-
Notifications
You must be signed in to change notification settings - Fork 0
/
1f_latsq_poisson.html
733 lines (640 loc) · 21.6 KB
/
1f_latsq_poisson.html
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8" />
<meta name="generator" content="pandoc" />
<meta http-equiv="X-UA-Compatible" content="IE=EDGE" />
<title>1 Beh.faktor - Lat.Quadrat - Poissondaten</title>
<script src="site_libs/jquery-1.11.3/jquery.min.js"></script>
<meta name="viewport" content="width=device-width, initial-scale=1" />
<link href="site_libs/bootstrap-3.3.5/css/lumen.min.css" rel="stylesheet" />
<script src="site_libs/bootstrap-3.3.5/js/bootstrap.min.js"></script>
<script src="site_libs/bootstrap-3.3.5/shim/html5shiv.min.js"></script>
<script src="site_libs/bootstrap-3.3.5/shim/respond.min.js"></script>
<script src="site_libs/jqueryui-1.11.4/jquery-ui.min.js"></script>
<link href="site_libs/tocify-1.9.1/jquery.tocify.css" rel="stylesheet" />
<script src="site_libs/tocify-1.9.1/jquery.tocify.js"></script>
<script src="site_libs/navigation-1.1/tabsets.js"></script>
<link href="site_libs/highlightjs-9.12.0/default.css" rel="stylesheet" />
<script src="site_libs/highlightjs-9.12.0/highlight.js"></script>
<style type="text/css">
code{white-space: pre-wrap;}
span.smallcaps{font-variant: small-caps;}
span.underline{text-decoration: underline;}
div.column{display: inline-block; vertical-align: top; width: 50%;}
div.hanging-indent{margin-left: 1.5em; text-indent: -1.5em;}
ul.task-list{list-style: none;}
</style>
<style type="text/css">code{white-space: pre;}</style>
<style type="text/css">
pre:not([class]) {
background-color: white;
}
</style>
<script type="text/javascript">
if (window.hljs) {
hljs.configure({languages: []});
hljs.initHighlightingOnLoad();
if (document.readyState && document.readyState === "complete") {
window.setTimeout(function() { hljs.initHighlighting(); }, 0);
}
}
</script>
<style type="text/css">
h1 {
font-size: 34px;
}
h1.title {
font-size: 38px;
}
h2 {
font-size: 30px;
}
h3 {
font-size: 24px;
}
h4 {
font-size: 18px;
}
h5 {
font-size: 16px;
}
h6 {
font-size: 12px;
}
.table th:not([align]) {
text-align: left;
}
</style>
<link rel="stylesheet" href="styles.css" type="text/css" />
<style type = "text/css">
.main-container {
max-width: 940px;
margin-left: auto;
margin-right: auto;
}
code {
color: inherit;
background-color: rgba(0, 0, 0, 0.04);
}
img {
max-width:100%;
}
.tabbed-pane {
padding-top: 12px;
}
.html-widget {
margin-bottom: 20px;
}
button.code-folding-btn:focus {
outline: none;
}
summary {
display: list-item;
}
</style>
<style type="text/css">
/* padding for bootstrap navbar */
body {
padding-top: 54px;
padding-bottom: 40px;
}
/* offset scroll position for anchor links (for fixed navbar) */
.section h1 {
padding-top: 59px;
margin-top: -59px;
}
.section h2 {
padding-top: 59px;
margin-top: -59px;
}
.section h3 {
padding-top: 59px;
margin-top: -59px;
}
.section h4 {
padding-top: 59px;
margin-top: -59px;
}
.section h5 {
padding-top: 59px;
margin-top: -59px;
}
.section h6 {
padding-top: 59px;
margin-top: -59px;
}
.dropdown-submenu {
position: relative;
}
.dropdown-submenu>.dropdown-menu {
top: 0;
left: 100%;
margin-top: -6px;
margin-left: -1px;
border-radius: 0 6px 6px 6px;
}
.dropdown-submenu:hover>.dropdown-menu {
display: block;
}
.dropdown-submenu>a:after {
display: block;
content: " ";
float: right;
width: 0;
height: 0;
border-color: transparent;
border-style: solid;
border-width: 5px 0 5px 5px;
