Last updated: 2022-04-13

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Introduction

Comparison of estimation methods for coverage, phytovolume, richness and diversity (shannon)

  • Prepara data

Cobertura

  • Summary values
Cobertura || Summary
metodo mean sd se cv median n
quadrat 29.92 18.47 1.89 61.75 26.50 96
dronQ 23.55 21.01 2.14 89.23 15.74 96
line_intercept 27.19 6.49 1.87 23.86 29.67 12
point_quadrat 55.50 7.62 2.20 13.73 56.00 12
dronT 17.46 2.71 0.78 15.51 17.07 12

1.1 Comparación cobertura Quadrat - DronQ

  • Comprobamos Normalidad y Homocedascticidad

  • Normality?

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    Shapiro-Wilk normality test

data:  cob_selected$value
W = 0.89104, p-value = 1.299e-10

Los resultados indican que los datos no son normales (W = 0.89; p<0.0001)

  • Homogeneidad de la varianza?

    Bartlett test of homogeneity of variances

data:  cob_selected$value and cob_selected$metodo
Bartlett's K-squared = 1.5582, df = 1, p-value = 0.2119

Según los resultados, no parece existir heterogeneidad en las varianzas (Bartlett’s K-squared = 1.56; p=0.2119)

Por tanto, dos opciones: aplicar método wilcox.test o transformar datos (log) y aplicar t-test

  • Wilcox test

    Wilcoxon rank sum test with continuity correction

data:  value by metodo
W = 5967.5, p-value = 0.0004154
alternative hypothesis: true location shift is not equal to 0
  • T-test de datos transformados (log)

En cualquier caso obtenemos los siguientes resultados: - Existen diferencias significativas tanto si usamos el test no paramétrico de Wilcoxon (W = 5967.5; p=0.0004), como si aplicamos el test paramétrico a los datos transformados (t = 3.997; p<0.0001). De forma gráfica

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Correlación Quadrat - Dron Q

Ver resultados presentados al congreso forestal

1.2 Correlación de dronT (500 m2) con Line Intercept y PointQuadrat

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1.3 Comparación Line-Intercept, Quadrat, PointQuadrat

Vamos a realizar la comparación seleccionando para cada parcela (n=12) un valor de cobertura de quadrats. Éste valor se calcula mediante dos aproximaciones:

  • Promediando para cada parcela el valor de los quadrats
  • Utilizando las medias ponderadas (valores de cobertura de los quadrats ponderados en función de la distribución inicial)
# A tibble: 12 x 3
   parcela  value metodo       
   <chr>    <dbl> <chr>        
 1 AL_NP_13  36.4 quadrat medio
 2 AL_NP_7   21.8 quadrat medio
 3 AL_NP_8   33   quadrat medio
 4 AL_NP_9   29.9 quadrat medio
 5 AL_P_11   24.9 quadrat medio
 6 AL_P_12   33.9 quadrat medio
 7 AL_P_14   31.8 quadrat medio
 8 AL_P_4    37.5 quadrat medio
 9 AL_PR_15  29.8 quadrat medio
10 AL_PR_16  32.6 quadrat medio
11 AL_PR_17  21.2 quadrat medio
12 AL_PR_18  26.4 quadrat medio
statistic p.value parameter method mi_variable
27.11094 5.6e-06 3 Kruskal-Wallis rank sum test cobertura
  • Posteriormente computamos las pruebas post-hoc
Cobertura || Non-parametric Kruskal-Wallis ANOVA - Post-hoc Dunn’s-test with Bonferroni adjustment
H0 statistic p.value
line_intercept = point_quadrat 4.56 <0.001
line_intercept = quadrat medio 0.80 >0.999
line_intercept = quadrat media ponderada 0.29 >0.999
point_quadrat = quadrat medio 3.76 0.001
point_quadrat = quadrat media ponderada 4.27 <0.001
quadrat medio = quadrat media ponderada 0.51 >0.999

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Observamos que no hay diferencias entre LI, y los quadrats medios, ni quadrats ponderado.

Correlaciones

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PQ ~ LI,Qm,Qmp

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LI ~ PQ,Qm,Qmp

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Qm ~ PQ,LI,Qp

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Qp ~ PQ,LI,Qm

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Coeficiente de Variación

Analizamos los datos de CV, si son diferentes significativamente. Aplicamos el test MSLRT (Modified signed-likelihood ratio test) para cada uno de los pares de métodos.

