# CCFRP Data Analysis + Statistics and R Notes
Modeling in Ecology:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5970551/
## Stats Notes
**ANOVA**- one-way analysis of variance used to determine whether there are any statistically significant differences between the means of three or more independent (unrelated) groups
*can tell you that two groups are statistically different from each other but not which two groups for that you need a post hoc test.
y = B0 + B1[x] + e
Categorical value for X
**T-test**- compare two groups only
`t.test(DependentVariable~category, data=dataset)`
When Category has only two options
DependentVariable is continuous
**One-way analysis of means** (not assuming equal variances)
`oneway.test(DependentVariable~category, data=dataset)`
When Category has more than two options
*or*
**lm test** (assuming equal variances)
`summary(lm(DependentVariable~category,data=dataset)`
Gives:
```
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4.1737 1.0461 3.990 7.27e-05 ***
Vertical_DistWC 4.1273 1.4007 2.947 0.00331 **
siteREF -1.3938 1.4470 -0.963 0.33575
locSP -1.3506 1.3976 -0.966 0.33418
siteREF:locSP -0.6799 2.0008 -0.340 0.73409
Vertical_DistWC:siteMPA:locBH -4.3670 2.3781 -1.836 0.06670 .
Vertical_DistWC:siteREF:locBH -1.3121 2.2106 -0.594 0.55298
Vertical_DistWC:siteMPA:locSP 8.7787 1.9130 4.589 5.23e-06 ***
Vertical_DistWC:siteREF:locSP NA NA NA NA
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 10.2 on 743 degrees of freedom
Multiple R-squared: 0.1817, Adjusted R-squared: 0.174
F-statistic: 23.57 on 7 and 743 DF, p-value: < 2.2e-16
```
Analysis of variance table: displays the significance of categories
`anova(lm(DependentVariable~category,data=dataset)`
```
Analysis of Variance Table
Response: CPUE_by_Guild
Df Sum Sq Mean Sq F value Pr(>F)
Vertical_Dist 1 7363 7362.7 70.8250 < 2.2e-16 ***
site 1 3523 3522.8 33.8872 8.687e-09 ***
loc 1 144 144.2 1.3874 0.2392192
site:loc 1 1564 1564.3 15.0475 0.0001141 ***
Vertical_Dist:site:loc 3 4556 1518.7 14.6093 2.974e-09 ***
Residuals 743 77239 104.0
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
```
Use a tukey test to determine which interactions are significant
```
m1 <- lm(CPUE_by_Guild ~ Vertical_Dist + site + loc + site:loc + site:loc:Vertical_Dist, data = df.sum.across.guilds.per.drift)
m1_tukey <- TukeyHSD(aov(m1))
m1_tukey
```
```
$`Vertical_Dist:site:loc`
diff lwr upr
WC:MPA:BH-BT:MPA:BH -0.23966429 -6.0810098 5.6016813
BT:REF:BH-BT:MPA:BH -1.39380690 -5.7921173 3.0045035
WC:REF:BH-BT:MPA:BH 1.42141188 -3.8602703 6.7030941
BT:MPA:SP-BT:MPA:BH -1.35062139 -5.5988727 2.8976299
WC:MPA:SP-BT:MPA:BH 11.55540186 7.3298132 15.7809906
BT:REF:SP-BT:MPA:BH -3.42431515 -7.8753324 1.0267021
WC:REF:SP-BT:MPA:BH 0.70302295 -3.6022107 5.0082566
BT:REF:BH-WC:MPA:BH -1.15414261 -6.9201128 4.6118276