border-left-color: #cccccc;
margin-top: 5px;
margin-right: -10px;
}
.dropdown-submenu:hover>a:after {
border-left-color: #ffffff;
}
.dropdown-submenu.pull-left {
float: none;
}
.dropdown-submenu.pull-left>.dropdown-menu {
left: -100%;
margin-left: 10px;
border-radius: 6px 0 6px 6px;
}
</style>
<script>
// manage active state of menu based on current page
$(document).ready(function () {
// active menu anchor
href = window.location.pathname
href = href.substr(href.lastIndexOf('/') + 1)
if (href === "")
href = "index.html";
var menuAnchor = $('a[href="' + href + '"]');
// mark it active
menuAnchor.parent().addClass('active');
// if it's got a parent navbar menu mark it active as well
menuAnchor.closest('li.dropdown').addClass('active');
});
</script>
<!-- tabsets -->
<style type="text/css">
.tabset-dropdown > .nav-tabs {
display: inline-table;
max-height: 500px;
min-height: 44px;
overflow-y: auto;
background: white;
border: 1px solid #ddd;
border-radius: 4px;
}
.tabset-dropdown > .nav-tabs > li.active:before {
content: "";
font-family: 'Glyphicons Halflings';
display: inline-block;
padding: 10px;
border-right: 1px solid #ddd;
}
.tabset-dropdown > .nav-tabs.nav-tabs-open > li.active:before {
content: "";
border: none;
}
.tabset-dropdown > .nav-tabs.nav-tabs-open:before {
content: "";
font-family: 'Glyphicons Halflings';
display: inline-block;
padding: 10px;
border-right: 1px solid #ddd;
}
.tabset-dropdown > .nav-tabs > li.active {
display: block;
}
.tabset-dropdown > .nav-tabs > li > a,
.tabset-dropdown > .nav-tabs > li > a:focus,
.tabset-dropdown > .nav-tabs > li > a:hover {
border: none;
display: inline-block;
border-radius: 4px;
background-color: transparent;
}
.tabset-dropdown > .nav-tabs.nav-tabs-open > li {
display: block;
float: none;
}
.tabset-dropdown > .nav-tabs > li {
display: none;
}
</style>
<!-- code folding -->
<style type="text/css">
#TOC {
margin: 25px 0px 20px 0px;
}
@media (max-width: 768px) {
#TOC {
position: relative;
width: 100%;
}
}
@media print {
.toc-content {
/* see https://github.com/w3c/csswg-drafts/issues/4434 */
float: right;
}
}
.toc-content {
padding-left: 30px;
padding-right: 40px;
}
div.main-container {
max-width: 1200px;
}
div.tocify {
width: 20%;
max-width: 260px;
max-height: 85%;
}
@media (min-width: 768px) and (max-width: 991px) {
div.tocify {
width: 25%;
}
}
@media (max-width: 767px) {
div.tocify {
width: 100%;
max-width: none;
}
}
.tocify ul, .tocify li {
line-height: 20px;
}
.tocify-subheader .tocify-item {
font-size: 0.90em;
}
.tocify .list-group-item {
border-radius: 0px;
}
</style>
</head>
<body>
<div class="container-fluid main-container">
<!-- setup 3col/9col grid for toc_float and main content -->
<div class="row-fluid">
<div class="col-xs-12 col-sm-4 col-md-3">
<div id="TOC" class="tocify">
</div>
</div>
<div class="toc-content col-xs-12 col-sm-8 col-md-9">
<div class="navbar navbar-default navbar-fixed-top" role="navigation">
<div class="container">
<div class="navbar-header">
<button type="button" class="navbar-toggle collapsed" data-toggle="collapse" data-target="#navbar">
<span class="icon-bar"></span>
<span class="icon-bar"></span>
<span class="icon-bar"></span>
</button>
<a class="navbar-brand" href="index.html">crashcouRse</a>
</div>
<div id="navbar" class="navbar-collapse collapse">
<ul class="nav navbar-nav">
<li>
<a href="index.html">Home</a>
</li>
<li class="dropdown">
<a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" aria-expanded="false">
R Anwendung