Cobertura || Pairwise Modified signed-likelihood ratio test (SLRT) for equality of CVs
V1 V2 MSLRT p_value
quadrat dronQ 6.13 0.01326
quadrat line_intercept 9.22 0.00240
quadrat point_quadrat 19.22 0.00001
quadrat dronT 16.88 0.00004
dronQ line_intercept 13.98 0.00019
dronQ point_quadrat 24.60 0.00000
dronQ dronT 22.16 0.00000
line_intercept point_quadrat 2.88 0.08977
line_intercept dronT 1.77 0.18398
point_quadrat dronT 0.14 0.70956

Fitovolumen

  • Summary values
Fitovolumen || Summary
metodo mean sd se cv median n
quadrat 778.57 1108.78 113.16 142.41 323.40 96
dronQ 421.70 678.47 69.25 160.89 125.90 96
line_intercept 531.04 274.90 79.36 51.77 543.13 12
dronT 450.63 141.74 40.92 31.45 408.39 12

Modelo

  • Aplicamos un modelo de Kruskal-Wallis con comparaciones post-hoc aplicando test de Dunn (correcciones de Bonferroni).
  • Los resultados son los siguientes:
statistic p.value parameter method mi_variable
23.40999 3.32e-05 3 Kruskal-Wallis rank sum test fitovolumen
  • Posteriormente computamos las pruebas post-hoc
Fitovolumen || Non-parametric Kruskal-Wallis ANOVA - Post-hoc Dunn’s-test with Bonferroni adjustment
H0 statistic p.value
quadrat = dronQ 4.20 0.0002
quadrat = line_intercept 0.74 1.0000
quadrat = dronT 0.68 1.0000
dronQ = line_intercept 2.72 0.0397
dronQ = dronT 2.66 0.0464
line_intercept = dronT 0.04 1.0000

Version Author Date
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Coeficiente de Variación

Analizamos los datos de CV, si son diferentes significativamente. Aplicamos el test MSLRT (Modified signed-likelihood ratio test) para cada uno de los pares de métodos.

Fitovolumen || Pairwise Modified signed-likelihood ratio test (SLRT) for equality of CVs
V1 V2 MSLRT p_value
quadrat dronQ 0.27 0.60538
quadrat line_intercept 4.69 0.03041
quadrat dronT 10.28 0.00135
dronQ line_intercept 4.89 0.02694
dronQ dronT 9.99 0.00158
line_intercept dronT 1.94 0.16351

Richness

  • Summary values
Richness || Summary
metodo mean sd se cv median n
quadrat 10.57 3.89 0.40 36.77 10.0 96
line_intercept 13.00 3.10 0.90 23.88 13.0 12
point_quadrat 13.17 4.24 1.22 32.20 14.0 12
point_quadrat_extenso 31.50 7.99 2.31 25.38 29.5 12
quadrat_parcela 34.08 10.39 3.00 30.48 34.5 12

Modelo

  • Aplicamos un modelo de Kruskal-Wallis con comparaciones post-hoc aplicando test de Dunn (correcciones de Bonferroni).
  • Los resultados son los siguientes:
statistic p.value parameter method mi_variable
64.59165 0 4 Kruskal-Wallis rank sum test riqueza
  • Posteriormente computamos las pruebas post-hoc
Riqueza || Non-parametric Kruskal-Wallis ANOVA - Post-hoc Dunn’s-test with Bonferroni adjustment
H0 statistic p.value
quadrat = line_intercept 1.82 0.6853
quadrat = point_quadrat 1.68 0.9341
quadrat = point_quadrat_extenso 5.90 0.0000
quadrat = quadrat_parcela 6.02 0.0000
line_intercept = point_quadrat 0.11 1.0000
line_intercept = point_quadrat_extenso 3.06 0.0221
line_intercept = quadrat_parcela 3.15 0.0163
point_quadrat = point_quadrat_extenso 3.17 0.0153
point_quadrat = quadrat_parcela 3.26 0.0112
point_quadrat_extenso = quadrat_parcela 0.09 1.0000

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Coeficiente de Variación

Analizamos los datos de CV, si son diferentes significativamente. Aplicamos el test MSLRT (Modified signed-likelihood ratio test) para cada uno de los pares de métodos.