WC:REF:BH-WC:MPA:BH 1.66107617 -4.8040181 8.1261705
BT:MPA:SP-WC:MPA:BH -1.11095710 -6.7632944 4.5413802
WC:MPA:SP-WC:MPA:BH 11.79506615 6.1597421 17.4303902
BT:REF:SP-WC:MPA:BH -3.18465086 -8.9909261 2.6216244
WC:REF:SP-WC:MPA:BH 0.94268724 -4.7526016 6.6379760
WC:REF:BH-BT:REF:BH 2.81521878 -2.3829791 8.0134166
BT:MPA:SP-BT:REF:BH 0.04318551 -4.1008142 4.1871852
WC:MPA:SP-BT:REF:BH 12.94920876 8.8284449 17.0699726
BT:REF:SP-BT:REF:BH -2.03050825 -6.3821343 2.3211178
WC:REF:SP-BT:REF:BH 2.09682985 -2.1055660 6.2992257
BT:MPA:SP-WC:REF:BH -2.77203327 -7.8438934 2.2998269
WC:MPA:SP-WC:REF:BH 10.13398998 5.0810971 15.1868828
BT:REF:SP-WC:REF:BH -4.84572703 -10.0885966 0.3971425
WC:REF:SP-WC:REF:BH -0.71838894 -5.8380728 4.4012950
WC:MPA:SP-BT:MPA:SP 12.90602325 8.9458214 16.8662251
BT:REF:SP-BT:MPA:SP -2.07369376 -6.2735930 2.1262055
WC:REF:SP-BT:MPA:SP 2.05364434 -1.9914312 6.0987198
BT:REF:SP-WC:MPA:SP -14.97971701 -19.1566913 -10.8027427
WC:REF:SP-WC:MPA:SP -10.85237892 -14.8736470 -6.8311109
WC:REF:SP-BT:REF:SP 4.12733809 -0.1301907 8.3848669
p adj
WC:MPA:BH-BT:MPA:BH 1.0000000
BT:REF:BH-BT:MPA:BH 0.9793221
WC:REF:BH-BT:MPA:BH 0.9921127
BT:MPA:SP-BT:MPA:BH 0.9789357
WC:MPA:SP-BT:MPA:BH 0.0000000
BT:REF:SP-BT:MPA:BH 0.2741201
WC:REF:SP-BT:MPA:BH 0.9996771
BT:REF:BH-WC:MPA:BH 0.9987720
WC:REF:BH-WC:MPA:BH 0.9940555
BT:MPA:SP-WC:MPA:BH 0.9989088
WC:MPA:SP-WC:MPA:BH 0.0000000
BT:REF:SP-WC:MPA:BH 0.7085774
WC:REF:SP-WC:MPA:BH 0.9996468
WC:REF:BH-BT:REF:BH 0.7218974
BT:MPA:SP-BT:REF:BH 1.0000000
WC:MPA:SP-BT:REF:BH 0.0000000
BT:REF:SP-BT:REF:BH 0.8488074
WC:REF:SP-BT:REF:BH 0.7984875
BT:MPA:SP-WC:REF:BH 0.7123254
WC:MPA:SP-WC:REF:BH 0.0000000
BT:REF:SP-WC:REF:BH 0.0941911
WC:REF:SP-WC:REF:BH 0.9998830
WC:MPA:SP-BT:MPA:SP 0.0000000
BT:REF:SP-BT:MPA:SP 0.8070926
WC:REF:SP-BT:MPA:SP 0.7836747
BT:REF:SP-WC:MPA:SP 0.0000000
WC:REF:SP-WC:MPA:SP 0.0000000
WC:REF:SP-BT:REF:SP 0.0651076
```
Only want
WC:REF:SP-WC:MPA:SP 0.0000000
BT:REF:SP-BT:MPA:SP 0.8070926
WC:REF:BH-WC:MPA:BH 0.9940555
BT:REF:BH-BT:MPA:BH 0.9793221
Does not meet regression assumptions and is over penalising
Interaction plot: MPA/REF vs BH/SP
```
with(df.sum.across.guilds.per.drift,interaction.plot(x.factor = loc,site,response = CPUE_by_Guild))
```
Interaction plot
loc,Vertical_Dist
Interaction plot
site,Vertical_Dist
### Vertical Distribution Graphs
p-values calculated in the section below:
WC_MPA_BH - WC_REF_BH 0.1733
BT_MPA_BH - BT_REF_BH 0.0304
p-values calculated in the section below:
WC_MPA_SP - WC_REF_SP <.0001
BT_MPA_SP - BT_REF_SP <.0001
## **ANOVA and TukeyHSD post-hoc with specific interactions**
```
m1 <- glm(CPUE_by_Guild ~ Vertical_Dist + site + loc + site:loc + site:loc:Vertical_Dist, data = df.sum.across.guilds.per.drift)
anova(m1, test = "F")
```
Analysis of Deviance Table
```
Df Deviance Resid. Df Resid. Dev F Pr(>F)
NULL 750 94390