<span class="caret"></span>
</a>
<ul class="dropdown-menu" role="menu">
<li>
<a href="datr_importexport.html">Import & Export</a>
</li>
<li>
<a href="datr_descriptivestats.html">Deskriptive Statistik</a>
</li>
<li>
<a href="datr_desplot.html">desplot package</a>
</li>
<li>
<a href="datr_multipledat.html">Loops & Listen</a>
</li>
<li>
<a href="datr_moreadvanced.html">Weitere Tipps</a>
</li>
</ul>
</li>
<li class="dropdown">
<a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" aria-expanded="false">
Auswertungen
<span class="caret"></span>
</a>
<ul class="dropdown-menu" role="menu">
<li>
<a href="1n_drinks.html">Korrelation & Regression</a>
</li>
<li>
<a href="outlier_vision.html">Ausreisser (Korr & Reg pt.2)</a>
</li>
<li>
<a href="1f_crd.html">1F crd</a>
</li>
<li>
<a href="1f_rcbd.html">1F rcbd</a>
</li>
<li>
<a href="1f_alpha.html">1F alpha</a>
</li>
<li>
<a href="2f_rcbd.html">2F rcbd</a>
</li>
<li>
<a href="2f_splitplot.html">2F split-plot</a>
</li>
<li>
<a href="1f_augmented_blockfixorrandom.html">1F augmented</a>
</li>
<li>
<a href="1f_rcbd_messwdh.html">1F rcbd Messwiederholungen</a>
</li>
<li>
<a href="1f_rcbd_binomial.html">1F rcbd Prozentwerte</a>
</li>
<li>
<a href="1f_latsq_poisson.html">1F lat square Zählwerte</a>
</li>
</ul>
</li>
<li class="dropdown">
<a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" aria-expanded="false">
Statistik
<span class="caret"></span>
</a>
<ul class="dropdown-menu" role="menu">
<li>
<a href="stat_korrelation.html">Korrelation</a>
</li>
<li>
<a href="stat_regression.html">Regression</a>
</li>
<li>
<a href="appendix_designs.html">Versuchsdesigns</a>
</li>
<li>
<a href="appendix_posthoc.html">ANOVA & Post Hoc</a>
</li>
<li>
<a href="appendix_interaktionen.html">Interaktionen</a>
</li>
<li>
<a href="stat_adjmeans.html">Adj. Mittelwerte</a>
</li>
<li>
<a href="stat_pvalue.html">p-Werte & Signifikanz</a>
</li>
<li>
<a href="stat_gemischtemodelle.html">Gemischte Modelle</a>
</li>
<li>
<a href="appendix_kovarstrukt.html">Kovarianzstrukturen 1</a>
</li>
<li>
<a href="3f_met_regions.html">Kovarianzstrukturen 2</a>
</li>
<li>
<a href="intro_glm_carrot.html">Nicht-Normalverteilte Daten</a>
</li>
<li>
<a href="stat_logisticregression.html">Logistische Regression</a>
</li>
<li>
<a href="appendix_modelrules.html">Modelle aufstellen</a>
</li>
<li>
<a href="stat_samplesize.html">Stichprobenplanung</a>
</li>
</ul>
</li>
<li>
<a href="kontaktseite.html">Kontakt</a>
</li>
</ul>
<ul class="nav navbar-nav navbar-right">
</ul>
</div><!--/.nav-collapse -->
</div><!--/.container -->
</div><!--/.navbar -->
<div class="fluid-row" id="header">
<h1 class="title toc-ignore">1 Beh.faktor - Lat.Quadrat - Poissondaten</h1>
</div>
<div id="datensatz" class="section level1">
<h1>Datensatz</h1>
<pre class="r"><code>library(data.table) # bessere Datenmanipulation
library(ggplot2); library(ggfortify) # bessere Plots
library(emmeans) # adjustierte Mittelwerte</code></pre>
<p>In diesem Beispiel wurden 5 verschiedene Begasungsbehandlungen für Schnellkäfer (<em>Elateridae</em>) mit 5 Wiederholungen getestet. Das Versuchsdesign war ein lateinisches Quadrat - sowohl die Spalten als auch die Zeilen sind also vollständige Blöcke. In jeder Parzelle wurden im Jahr nach der Behandlung die Schnellkäferlarven gezählt.</p>
<div class="row">
<div class="col-md-6">
<pre><code>## Warning in if (class(data) == "formula") {: the condition has length > 1 and only
