setwd("~/Dropbox/Wall")
library (nlme)
library (MASS)
library (tidyverse)
## ── Attaching packages ────────────────────────────────── tidyverse 1.2.1 ──
## ✔ ggplot2 3.0.0 ✔ purrr 0.2.4
## ✔ tibble 1.4.2 ✔ dplyr 0.7.6
## ✔ tidyr 0.8.0 ✔ stringr 1.3.0
## ✔ readr 1.1.1 ✔ forcats 0.3.0
## Warning: package 'ggplot2' was built under R version 3.4.4
## Warning: package 'tibble' was built under R version 3.4.3
## Warning: package 'tidyr' was built under R version 3.4.3
## Warning: package 'dplyr' was built under R version 3.4.4
## Warning: package 'stringr' was built under R version 3.4.3
## Warning: package 'forcats' was built under R version 3.4.3
## ── Conflicts ───────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::collapse() masks nlme::collapse()
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ✖ dplyr::select() masks MASS::select()
#read datset
df<- read.csv ("Survial Study Rate and Mortality.csv")
str (df)
## 'data.frame': 39 obs. of 21 variables:
## $ Observation : int 1 2 3 4 5 6 7 8 9 10 ...
## $ Date : int 50818 50818 50818 52218 52218 52218 52518 52518 52518 10918 ...
## $ E3 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ E3.pH6.5 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ E3..20uM. : int 1 0 0 1 0 0 1 0 0 1 ...
## $ E3..200uM. : int 0 1 0 0 1 0 0 1 0 0 ...
## $ E3..20uM..pH.6.5 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ E3..200uM..pH.6.5 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ E3.Ca..200uM. : int 0 0 0 0 0 0 0 0 0 0 ...
## $ E3.Mg..200uM. : int 0 0 0 0 0 0 0 0 0 0 ...
## $ E3.Ca.Mg..200uM. : int 0 0 0 0 0 0 0 0 0 0 ...
## $ E3.Ca..200uM..pH.6.5 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ E3.Mg..200uM.p.H.6.5 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ E3.phosphate.buffers..200uM. : int 0 0 0 0 0 0 0 0 0 0 ...
## $ E3.carbonate.200uM. : int 0 0 0 0 0 0 0 0 0 0 ...
## $ E3.phosphate.buffers.and.carbonate..200uM.: int 0 0 0 0 0 0 0 0 0 0 ...
## $ E3.phosphate.buffers..200uM..pH.6.5 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ E3.carbonate.200uM..pH.6.5 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ E2 : int 0 0 1 0 0 1 0 0 1 0 ...
## $ Mortality : int 1 15 0 1 0 1 0 9 0 0 ...
## $ Survival.Rate.Rate : num 0.94 0 1 1 0 0.93 1 0 1 1 ...
summary (df)
## Observation Date E3 E3.pH6.5
## Min. : 1.0 Min. :10918 Min. :0 Min. :0.00000
## 1st Qu.:10.5 1st Qu.:52218 1st Qu.:0 1st Qu.:0.00000
## Median :20.0 Median :72418 Median :0 Median :0.00000
## Mean :20.0 Mean :61145 Mean :0 Mean :0.07692
## 3rd Qu.:29.5 3rd Qu.:72818 3rd Qu.:0 3rd Qu.:0.00000
## Max. :39.0 Max. :80810 Max. :0 Max. :1.00000
## E3..20uM. E3..200uM. E3..20uM..pH.6.5 E3..200uM..pH.6.5
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.0000 Median :0.0000
## Mean :0.1538 Mean :0.1538 Mean :0.1026 Mean :0.1026
## 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## E3.Ca..200uM. E3.Mg..200uM. E3.Ca.Mg..200uM. E3.Ca..200uM..pH.6.5