Vertical_Dist 1 7362.7 749 87027 70.8250 < 2.2e-16 ***
site 1 3522.8 748 83504 33.8872 8.687e-09 ***
loc 1 144.2 747 83360 1.3874 0.2392192
site:loc 1 1564.3 746 81796 15.0475 0.0001141 ***
Vertical_Dist:site:loc 3 4556.2 743 77239 14.6093 2.974e-09 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
```
Test if the model fits:
`hist(residuals(m1))`
Does not fit well (assues normal distribution): looks like a gamma distribution which can be often log into a normal distribution with
`glm(…, family = Gamma(link = log))`
so
```
m1 <- glm((CPUE_by_Guild + 1) ~ Vertical_Dist + site + loc + site:loc + site:loc:Vertical_Dist, family = Gamma(link = log), data =
df.sum.across.guilds.per.drift)
```
(CPUE_by_Guild + 1) becuase you can't have log(0)
To fit the model better
Need only specific contrasts for the TukeyHSD post-hoc
Tried:
```
emmeans::ref_grid(m1, at = list(Vertical_Dist = 0:1, site = 0:1, loc = 0:1))
```
error: Error in ``contrasts<-`(`*tmp*`, value = contrasts.arg[[nn]]) :
contrasts apply only to factors``
To fix error: I changed loc, site, and Vertical_Dist into factors
```
df.sum.across.guilds.per.drift$loc <- factor(df.sum.across.guilds.per.drift$loc)
df.sum.across.guilds.per.drift$site <- factor(df.sum.across.guilds.per.drift$site)
df.sum.across.guilds.per.drift$Vertical_Dist <- factor(df.sum.across.guilds.per.drift$Vertical_Dist)
```
Then ran the model and created the ref_grid
```
#create model
m1 <- glm((CPUE_by_Guild + 1) ~ Vertical_Dist + site + loc + site:loc + site:loc:Vertical_Dist, family = Gamma(link = log), data = df.sum.across.guilds.per.drift)
#specify contrasts
m2<- emmeans::ref_grid(m1, at = c(Vertical_Dist = 0:1, site = 0:1, loc = 0:1))
```
great referance for Anova and fitting models: https://www.r-bloggers.com/linear-models-anova-glms-and-mixed-effects-models-in-r/
Now `plot(m2)` gives:
Now I am unsure how to use the ref_grid to get only the contrasts I want, I can get all of them again pairwise:
`pairs(m2)` gives:
```
contrast estimate SE df z.ratio p.value
BT,MPA,BH - WC,MPA,BH 0.0474 0.193 Inf 0.246 1.0000
**BT,MPA,BH - BT,REF,BH** 0.3139 0.145 Inf 2.165 0.3730
BT,MPA,BH - WC,REF,BH -0.2427 0.174 Inf -1.394 0.8602
BT,MPA,BH - BT,MPA,SP 0.3025 0.140 Inf 2.161 0.3759
BT,MPA,BH - WC,MPA,SP -1.1736 0.139 Inf -8.426 <.0001
BT,MPA,BH - BT,REF,SP 1.0843 0.147 Inf 7.391 <.0001
BT,MPA,BH - WC,REF,SP -0.1274 0.142 Inf -0.898 0.9863
WC,MPA,BH - BT,REF,BH 0.2665 0.190 Inf 1.402 0.8567
**WC,MPA,BH - WC,REF,BH** -0.2902 0.213 Inf -1.362 0.8746
WC,MPA,BH - BT,MPA,SP 0.2551 0.186 Inf 1.369 0.8713
WC,MPA,BH - WC,MPA,SP -1.2210 0.186 Inf -6.574 <.0001
WC,MPA,BH - BT,REF,SP 1.0369 0.191 Inf 5.418 <.0001
WC,MPA,BH - WC,REF,SP -0.1748 0.188 Inf -0.931 0.9831
BT,REF,BH - WC,REF,BH -0.5566 0.171 Inf -3.249 0.0256
BT,REF,BH - BT,MPA,SP -0.0114 0.137 Inf -0.083 1.0000