## the first element will be used</code></pre>
<p><img src="1f_latsq_poisson_files/figure-html/unnamed-chunk-3-1.png" width="384" style="display: block; margin: auto;" /></p>
</div>
<div class="col-md-6">
<pre><code>## Warning in if (class(data) == "formula") {: the condition has length > 1 and only
## the first element will be used</code></pre>
<p><img src="1f_latsq_poisson_files/figure-html/unnamed-chunk-4-1.png" width="384" style="display: block; margin: auto;" /></p>
</div>
</div>
<div class="row">
<div class="col-md-6">
<pre class="r"><code>print(bugs, nrows=10)</code></pre>
<pre><code>## trt row col bugs
## 1: P 1 1 3
## 2: M 2 1 6
## 3: O 3 1 4
## 4: N 4 1 17
## 5: K 5 1 4
## ---
## 21: M 1 5 4
## 22: P 2 5 4
## 23: N 3 5 5
## 24: K 4 5 0
## 25: O 5 5 8</code></pre>
</div>
<div class="col-md-6">
<pre class="r"><code>str(bugs)</code></pre>
<pre><code>## Classes 'data.table' and 'data.frame': 25 obs. of 4 variables:
## $ trt : Factor w/ 5 levels "K","M",""..
## $ row : Factor w/ 5 levels "1","2",""..
## $ col : Factor w/ 5 levels "1","2",""..
## $ bugs: int 3 6 4 17 4 2 0 9 8 4 ...
## - attr(*, ".internal.selfref")=<exter..</code></pre>
</div>
</div>
</div>
<div id="deskriptive-statistik" class="section level1">
<h1>Deskriptive Statistik</h1>
<p>Erst wollen wir ein Gefühl für den Datensatz bekommen und betrachten einen Boxplot für die Anzahl gefundener Larven pro Behandlung. Die Füllfarben die Boxen sind dieselben Farben wie im Feldplan und wurden zuvor von uns im Vektor <code>trtfarben</code> gespeichert - <a href="datr_desplot.html">mehr Infos dazu hier</a>.</p>
<pre class="r"><code>boxplot(bugs ~ trt, col=trtfarben, data=bugs, las=2) # las=2 dreht die Achsenbeschriftung</code></pre>
<p><img src="1f_latsq_poisson_files/figure-html/unnamed-chunk-8-1.png" width="384" style="display: block; margin: auto;" /></p>
</div>
<div id="schließende-statistik" class="section level1">
<h1>Schließende Statistik</h1>
<div id="generalisiertes-modell" class="section level2">
<h2>Generalisiertes Modell</h2>
<p>Wie zu erkennen, ist das Auftreten der Larven ein relativ seltenes Ereignis, sodass die meisten Werte nahe 0 liegen. Wir haben also <em>Zählwerte ohne feste Beschränkung nach oben</em> und können uns entscheiden eine Poissonverteilung für diese Daten anzunehmen und ein entsprechendes generalisiertes lineares Modell anpassen (<a href="appendix_nichtnormalverteilt.html">mehr dazu hier</a>). Bezüglich der Effekte im Modell verfahren wir ähnlich einer <a href="1f_rcbd.html">einfaktoriellen ANOVA in einem RCBD</a>, allerdings mit noch einem zweiten vollständigen Block Effekt, sodass wir Effekte für Zeilen und Spalten haben.</p>
<pre class="r"><code>mod <- glm(bugs ~ trt + row + col, family=quasipoisson(link="log"), data=bugs)</code></pre>
<p>Wie im <a href="1f_rcbd_binomial.html">vorangegangenen Beispiel</a>, legen wir die erwartete Verteileung mit dem <code>family=</code> statement fest. Ebenso entscheiden wir uns direkt für <code>quasipoisson</code> anstelle der einfacheren <code>poisson</code> Verteilung, da diese in gewisser Hinischt flexibler/robuster ist (<a href="intro_glm_carrot.html">mehr dazu hier</a>). Auch hier ist der Zusatz <code>(link="log")</code> eigentlich überflüssig, weil dies die standardmäßige Linkfunktion für poissonverteilte Daten ist. Sie wird hier aber zur Verdeutlichung mit ins Modell geschrieben.</p>
<pre class="r"><code>autoplot(mod)[1:2] # Residuenplots</code></pre>
<pre><code>## Warning: `arrange_()` is deprecated as of dplyr 0.7.0.