## Min. :0.00000 Min. :0.00000 Min. :0 Min. :0
## 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0 1st Qu.:0
## Median :0.00000 Median :0.00000 Median :0 Median :0
## Mean :0.02564 Mean :0.02564 Mean :0 Mean :0
## 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0 3rd Qu.:0
## Max. :1.00000 Max. :1.00000 Max. :0 Max. :0
## E3.Mg..200uM.p.H.6.5 E3.phosphate.buffers..200uM. E3.carbonate.200uM.
## Min. :0.00000 Min. :0.00000 Min. :0.00000
## 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.00000
## Median :0.00000 Median :0.00000 Median :0.00000
## Mean :0.02564 Mean :0.07692 Mean :0.07692
## 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.00000
## Max. :1.00000 Max. :1.00000 Max. :1.00000
## E3.phosphate.buffers.and.carbonate..200uM.
## Min. :0.00000
## 1st Qu.:0.00000
## Median :0.00000
## Mean :0.07692
## 3rd Qu.:0.00000
## Max. :1.00000
## E3.phosphate.buffers..200uM..pH.6.5 E3.carbonate.200uM..pH.6.5
## Min. :0 Min. :0
## 1st Qu.:0 1st Qu.:0
## Median :0 Median :0
## Mean :0 Mean :0
## 3rd Qu.:0 3rd Qu.:0
## Max. :0 Max. :0
## E2 Mortality Survival.Rate.Rate
## Min. :0.00000 Min. : 0.000 Min. :0.0000
## 1st Qu.:0.00000 1st Qu.: 0.000 1st Qu.:0.2850
## Median :0.00000 Median : 1.000 Median :0.9100
## Mean :0.07692 Mean : 3.436 Mean :0.6808
## 3rd Qu.:0.00000 3rd Qu.: 7.500 3rd Qu.:1.0000
## Max. :1.00000 Max. :15.000 Max. :1.0000
#build glm
model1<- glm (data= df, Survival.Rate.Rate ~ E3..200uM. + E3..20uM. +E3.Ca..200uM. +
E3.Mg..200uM. + E3.phosphate.buffers..200uM. + E2 , family =binomial)
## Warning in eval(family$initialize): non-integer #successes in a binomial
## glm!
summary (model1)
##
## Call:
## glm(formula = Survival.Rate.Rate ~ E3..200uM. + E3..20uM. + E3.Ca..200uM. +
## E3.Mg..200uM. + E3.phosphate.buffers..200uM. + E2, family = binomial,
## data = df)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.8074 -0.2502 0.1418 0.4264 0.6592
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.4162 0.5787 2.447 0.0144 *
## E3..200uM. -3.9047 1.6399 -2.381 0.0173 *
## E3..20uM. 3.1790 4.1436 0.767 0.4430
## E3.Ca..200uM. 0.8975 3.5419 0.253 0.8000
## E3.Mg..200uM. -2.4108 2.3256 -1.037 0.2999
## E3.phosphate.buffers..200uM. -2.5148 1.4535 -1.730 0.0836 .
## E2 2.3181 3.8681 0.599 0.5490
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 31.401 on 38 degrees of freedom
## Residual deviance: 11.042 on 32 degrees of freedom
## AIC: 37.348
##
## Number of Fisher Scoring iterations: 7
#step AIC to simplify the model
stepAIC(model1)