BT,REF,BH - WC,MPA,SP -1.4875 0.136 Inf -10.952 <.0001
BT,REF,BH - BT,REF,SP 0.7704 0.143 Inf 5.372 <.0001
BT,REF,BH - WC,REF,SP -0.4413 0.139 Inf -3.186 0.0312
WC,REF,BH - BT,MPA,SP 0.5453 0.167 Inf 3.262 0.0245
WC,REF,BH - WC,MPA,SP -0.9308 0.167 Inf -5.589 <.0001
WC,REF,BH - BT,REF,SP 1.3271 0.173 Inf 7.680 <.0001
WC,REF,BH - WC,REF,SP 0.1153 0.169 Inf 0.683 0.9974
BT,MPA,SP - WC,MPA,SP -1.4761 0.131 Inf -11.309 <.0001
**BT,MPA,SP - BT,REF,SP** 0.7818 0.138 Inf 5.648 <.0001
BT,MPA,SP - WC,REF,SP -0.4299 0.133 Inf -3.225 0.0276
WC,MPA,SP - BT,REF,SP 2.2579 0.138 Inf 16.401 <.0001
**WC,MPA,SP - WC,REF,SP** 1.0462 0.133 Inf 7.893 <.0001
BT,REF,SP - WC,REF,SP -1.2117 0.140 Inf -8.635 <.0001
```
Only want p-value
WC,MPA,SP - WC,REF,SP <.0001
BT,MPA,SP - BT,REF,SP <.0001
WC,MPA,BH - WC,REF,BH 0.8746
BT,MPA,BH - BT,REF,BH 0.3730
*These p-values seem more reasonable are they still over penalizing because we are no longer using Tukey???
**Values confirmed by Connor **
Pairwise P-Value Plot:
`emmeans::pwpp(m2)`
```
> multcomp::cld(m2)
Vertical_Dist site loc prediction SE df .group
BT REF SP 0.559 0.1027 Inf 1
BT REF BH 1.330 0.1002 Inf 2
BT MPA SP 1.341 0.0929 Inf 2
WC MPA BH 1.596 0.1615 Inf 23
BT MPA BH 1.644 0.1048 Inf 23
WC REF SP 1.771 0.0957 Inf 3
WC REF BH 1.886 0.1390 Inf 3
WC MPA SP 2.817 0.0917 Inf 4
```
Bonforoni Test
Papers to refer to:
Mace Morgan 2006, 2011
invertabrate recruitment in low at the headland and higher in the lee of the headland
Review paper 2014 Morgan
advances in oceanography
### Code for Vertical_Dist Direct Comparsions
```
refGrid <- emmeans::ref_grid(m1, at = c(Vertical_Dist = 0:1, site = 0:1, loc = 0:1))
refGrid.s <- emmeans::emmeans(refGrid, specs = c("Vertical_Dist", "site", "loc"))
refGrid.s <- emmeans::emmeans(m1, specs = c("Vertical_Dist", "site", "loc"))
refGrid.s
WC_MPA_SP = c(0, 0, 0, 0, 0, 1, 0, 0)
WC_REF_SP = c(0, 0, 0, 0, 0, 0, 0, 1)
BT_MPA_SP = c(0, 0, 0, 0, 1, 0, 0, 0)
BT_REF_SP = c(0, 0, 0, 0, 0, 0, 1, 0)
WC_MPA_BH = c(0, 1, 0, 0, 0, 0, 0, 0)
WC_REF_BH = c(0, 0, 0, 1, 0, 0, 0, 0)
BT_MPA_BH = c(1, 0, 0, 0, 0, 0, 0, 0)
BT_REF_BH = c(0, 0, 1, 0, 0, 0, 0, 0)
emmeans::contrast(refGrid.s, method = list(WC_MPA_SP - WC_REF_SP) )
emmeans::contrast(refGrid.s, method = list(BT_MPA_SP - BT_REF_SP) )
emmeans::contrast(refGrid.s, method = list(WC_MPA_BH - WC_REF_BH) )
emmeans::contrast(refGrid.s, method = list(BT_MPA_BH - BT_REF_BH) )
```
### Output
```
> refGrid.s
Vertical_Dist site loc emmean SE df asymp.LCL asymp.UCL
BT MPA BH 1.644 0.1048 Inf 1.438 1.85
WC MPA BH 1.596 0.1615 Inf 1.280 1.91
BT REF BH 1.330 0.1002 Inf 1.133 1.53
WC REF BH 1.886 0.1390 Inf 1.614 2.16
BT MPA SP 1.341 0.0929 Inf 1.159 1.52
WC MPA SP 2.817 0.0917 Inf 2.637 3.00
BT REF SP 0.559 0.1027 Inf 0.358 0.76
WC REF SP 1.771 0.0957 Inf 1.583 1.96
Results are given on the log(mu + 1) (not the response) scale.