## Please use `arrange()` instead.
## See vignette('programming') for more help
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_warnings()` to see where this warning was generated.</code></pre>
<p><img src="1f_latsq_poisson_files/figure-html/unnamed-chunk-10-1.png" width="384" style="display: block; margin: auto;" /></p>
</div>
<div id="test-der-festen-effekte" class="section level2">
<h2>Test der festen Effekte</h2>
<pre class="r"><code>anova(mod, test="Chisq")</code></pre>
<pre><code>## Analysis of Deviance Table
##
## Model: quasipoisson, link: log
##
## Response: bugs
##
## Terms added sequentially (first to last)
##
##
## Df Deviance Resid. Df Resid. Dev Pr(>Chi)
## NULL 24 64.555
## trt 4 26.5294 20 38.026 0.001428 **
## row 4 15.6955 16 22.331 0.033385 *
## col 4 2.8225 12 19.508 0.757711
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1</code></pre>
<pre class="r"><code>car::Anova(mod, test.statistic="Wald")</code></pre>
<pre><code>## Registered S3 methods overwritten by 'car':
## method from
## influence.merMod lme4
## cooks.distance.influence.merMod lme4
## dfbeta.influence.merMod lme4
## dfbetas.influence.merMod lme4</code></pre>
<pre><code>## Analysis of Deviance Table (Type II tests)
##
## Response: bugs
## Df Chisq Pr(>Chisq)
## trt 4 10.8143 0.02873 *
## row 4 9.6828 0.04612 *
## col 4 1.9627 0.74262
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1</code></pre>
<p>Der p-Wert für den Behandlungseffekt weist in diesem Fall auf unterschiedliche Häufigkeiten der gefundenen Larven hin.</p>
</div>
<div id="multipler-mittelwertvergleich" class="section level2">
<h2>Multipler Mittelwertvergleich</h2>
<p>Mittels des <code>emmeans()</code> package lassen wir uns <a href="1f_rcbd_binomial.html">wie im vorigen Beispiel</a> direkt die rücktransformierten Mittelwerte schätzen. Dazu muss lediglich <code>type="response"</code> hinzugefügt werden.</p>
<pre class="r"><code>means <- emmeans(mod, pairwise ~ trt, type="response") # Mittelwertvergleiche
means <- CLD(means$emmeans, Letters = letters) # Buchstabenddarstellung
means$.group <- gsub(" ", "", means$.group, fixed = TRUE) # Entferne Leerzeichen
means</code></pre>
<pre><code>## trt rate SE df asymp.LCL asymp.UCL .group
## K 1.116262 0.5634313 Inf 0.415072 3.001986 a
## P 4.435874 1.1504576 Inf 2.668194 7.374642 ab
## O 5.419780 1.2711275 Inf 3.422513 8.582585 b
## M 5.934068 1.3345778 Inf 3.818708 9.221224 b
## N 6.184781 1.3733085 Inf 4.002377 9.557198 b
##
## Results are averaged over the levels of: row, col
## Confidence level used: 0.95
## Intervals are back-transformed from the log scale
## P value adjustment: tukey method for comparing a family of 5 estimates
## Tests are performed on the log scale
## significance level used: alpha = 0.05</code></pre>
</div>
</div>
<div id="ergebnisaufbereitung" class="section level1">
<h1>Ergebnisaufbereitung</h1>
<pre class="r"><code>ggplot() + theme_classic() +
# Rohdaten (bugs)
geom_boxplot(data=bugs, aes(x=trt, y=bugs), outlier.shape=NA, width=0.6, fill=trtfarben) +
geom_jitter(data=bugs, aes(x=trt, y=bugs), width=0.1, shape=1, size=2) +