## Start: AIC=37.35
## Survival.Rate.Rate ~ E3..200uM. + E3..20uM. + E3.Ca..200uM. +
## E3.Mg..200uM. + E3.phosphate.buffers..200uM. + E2
## Warning in eval(family$initialize): non-integer #successes in a binomial
## glm!
## Warning in eval(family$initialize): non-integer #successes in a binomial
## glm!
## Warning in eval(family$initialize): non-integer #successes in a binomial
## glm!
## Warning in eval(family$initialize): non-integer #successes in a binomial
## glm!
## Warning in eval(family$initialize): non-integer #successes in a binomial
## glm!
## Warning in eval(family$initialize): non-integer #successes in a binomial
## glm!
## Df Deviance AIC
## - E3.Ca..200uM. 1 11.123 35.429
## - E2 1 11.800 36.106
## - E3.Mg..200uM. 1 12.289 36.596
## - E3..20uM. 1 12.812 37.118
## <none> 11.042 37.348
## - E3.phosphate.buffers..200uM. 1 14.608 38.914
## - E3..200uM. 1 21.980 46.286
## Warning in eval(family$initialize): non-integer #successes in a binomial
## glm!
##
## Step: AIC=35.6
## Survival.Rate.Rate ~ E3..200uM. + E3..20uM. + E3.Mg..200uM. +
## E3.phosphate.buffers..200uM. + E2
## Warning in eval(family$initialize): non-integer #successes in a binomial
## glm!
## Warning in eval(family$initialize): non-integer #successes in a binomial
## glm!
## Warning in eval(family$initialize): non-integer #successes in a binomial
## glm!
## Warning in eval(family$initialize): non-integer #successes in a binomial
## glm!
## Warning in eval(family$initialize): non-integer #successes in a binomial
## glm!
## Df Deviance AIC
## - E2 1 11.853 34.334
## - E3.Mg..200uM. 1 12.407 34.888
## - E3..20uM. 1 12.843 35.325
## <none> 11.123 35.604
## - E3.phosphate.buffers..200uM. 1 14.806 37.287
## - E3..200uM. 1 22.382 44.863
## Warning in eval(family$initialize): non-integer #successes in a binomial
## glm!
##
## Step: AIC=34.69
## Survival.Rate.Rate ~ E3..200uM. + E3..20uM. + E3.Mg..200uM. +
## E3.phosphate.buffers..200uM.
## Warning in eval(family$initialize): non-integer #successes in a binomial
## glm!
## Warning in eval(family$initialize): non-integer #successes in a binomial
## glm!
## Warning in eval(family$initialize): non-integer #successes in a binomial
## glm!
## Warning in eval(family$initialize): non-integer #successes in a binomial
## glm!
## Df Deviance AIC
## - E3.Mg..200uM. 1 13.297 34.137
## - E3..20uM. 1 13.348 34.188
## <none> 11.853 34.692
## - E3.phosphate.buffers..200uM. 1 16.012 36.851
## - E3..200uM. 1 24.314 45.154
## Warning in eval(family$initialize): non-integer #successes in a binomial
## glm!
##
## Step: AIC=35.41
## Survival.Rate.Rate ~ E3..200uM. + E3..20uM. + E3.phosphate.buffers..200uM.
##
## Call: glm(formula = Survival.Rate.Rate ~ E3..200uM. + E3..20uM. + E3.phosphate.buffers..200uM.,
## family = binomial, data = df)
##
## Coefficients:
## (Intercept) E3..200uM.
## 1.439 -3.928
## E3..20uM. E3.phosphate.buffers..200uM.
## 3.156 -2.538
##
## Degrees of Freedom: 38 Total (i.e. Null); 35 Residual
## Null Deviance: 31.4
## Residual Deviance: 13.3 AIC: 35.41
Plotting the diffrences
#pull out only the information you need
df.2<- select (df, c(1, 3:19, 21) ); head (df.2) #reduce to key factors only
## Observation E3 E3.pH6.5 E3..20uM. E3..200uM. E3..20uM..pH.6.5
## 1 1 0 0 1 0 0
## 2 2 0 0 0 1 0
## 3 3 0 0 0 0 0
## 4 4 0 0 1 0 0
## 5 5 0 0 0 1 0
## 6 6 0 0 0 0 0
## E3..200uM..pH.6.5 E3.Ca..200uM. E3.Mg..200uM. E3.Ca.Mg..200uM.
## 1 0 0 0 0
## 2 0 0 0 0
## 3 0 0 0 0
## 4 0 0 0 0
## 5 0 0 0 0
## 6 0 0 0 0
## E3.Ca..200uM..pH.6.5 E3.Mg..200uM.p.H.6.5 E3.phosphate.buffers..200uM.
## 1 0 0 0
## 2 0 0 0
## 3 0 0 0
## 4 0 0 0
## 5 0 0 0
## 6 0 0 0
## E3.carbonate.200uM. E3.phosphate.buffers.and.carbonate..200uM.
## 1 0 0
## 2 0 0
## 3 0 0
## 4 0 0
## 5 0 0
## 6 0 0
## E3.phosphate.buffers..200uM..pH.6.5 E3.carbonate.200uM..pH.6.5 E2
## 1 0 0 0
## 2 0 0 0
## 3 0 0 1
## 4 0 0 0
## 5 0 0 0
## 6 0 0 1
## Survival.Rate.Rate
## 1 0.94
## 2 0.00
## 3 1.00
## 4 1.00
## 5 0.00
## 6 0.93
df.long<- gather (df.2, key=Treatment, value = value, -Observation, -Survival.Rate.Rate) # Melt to Treatment
df.long[df.long == 0] <- NA ; df.long<-na.omit (df.long) #omit anything that is zero
#plot it (flipped axes UGHH )
ggplot (df.long, aes (x=Treatment, y=Survival.Rate.Rate, fill=Treatment)) + geom_boxplot () + coord_flip() +
theme_bw() + theme(axis.text.x = element_text(angle=45, vjust=0.5, size=10)) + theme(legend.position="none")
#consider it as an ANOVA framework
aov1<- aov (Survival.Rate.Rate ~ Treatment, data=df.long)
summary (aov1)
## Df Sum Sq Mean Sq F value Pr(>F)
## Treatment 11 3.531 0.3210 118.3 <2e-16 ***
## Residuals 22 0.060 0.0027
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
TukeyHSD(aov1) #reading this is easier at looking at only the non-significant differences is easier.