Confidence level used: 0.95
> emmeans::contrast(refGrid.s, method = list(WC_MPA_SP - WC_REF_SP) )
contrast estimate SE df z.ratio p.value
c(0, 0, 0, 0, 0, 1, 0, -1) 1.05 0.133 Inf 7.893 <.0001
Results are given on the log (not the response) scale.
> emmeans::contrast(refGrid.s, method = list(BT_MPA_SP - BT_REF_SP) )
contrast estimate SE df z.ratio p.value
c(0, 0, 0, 0, 1, 0, -1, 0) 0.782 0.138 Inf 5.648 <.0001
Results are given on the log (not the response) scale.
> emmeans::contrast(refGrid.s, method = list(WC_MPA_BH - WC_REF_BH) )
contrast estimate SE df z.ratio p.value
c(0, 1, 0, -1, 0, 0, 0, 0) -0.29 0.213 Inf -1.362 0.1733
Results are given on the log (not the response) scale.
> emmeans::contrast(refGrid.s, method = list(BT_MPA_BH - BT_REF_BH) )
contrast estimate SE df z.ratio p.value
c(1, 0, -1, 0, 0, 0, 0, 0) 0.314 0.145 Inf 2.165 0.0304
```
### North Central MPAs
MPA,BH - REF,BH 0.8586
MPA,SP - REF,SP <.0001
### Model Simplified for only Site and Loc
Pairwise
```
> pairs(m2)
contrast estimate SE df z.ratio p.value
MPA,BH - REF,BH 0.0296 0.166 Inf 0.178 0.9980
MPA,BH - MPA,SP -1.0482 0.160 Inf -6.549 <.0001
MPA,BH - REF,SP 0.0527 0.163 Inf 0.324 0.9883
REF,BH - MPA,SP -1.0778 0.156 Inf -6.923 <.0001
REF,BH - REF,SP 0.0231 0.158 Inf 0.146 0.9989
MPA,SP - REF,SP 1.1010 0.152 Inf 7.245 <.0001
```
MPA,BH - REF,BH 0.9980
MPA,SP - REF,SP <.0001
#### Direct Contrasts
```
site loc emmean SE df z.ratio p.value
MPA BH 1.92 0.120 Inf 15.953 <.0001
REF BH 1.89 0.115 Inf 16.513 <.0001
MPA SP 2.97 0.105 Inf 28.170 <.0001
REF SP 1.87 0.109 Inf 17.071 <.0001
Results are given on the log(mu + 1) (not the response) scale.
P value adjustment: bonferroni method for 4 tests
> #pairs(refGrid.s)
>
> MPA_BH = c(1, 0, 0, 0)
> REF_BH = c(0, 1, 0, 0)
>
> MPA_SP = c(0, 0, 1, 0)
> REF_SP = c(0, 0, 0, 1)
>
>
> emmeans::contrast(refGrid.s, method = list(MPA_BH - REF_BH) )
contrast estimate SE df z.ratio p.value
c(1, -1, 0, 0) 0.0296 0.166 Inf 0.178 0.8586
Results are given on the log (not the response) scale.
> emmeans::contrast(refGrid.s, method = list( MPA_SP - REF_SP) )
contrast estimate SE df z.ratio p.value
c(0, 0, 1, -1) 1.1 0.152 Inf 7.245 <.0001
Results are given on the log (not the response) scale.
```
## Species MPA vs. REF
**Key: * = significant**
Deacon* (SP & BH)
```
emmeans::contrast(refGrid.s, method = list(DEA_MPA_SP - DEA_REF_SP) )
contrast estimate
c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.767
SE df z.ratio p.value
0.125 Inf 6.133 <.0001
Results are given on the log (not the response) scale.
