389384663780996 -7.618556612450722 … 1.3595844397118169 0.89911474206312; -3.5767735100748306 -0.30843418447498117 … 2.5866028445011846 -0.5132850019084954; … ; 1.3968065710167448 4.064826278034884 … 20.59119020676338 15.167853967159978; -27.014555021283574 -12.020921093458888 … 13.363788037149643 4.117227772690271;;; … ;;; 18.569309294713733 22.89311361283536 … 4.754504204065761 1.2053936473657352; 4.494714018514111 13.02609030059181 … 5.464449674126968 -2.6002896761179723; … ; -0.20841131938738222 12.507075249278618 … -7.241776899887379 -16.6315533872683; -29.255972440543367 -19.25691477874347 … 51.4201275519938 43.947841516236736;;; -1.4299687612461471 -1.312451759360422 … -0.5864522963548433 -6.796427233556682; 0.012850100616558002 0.570051044210814 … 4.181275800561462 -2.4365803124421292; … ; -6.719338934443345 -5.029725597318926 … 3.433495081847715 -3.6700683194834482; 56.10007507089348 40.45064953005437 … 7.692870188391213 -0.9038428781168477;;; -5.560172661791544 -0.11512766557237253 … 19.084481856614218 16.407156218345452; 5.141449021164782 -3.3199724764366856 … 3.3810434974559325 3.5815380669519286; … ; 3.114487125536476 -6.350212297090032 … 9.640660281430884 10.73198290953739; 9.746916484991555 3.5775514229256995 … -21.665073186614904 -26.318948530205475], Dict{Any, Any}(), 0×5 DataFrame
 Row │ id      start    length   description  channel 
     │ String  Float64  Float64  String       Int64   
─────┴────────────────────────────────────────────────, 23×9 DataFrame
 Row │ label   loc_radius  loc_theta  loc_x    loc_y    loc_z    loc_radius_sp ⋯
     │ String  Float64     Float64    Float64  Float64  Float64  Float64       ⋯
─────┼──────────────────────────────────────────────────────────────────────────
   1 │ Fp1           1.0       108.0    -0.31     0.95    -0.03            1.0 ⋯
   2 │ Fp2           1.0        72.0     0.31     0.95    -0.03            1.0
   3 │ F7            1.0       144.0    -0.81     0.59    -0.03            1.0
   4 │ F3            0.65      129.0    -0.55     0.67     0.5             1.0
   5 │ Fz            0.51       90.0     0.0      0.72     0.7             1.0 ⋯
   6 │ F4            0.65       51.0     0.55     0.67     0.5             1.0
   7 │ F8            1.0        36.0     0.81     0.59    -0.03            1.0
   8 │ T3            1.0       180.0    -1.0      0.0     -0.03            1.0
   9 │ C3            0.51      180.0    -0.72     0.0      0.7             1.0 ⋯
  10 │ Cz            0.0         0.0     0.0      0.0      1.0             1.0
  11 │ C4            0.51        0.0     0.72     0.0      0.7             1.0
  ⋮  │   ⋮         ⋮           ⋮         ⋮        ⋮        ⋮           ⋮       ⋱
  14 │ P3            0.65      231.0    -0.55    -0.67     0.5             1.0
  15 │ Pz            0.51      270.0     0.0     -0.72     0.7             1.0 ⋯
  16 │ P4            0.65      309.0     0.55    -0.67     0.5             1.0
  17 │ T6            1.0       324.0     0.81    -0.59    -0.03            1.0
  18 │ O1            1.0       252.0    -0.31    -0.95    -0.03            1.0
  19 │ O2            1.0       288.0     0.31    -0.95    -0.03            1.0 ⋯
  20 │ A1            1.0       192.0    -0.92    -0.23    -0.55            1.1
  21 │ A2            1.0       -12.0     0.92    -0.23    -0.55            1.1
  22 │ EOG1          1.01      149.0    -0.87     0.51    -0.37            1.0
  23 │ EOG2          1.01       31.0     0.87     0.51    -0.37            1.0 ⋯
                                                    3 columns and 2 rows omitted, ["reset_components(OBJ)", "filter(OBJ, ch=[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24], fprototype=iirnotch, ftype=nothing, cutoff=50, order=8, rp=-1, rs=-1, dir=twopass, w=nothing)", "reset_components(OBJ)", "filter(OBJ, ch=[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24], fprototype=fir, ftype=hp, cutoff=0.1, order=8, rp=-1, rs=-1, dir=twopass, w=nothing)", "reset_components(OBJ)", "epoch(OBJ, marker=, offset=0, ep_n=nothing, ep_len=2560)"])

(!) Most statistical functions used by the NeuroAnalyzer are in the separate package: NeuroStats.jl.

Calculate and plot CI using bootstrapping

Get the first 2 seconds of the channel 1 and calculate its 95%CI:

s = e10.data[1, 1:512, :]
t = e10.epoch_time[1:512]
s_avg, s_l, s_u = bootstrap_ci(s, cl=0.95)

Progress:  33%|██████▌             |  ETA: 0:00:02Progress: 100%|████████████████████| Time: 0:00:02