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = Survival.Rate.Rate ~ Treatment, data = df.long)
##
## $Treatment
## diff
## E3..200uM.-E2 -0.823333333
## E3..200uM..pH.6.5-E2 -0.476666667
## E3..20uM.-E2 0.013333333
## E3..20uM..pH.6.5-E2 0.023333333
## E3.Ca..200uM.-E2 -0.066666667
## E3.carbonate.200uM.-E2 -0.006666667
## E3.Mg..200uM.-E2 -0.706666667
## E3.Mg..200uM.p.H.6.5-E2 -0.556666667
## E3.pH6.5-E2 0.010000000
## E3.phosphate.buffers..200uM.-E2 -0.726666667
## E3.phosphate.buffers.and.carbonate..200uM.-E2 -0.043333333
## E3..200uM..pH.6.5-E3..200uM. 0.346666667
## E3..20uM.-E3..200uM. 0.836666667
## E3..20uM..pH.6.5-E3..200uM. 0.846666667
## E3.Ca..200uM.-E3..200uM. 0.756666667
## E3.carbonate.200uM.-E3..200uM. 0.816666667
## E3.Mg..200uM.-E3..200uM. 0.116666667
## E3.Mg..200uM.p.H.6.5-E3..200uM. 0.266666667
## E3.pH6.5-E3..200uM. 0.833333333
## E3.phosphate.buffers..200uM.-E3..200uM. 0.096666667
## E3.phosphate.buffers.and.carbonate..200uM.-E3..200uM. 0.780000000
## E3..20uM.-E3..200uM..pH.6.5 0.490000000
## E3..20uM..pH.6.5-E3..200uM..pH.6.5 0.500000000
## E3.Ca..200uM.-E3..200uM..pH.6.5 0.410000000
## E3.carbonate.200uM.-E3..200uM..pH.6.5 0.470000000
## E3.Mg..200uM.-E3..200uM..pH.6.5 -0.230000000
## E3.Mg..200uM.p.H.6.5-E3..200uM..pH.6.5 -0.080000000
## E3.pH6.5-E3..200uM..pH.6.5 0.486666667
## E3.phosphate.buffers..200uM.-E3..200uM..pH.6.5 -0.250000000
## E3.phosphate.buffers.and.carbonate..200uM.-E3..200uM..pH.6.5 0.433333333
## E3..20uM..pH.6.5-E3..20uM. 0.010000000
## E3.Ca..200uM.-E3..20uM. -0.080000000
## E3.carbonate.200uM.-E3..20uM. -0.020000000
## E3.Mg..200uM.-E3..20uM. -0.720000000
## E3.Mg..200uM.p.H.6.5-E3..20uM. -0.570000000
## E3.pH6.5-E3..20uM. -0.003333333
## E3.phosphate.buffers..200uM.-E3..20uM. -0.740000000
## E3.phosphate.buffers.and.carbonate..200uM.-E3..20uM. -0.056666667
## E3.Ca..200uM.-E3..20uM..pH.6.5 -0.090000000
## E3.carbonate.200uM.-E3..20uM..pH.6.5 -0.030000000
## E3.Mg..200uM.-E3..20uM..pH.6.5 -0.730000000
## E3.Mg..200uM.p.H.6.5-E3..20uM..pH.6.5 -0.580000000
## E3.pH6.5-E3..20uM..pH.6.5 -0.013333333
## E3.phosphate.buffers..200uM.-E3..20uM..pH.6.5 -0.750000000
## E3.phosphate.buffers.and.carbonate..200uM.-E3..20uM..pH.6.5 -0.066666667
## E3.carbonate.200uM.-E3.Ca..200uM. 0.060000000
## E3.Mg..200uM.-E3.Ca..200uM. -0.640000000
## E3.Mg..200uM.p.H.6.5-E3.Ca..200uM. -0.490000000
## E3.pH6.5-E3.Ca..200uM. 0.076666667
## E3.phosphate.buffers..200uM.-E3.Ca..200uM. -0.660000000
## E3.phosphate.buffers.and.carbonate..200uM.-E3.Ca..200uM. 0.023333333
## E3.Mg..200uM.-E3.carbonate.200uM. -0.700000000
## E3.Mg..200uM.p.H.6.5-E3.carbonate.200uM. -0.550000000
## E3.pH6.5-E3.carbonate.200uM. 0.016666667
## E3.phosphate.buffers..200uM.