> emmeans::contrast(refGrid.s, method = list(DEA_MPA_BH - DEA_REF_BH) )
contrast estimate
c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.54
SE df z.ratio p.value
0.235 Inf -2.297 0.0216
Results are given on the log (not the response) scale.
>
```
Blue* (SP)
```
> emmeans::contrast(refGrid.s, method = list(BLU_MPA_SP - BLU_REF_SP) )
contrast estimate
c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.919
SE df z.ratio p.value
0.126 Inf 7.321 <.0001
Results are given on the log (not the response) scale.
> emmeans::contrast(refGrid.s, method = list(BLU_MPA_BH - BLU_REF_BH) )
contrast estimate
c(0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.446
SE df z.ratio p.value
0.271 Inf 1.646 0.0997
```
Vermillion
```
> emmeans::contrast(refGrid.s, method = list(VER_MPA_SP - VER_REF_SP) )
contrast estimate SE df
c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.262 0.257 Inf
z.ratio p.value
1.019 0.3082
Results are given on the log (not the response) scale.
> emmeans::contrast(refGrid.s, method = list(VER_MPA_BH - VER_REF_BH) )
contrast estimate SE df
c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.387 0.385 Inf
z.ratio p.value
-1.005 0.3149
```
Lingcod
```
emmeans::contrast(refGrid.s, method = list(LING_MPA_SP - LING_REF_SP) )
contrast estimate SE df z.ratio
c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.185 0.186 Inf 0.995
p.value
0.3197
Results are given on the log (not the response) scale.
> emmeans::contrast(refGrid.s, method = list(LING_MPA_BH - LING_REF_BH) )
contrast estimate SE df z.ratio
c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0.207 0.163 Inf 1.273
p.value
0.2031
```
Black* (SP)
```
> emmeans::contrast(refGrid.s, method = list(BLA_MPA_SP - BLA_REF_SP) )
contrast estimate SE df z.ratio
c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.412 0.154 Inf 2.675
p.value
0.0075
Results are given on the log (not the response) scale.
> emmeans::contrast(refGrid.s, method = list(BLA_MPA_BH - BLA_REF_BH) )
contrast estimate SE df z.ratio
c(0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.326 0.27 Inf -1.208
p.value
0.2272
```
Brown
```
> emmeans::contrast(refGrid.s, method = list(BWN_MPA_SP - BWN_REF_SP) )
contrast estimate SE df z.ratio
c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.256 0.591 Inf 0.433
p.value
0.6649
Results are given on the log (not the response) scale.
> emmeans::contrast(refGrid.s, method = list(BWN_MPA_BH - BWN_REF_BH) )
contrast estimate SE df z.ratio
c(0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.187 0.177 Inf 1.056
p.value
0.2909
```
China
```
> emmeans::contrast(refGrid.s, method = list(CHN_MPA_SP - CHN_REF_SP) )
contrast estimate SE df z.ratio
c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.233 0.166 Inf 1.399
p.value
0.1618
Results are given on the log (not the response) scale.
> emmeans::contrast(refGrid.s, method = list(CHN_MPA_BH - CHN_REF_BH) )
contrast estimate SE df z.ratio
c(0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.235 0.242 Inf 0.973
p.value
0.3307
```
Gopher* (SP)
```
> emmeans::contrast(refGrid.s, method = list(GPR_MPA_SP - GPR_REF_SP) )
contrast estimate SE df z.ratio
c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.453 0.14 Inf 3.246
p.value
0.0012
Results are given on the log (not the response) scale.
> emmeans::contrast(refGrid.s, method = list(GPR_MPA_BH - GPR_REF_BH) )
contrast estimate SE df z.ratio
c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -0.108 0.17 Inf -0.637
p.value
0.5241
```
Olive* (SP)
```
emmeans::contrast(refGrid.s, method = list(OLV_MPA_SP - OLV_REF_SP) )
contrast estimate SE df z.ratio
c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.463 0.156 Inf 2.967
p.value
0.0030
Results are given on the log (not the response) scale.