Riqueza || Pairwise Modified signed-likelihood ratio test (SLRT) for equality of CVs
V1 V2 MSLRT p_value
quadrat line_intercept 2.82 0.09335
quadrat point_quadrat 0.40 0.52492
quadrat point_quadrat_extenso 2.18 0.14018
quadrat quadrat_parcela 0.70 0.40309
line_intercept point_quadrat 0.80 0.37022
line_intercept point_quadrat_extenso 0.02 0.87866
line_intercept quadrat_parcela 0.54 0.46359
point_quadrat point_quadrat_extenso 0.50 0.47807
point_quadrat quadrat_parcela 0.01 0.90371
point_quadrat_extenso quadrat_parcela 0.30 0.58628

Shannon

  • Summary values
Richness || Summary
metodo mean sd se cv median n
quadrat 1.34 0.56 0.06 41.72 1.37 96
line_intercept 1.72 0.49 0.14 28.71 1.63 12
point_quadrat 1.99 0.45 0.13 22.82 1.95 12

Modelo

  • Aplicamos un modelo de ANOVA con comparaciones post-hoc aplicando test de Dunn (correcciones de Bonferroni).
  • Los resultados son los siguientes:
OK: There is not clear evidence for different variances across groups (Bartlett Test, p = 0.611).
OK: residuals appear as normally distributed (p = 0.168).
Parameter Sum_Squares df Mean_Square F p Eta2 Eta2_CI_low Eta2_CI_high
metodo 5.41 2 2.71 9.09 0.00021 0.134 0.046 0.227
Residuals 34.83 117 0.30 
The ANOVA (formula: value ~ metodo) suggests that:

  - The main effect of metodo is statistically significant and medium (F(2, 117) = 9.09, p < .001; Eta2 = 0.13, 90% CI [0.05, 0.23])

Effect sizes were labelled following Field's (2013) recommendations.
  • Posteriormente computamos las pruebas post-hoc
Diversidad || ANOVA - Post-hoc Bonferroni adjustment
contrast estimate SE df t.ratio p.value
quadrat - line_intercept -0.378 0.167 117 -2.27 0.0760
quadrat - point_quadrat -0.642 0.167 117 -3.84 0.0006
line_intercept - point_quadrat -0.263 0.223 117 -1.18 0.7181

Version Author Date
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Coeficiente de Variación

Analizamos los datos de CV, si son diferentes significativamente. Aplicamos el test MSLRT (Modified signed-likelihood ratio test) para cada uno de los pares de métodos.

Diversidad || Pairwise Modified signed-likelihood ratio test (SLRT) for equality of CVs
V1 V2 MSLRT p_value
quadrat line_intercept 2.13 0.14465
quadrat point_quadrat 4.81 0.02832
line_intercept point_quadrat 0.48 0.48795 

R version 4.0.2 (2020-06-22)
Platform: x86_64-apple-darwin17.0 (64-bit)
Running under: macOS Catalina 10.15.3

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
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[13] Metrics_0.1.4      ggstatsplot_0.7.2  colorspace_2.0-2   ggpubr_0.4.0      
[17] ggforce_0.3.2      ggdark_0.2.1       janitor_2.1.0      here_1.0.1        
[21] forcats_0.5.1      stringr_1.4.0      dplyr_1.0.6        purrr_0.3.4       
[25] readr_1.4.0        tidyr_1.1.3        tibble_3.1.2       ggplot2_3.3.5     
[29] tidyverse_1.3.1    workflowr_1.7.0   

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 [17] paletteer_1.3.0           openxlsx_4.2.3           
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 [25] xfun_0.23                 prismatic_1.0.0          
 [27] callr_3.7.0               crayon_1.4.1             
 [29] jsonlite_1.7.2            zeallot_0.1.0            
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 [37] webshot_0.5.2             MatrixModels_0.4-1       
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 [45] mvtnorm_1.1-1             DBI_1.1.1                
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[127] hms_1.0.0                 grid_4.0.2               
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[133] git2r_0.28.0              getPass_0.2-2            
[135] lubridate_1.7.10