(s_avg = [2.2302293829729134, 3.204319681541593, 3.572561282881744, 4.245264512909742, 3.001264784932195, 2.618258253170263, 3.425204294380854, 3.550552206325591, 3.950341027877392, 2.8156151198643284  …  -1.0859218302694855, -1.4426220778435497, -1.6190453657201211, -0.6431429259639172, -0.938739212080924, -0.7869093718487821, -1.0608479959478336, -1.2606593067942307, -0.28348950189438077, -0.8926225926080597],
 s_ci_l = [1.4824360278340651, 2.305715911633895, 2.1803372317461625, 2.9088174324252205, 2.1247401599910773, 1.8785947782979717, 2.536690471027256, 2.2984182361473837, 2.674739120295025, 1.9172730359264882  …  -2.134266930326906, -2.634502173185566, -2.807976176542293, -1.6944459167790584, -1.884846799430472, -1.811737407204044, -2.2375468473087534, -2.4395661350132745, -1.322686530534247, -1.8530496737448958],
 s_ci_h = [2.951105612339974, 4.110298892466913, 5.037104379393726, 5.610408609695974, 3.8556517069268597, 3.3528094354997364, 4.278236638711351, 4.885525515195466, 5.275845121375838, 3.708410757303419  …  -0.0883963269084531, -0.3674821074795067, -0.5212164701279347, 0.316730237491028, -0.04543300204570138, 0.1964401598787773, 0.029633738135529955, -0.15458144605345636, 0.7298667969679555, 0.050154031017129085],)

Plot CI:

plot_ci(s_avg, s_l, s_u, t)

Calculate statistic using bootstrapping

Any statistical function may be calculated using bootstrapping method. The function must be provided as f="function_name(obj)", obj will be replaced with the signal data, e.g. f="mean(obj)".

s = e10.data[1, :, :]
s_stat = abs(maximum(s))
s_dist  = bootstrap_stat(s, f="abs(maximum(obj))")

Progress:   2%|▍                   |  ETA: 0:00:57Progress:   4%|▊                   |  ETA: 0:00:48Progress:   6%|█▎                  |  ETA: 0:00:47Progress:   8%|█▋                  |  ETA: 0:00:47Progress:  10%|██                  |  ETA: 0:00:46Progress:  12%|██▌                 |  ETA: 0:00:45Progress:  14%|██▉                 |  ETA: 0:00:44Progress:  16%|███▎                |  ETA: 0:00:43Progress:  18%|███▋                |  ETA: 0:00:42Progress:  20%|████                |  ETA: 0:00:41Progress:  22%|████▍               |  ETA: 0:00:40Progress:  24%|████▉               |  ETA: 0:00:39Progress:  26%|█████▎              |  ETA: 0:00:38Progress:  28%|█████▋              |  ETA: 0:00:37Progress:  30%|██████              |  ETA: 0:00:36Progress:  32%|██████▍             |  ETA: 0:00:35Progress:  34%|██████▉             |  ETA: 0:00:34Progress:  36%|███████▎            |  ETA: 0:00:33Progress:  38%|███████▋            |  ETA: 0:00:32Progress:  40%|████████            |  ETA: 0:00:31Progress:  42%|████████▍           |  ETA: 0:00:30Progress:  44%|████████▊           |  ETA: 0:00:29Progress:  46%|█████████▏          |  ETA: 0:00:28Progress:  48%|█████████▌          |  ETA: 0:00:27Progress:  50%|██████████          |  ETA: 0:00:26Progress:  52%|██████████▍         |  ETA: 0:00:25Progress:  54%|██████████▊         |  ETA: 0:00:24Progress:  56%|███████████▏        |  ETA: 0:00:23Progress:  58%|███████████▌        |  ETA: 0:00:22Progress:  60%|███████████▉        |  ETA: 0:00:21Progress:  62%|████████████▎       |  ETA: 0:00:20Progress:  64%|████████████▊       |  ETA: 0:00:19Progress:  65%|█████████████▏      |  ETA: 0:00:18Progress:  67%|█████████████▌      |  ETA: 0:00:17Progress:  69%|█████████████▉      |  ETA: 0:00:16Progress:  71%|██████████████▎     |  ETA: 0:00:15Progress:  73%|██████████████▊     |  ETA: 0:00:14Progress:  75%|███████████████▏    |  ETA: 0:00:13Progress:  77%|███████████████▌    |  ETA: 0:00:12Progress:  79%|███████████████▉    |  ETA: 0:00:11Progress:  81%|████████████████▎   |  ETA: 0:00:10Progress:  83%|████████████████▋   |  ETA: 0:00:09Progress:  85%|█████████████████   |  ETA: 0:00:08Progress:  87%|█████████████████▌  |  ETA: 0:00:07Progress:  89%|█████████████████▉  |  ETA: 0:00:06Progress:  91%|██████████████████▎ |  ETA: 0:00:05Progress:  93%|██████████████████▋ |  ETA: 0:00:04Progress:  95%|███████████████████ |  ETA: 0:00:03Progress:  97%|███████████████████▍|  ETA: 0:00:02Progress:  99%|███████████████████▊|  ETA: 0:00:01Progress: 100%|████████████████████| Time: 0:00:51

3000-element Vector{Float64}:
 5.390635738157565
 7.884301629509923
 6.684582843195923
 6.04888140381616
 6.367437529297428
 4.424456285216674
 4.74850588334943
 7.03097528665289
 8.966863110941418
 4.887081431253189
 6.251797217694902
 8.716401123981768
 6.149151681951605
 ⋮
 6.610612105830213
 5.796868402283184
 9.255240380421403
 5.992759171680086
 6.290384392036015
 7.7010629739861525
 5.893860410585405
 5.9903280932735194
 8.400433275712368
 6.274588782472684
 7.135399554428481
 5.562090290470292

plot_histogram(s_dist, s_stat, draw_median=true, draw_mean=false)

m[ Info: Proportion of values > 561.9193061631547: 0.0
[ Info: Proportion of values < 561.9193061631547: 1.0