> emmeans::contrast(refGrid.s, method = list(OLV_MPA_BH - OLV_REF_BH) )
contrast estimate SE df z.ratio
c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -0.155 0.889 Inf -0.174
p.value
0.8619
```
Quillback
```
> emmeans::contrast(refGrid.s, method = list(QBK_MPA_SP - QBK_REF_SP) )
contrast estimate SE df z.ratio
c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.419 0.965 Inf 0.434
p.value
0.6640
Results are given on the log (not the response) scale.
> emmeans::contrast(refGrid.s, method = list(QBK_MPA_BH - QBK_REF_BH) )
contrast estimate SE df z.ratio
c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0.126 0.689 Inf 0.182
p.value
0.8552
```
## Species Length MPA vs. REF
Deacon* (SP)
```
emmeans::contrast(refGrid.s, method = list(DEA_MPA_SP - DEA_REF_SP) )
contrast
c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
estimate SE df z.ratio p.value
0.0445 0.00846 Inf 5.260 <.0001
Results are given on the log (not the response) scale.
> emmeans::contrast(refGrid.s, method = list(DEA_MPA_BH - DEA_REF_BH) )
contrast
c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
estimate SE df z.ratio p.value
0.0178 0.025 Inf 0.713 0.4758
```
Blue* (SP & BH)
```
> emmeans::contrast(refGrid.s, method = list(BLU_MPA_SP - BLU_REF_SP) )
contrast estimate
c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.035
SE df z.ratio p.value
0.00861 Inf 4.063 <.0001
Results are given on the log (not the response) scale.
> emmeans::contrast(refGrid.s, method = list(BLU_MPA_BH - BLU_REF_BH) )
contrast estimate
c(0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.127
SE df z.ratio p.value
0.0277 Inf 4.599 <.0001
```
Vermillion
```
> emmeans::contrast(refGrid.s, method = list(VER_MPA_SP - VER_REF_SP) )
contrast estimate
c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0328
SE df z.ratio p.value
0.0534 Inf 0.615 0.5387
Results are given on the log (not the response) scale.
> emmeans::contrast(refGrid.s, method = list(VER_MPA_BH - VER_REF_BH) )
contrast estimate
c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0767
SE df z.ratio p.value
0.0735 Inf 1.044 0.2966
```
Lingcod* (SP & BH)
```
> emmeans::contrast(refGrid.s, method = list(LING_MPA_SP - LING_REF_SP) )
contrast estimate SE
c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0929 0.036
df z.ratio p.value
Inf 2.582 0.0098
Results are given on the log (not the response) scale.
> emmeans::contrast(refGrid.s, method = list(LING_MPA_BH - LING_REF_BH) )
contrast estimate
c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0.0623
SE df z.ratio p.value
0.0281 Inf 2.221 0.0264
```
Black*
```
> emmeans::contrast(refGrid.s, method = list(BLA_MPA_SP - BLA_REF_SP) )
contrast estimate
c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0436
SE df z.ratio p.value
0.0161 Inf 2.701 0.0069
Results are given on the log (not the response) scale.
> emmeans::contrast(refGrid.s, method = list(BLA_MPA_BH - BLA_REF_BH) )
contrast estimate
c(0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.102
SE df z.ratio p.value
0.0361 Inf 2.819 0.0048
```
Brown
```
> emmeans::contrast(refGrid.s, method = list(BWN_MPA_SP - BWN_REF_SP) )
contrast estimate SE
c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0795 0.124
df z.ratio p.value
Inf 0.643 0.5202
Results are given on the log (not the response) scale.
> emmeans::contrast(refGrid.s, method = list(BWN_MPA_BH - BWN_REF_BH) )
contrast estimate
c(0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0244
SE df z.ratio p.value
0.0227 Inf 1.078 0.2810
```
China* (SP)
```
> emmeans::contrast(refGrid.s, method = list(CHN_MPA_SP - CHN_REF_SP) )
contrast estimate
c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0866
SE df z.ratio p.value
0.0287 Inf 3.015 0.0026
Results are given on the log (not the response) scale.
> emmeans::contrast(refGrid.s, method = list(CHN_MPA_BH - CHN_REF_BH) )
contrast estimate
c(0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0399
SE df z.ratio p.value
0.0379 Inf 1.053 0.2926
```
Gopher* (SP & BH)
```
> emmeans::contrast(refGrid.s, method = list(GPR_MPA_SP - GPR_REF_SP) )
contrast estimate
c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.105
SE df z.ratio p.value
0.0196 Inf 5.351 <.0001
Results are given on the log (not the response) scale.