# Ergebnisse (means)
geom_point(data=means, aes(x=as.numeric(trt)+0.4, y=rate), col="red", shape=16, size=2) +
geom_errorbar(data=means, aes(x=as.numeric(trt)+0.4, ymin=asymp.LCL, ymax=asymp.UCL), col="red", width=0.1) +
geom_text(data=means, aes(x=trt, y=11, label =.group), col="red") +
labs(y="Schwarz: Beobachtete Anzahl Larven\nRot: Rücktransformierter, adjustierter Mittelwert für die \nHäufigkeit ± 95% asympt. Konfidenzintervall", x="Behandlung",
caption="Mittelwerte, die mit einem gemeinsamen Buchstaben versehen sind,\n sind laut Tukey-test auf der Log-Skala nicht signifikant voneinander verschieden.")</code></pre>
<p><img src="1f_latsq_poisson_files/figure-html/unnamed-chunk-13-1.png" width="672" /></p>
</div>
<hr />
<p style="text-align: center;">Bei Fragen kannst du mir gerne schreiben!</p>
<p style="text-align: center;"><span style="color: #808080;"><em>schmidtpaul@hotmail.de</em></span></p>
<!-- Add icon library -->
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/4.7.0/css/font-awesome.min.css">
<!-- Add font awesome icons -->
<p style="text-align: center;">
<a href="https://www.researchgate.net/profile/Paul_Schmidt17/research" class="fa fa-pencil"></a>
<a href="https://www.linkedin.com/in/schmidtpaul1989/" class="fa fa-linkedin"></a>
<a href="https://www.xing.com/profile/Paul_Schmidt203/cv/" class="fa fa-xing"></a>
<a href="https://github.com/SchmidtPaul/" class="fa fa-github"></a>
</p>
<a href="https://hits.seeyoufarm.com"><img src="https://hits.seeyoufarm.com/api/count/incr/badge.svg?url=https%3A%2F%2Fschmidtpaul.github.io%2FcrashcouRse%2F&count_bg=%23003F75&title_bg=%23555555&icon=&icon_color=%23E7E7E7&title=hits&edge_flat=false" class="center"/></a>
</div>
</div>
</div>
<script>
// add bootstrap table styles to pandoc tables
function bootstrapStylePandocTables() {
$('tr.header').parent('thead').parent('table').addClass('table table-condensed');
}
$(document).ready(function () {
bootstrapStylePandocTables();
});
</script>
<!-- tabsets -->
<script>
$(document).ready(function () {
window.buildTabsets("TOC");
});
$(document).ready(function () {
$('.tabset-dropdown > .nav-tabs > li').click(function () {
$(this).parent().toggleClass('nav-tabs-open')
});
});
</script>
<!-- code folding -->
<script>
$(document).ready(function () {
// move toc-ignore selectors from section div to header
$('div.section.toc-ignore')
.removeClass('toc-ignore')
.children('h1,h2,h3,h4,h5').addClass('toc-ignore');
// establish options
var options = {
selectors: "h1,h2,h3",
theme: "bootstrap3",
context: '.toc-content',
hashGenerator: function (text) {
return text.replace(/[.\\/?&!#<>]/g, '').replace(/\s/g, '_');
},
ignoreSelector: ".toc-ignore",
scrollTo: 0
};
options.showAndHide = true;
options.smoothScroll = true;
// tocify
var toc = $("#TOC").tocify(options).data("toc-tocify");
});
</script>
<!-- dynamically load mathjax for compatibility with self-contained -->
<script>
(function () {
var script = document.createElement("script");
script.type = "text/javascript";
script.src = "https://mathjax.rstudio.com/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML";
document.getElementsByTagName("head")[0].appendChild(script);
})();
</script>
</body>
</html>