> emmeans::contrast(refGrid.s, method = list(GPR_MPA_BH - GPR_REF_BH) )
contrast estimate
c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0.0807
SE df z.ratio p.value
0.0259 Inf 3.111 0.0019
```
Olive* (SP & BH)
```
> emmeans::contrast(refGrid.s, method = list(OLV_MPA_SP - OLV_REF_SP) )
contrast estimate
c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0935
SE df z.ratio p.value
0.0228 Inf 4.105 <.0001
Results are given on the log (not the response) scale.
> emmeans::contrast(refGrid.s, method = list(OLV_MPA_BH - OLV_REF_BH) )
contrast estimate SE
c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1.1 0.203
df z.ratio p.value
Inf -5.410 <.0001
```
Quillback
```
> emmeans::contrast(refGrid.s, method = list(QBK_MPA_SP - QBK_REF_SP) )
contrast estimate SE
c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.537 0.218
df z.ratio p.value
Inf 2.461 0.0138
Results are given on the log (not the response) scale.
> emmeans::contrast(refGrid.s, method = list(QBK_MPA_BH - QBK_REF_BH) )
contrast estimate SE
c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0.202 0.155
df z.ratio p.value
Inf 1.304 0.1924
```
Canary* (SP & BH)
```
> emmeans::contrast(refGrid.s, method = list(CNY_MPA_SP - CNY_REF_SP) )
contrast estimate
c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.165
SE df z.ratio p.value
0.0279 Inf 5.926 <.0001
Results are given on the log (not the response) scale.
> emmeans::contrast(refGrid.s, method = list(CNY_MPA_BH - CNY_REF_BH) )
contrast estimate
c(0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.238
SE df z.ratio p.value
0.0529 Inf 4.501 <.0001
```
Copper* (SP & BH)
```
> emmeans::contrast(refGrid.s, method = list(CPR_MPA_SP - CPR_REF_SP) )
contrast estimate
c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.161
SE df z.ratio p.value
0.0693 Inf 2.320 0.0203
Results are given on the log (not the response) scale.
> emmeans::contrast(refGrid.s, method = list(CPR_MPA_BH - CPR_REF_BH) )
contrast estimate
c(0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0984
SE df z.ratio p.value
0.0334 Inf 2.943 0.0032
```
Kelp Greenling* (BH)
```
> emmeans::contrast(refGrid.s, method = list(KGL_MPA_SP - KGL_REF_SP) )
contrast estimate
c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.048
SE df z.ratio p.value
0.0573 Inf 0.838 0.4019
Results are given on the log (not the response) scale.
> emmeans::contrast(refGrid.s, method = list(KGL_MPA_BH - KGL_REF_BH) )
contrast estimate
c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0.257
SE df z.ratio p.value
0.0322 Inf 7.966 <.0001
```
Rosy
```
> emmeans::contrast(refGrid.s, method = list(RSY_MPA_SP - RSY_REF_SP) )
contrast estimate
c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0742
SE df z.ratio p.value
0.0556 Inf 1.335 0.1819
Results are given on the log (not the response) scale.
> emmeans::contrast(refGrid.s, method = list(RSY_MPA_BH - RSY_REF_BH) )
contrast estimate SE df
c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, nonEst NA NA
z.ratio p.value
NA NA
```
Yellow Eye* (SP)
```
> emmeans::contrast(refGrid.s, method = list(YLE_MPA_SP - YLE_REF_SP) )
contrast estimate
c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.319
SE df z.ratio p.value
0.0574 Inf 5.547 <.0001
```
Yellow Tail* (SP)
```
> emmeans::contrast(refGrid.s, method = list(YTL_MPA_SP - YTL_REF_SP) )
contrast estimate
c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.131
SE df z.ratio p.value
0.0193 Inf 6.786 <.0001
Results are given on the log (not the response) scale.
> emmeans::contrast(refGrid.s, method = list(YTL_MPA_BH - YTL_REF_BH) )
contrast estimate
c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0488
SE df z.ratio p.value
0.0478 Inf 1.020 0.3077
```
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