-E3.carbonate.200uM. -0.720000000
## E3.phosphate.buffers.and.carbonate..200uM.-E3.carbonate.200uM. -0.036666667
## E3.Mg..200uM.p.H.6.5-E3.Mg..200uM. 0.150000000
## E3.pH6.5-E3.Mg..200uM. 0.716666667
## E3.phosphate.buffers..200uM.-E3.Mg..200uM. -0.020000000
## E3.phosphate.buffers.and.carbonate..200uM.-E3.Mg..200uM. 0.663333333
## E3.pH6.5-E3.Mg..200uM.p.H.6.5 0.566666667
## E3.phosphate.buffers..200uM.-E3.Mg..200uM.p.H.6.5 -0.170000000
## E3.phosphate.buffers.and.carbonate..200uM.-E3.Mg..200uM.p.H.6.5 0.513333333
## E3.phosphate.buffers..200uM.-E3.pH6.5 -0.736666667
## E3.phosphate.buffers.and.carbonate..200uM.-E3.pH6.5 -0.053333333
## E3.phosphate.buffers.and.carbonate..200uM.-E3.phosphate.buffers..200uM. 0.683333333
## lwr
## E3..200uM.-E2 -0.97800907
## E3..200uM..pH.6.5-E2 -0.63134241
## E3..20uM.-E2 -0.12061979
## E3..20uM..pH.6.5-E2 -0.12135257
## E3.Ca..200uM.-E2 -0.28541120
## E3.carbonate.200uM.-E2 -0.16134241
## E3.Mg..200uM.-E2 -0.92541120
## E3.Mg..200uM.p.H.6.5-E2 -0.77541120
## E3.pH6.5-E2 -0.14467574
## E3.phosphate.buffers..200uM.-E2 -0.88134241
## E3.phosphate.buffers.and.carbonate..200uM.-E2 -0.19800907
## E3..200uM..pH.6.5-E3..200uM. 0.19199093
## E3..20uM.-E3..200uM. 0.70271355
## E3..20uM..pH.6.5-E3..200uM. 0.70198076
## E3.Ca..200uM.-E3..200uM. 0.53792214
## E3.carbonate.200uM.-E3..200uM. 0.66199093
## E3.Mg..200uM.-E3..200uM. -0.10207786
## E3.Mg..200uM.p.H.6.5-E3..200uM. 0.04792214
## E3.pH6.5-E3..200uM. 0.67865759
## E3.phosphate.buffers..200uM.-E3..200uM. -0.05800907
## E3.phosphate.buffers.and.carbonate..200uM.-E3..200uM. 0.62532426
## E3..20uM.-E3..200uM..pH.6.5 0.35604688
## E3..20uM..pH.6.5-E3..200uM..pH.6.5 0.35531409
## E3.Ca..200uM.-E3..200uM..pH.6.5 0.19125547
## E3.carbonate.200uM.-E3..200uM..pH.6.5 0.31532426
## E3.Mg..200uM.-E3..200uM..pH.6.5 -0.44874453
## E3.Mg..200uM.p.H.6.5-E3..200uM..pH.6.5 -0.29874453
## E3.pH6.5-E3..200uM..pH.6.5 0.33199093
## E3.phosphate.buffers..200uM.-E3..200uM..pH.6.5 -0.40467574
## E3.phosphate.buffers.and.carbonate..200uM.-E3..200uM..pH.6.5 0.27865759
## E3..20uM..pH.6.5-E3..20uM. -0.11228191
## E3.Ca..200uM.-E3..20uM. -0.28461677
## E3.carbonate.200uM.-E3..20uM. -0.15395312
## E3.Mg..200uM.-E3..20uM. -0.92461677
## E3.Mg..200uM.p.H.6.5-E3..20uM. -0.77461677
## E3.pH6.5-E3..20uM. -0.13728645
## E3.phosphate.buffers..200uM.-E3..20uM. -0.87395312
## E3.phosphate.buffers.and.carbonate..200uM.-E3..20uM. -0.19061979
## E3.Ca..200uM.-E3..20uM..pH.6.5 -0.30179848
## E3.carbonate.200uM.-E3..20uM..pH.6.5 -0.17468591
## E3.Mg..200uM.-E3..20uM..pH.6.5 -0.94179848
## E3.Mg..200uM.p.H.6.5-E3..20uM..pH.6.5 -0.79179848
## E3.pH6.5-E3..20uM..pH.6.5 -0.15801924
## E3.phosphate.buffers..200uM.-E3..20uM..pH.6.5 -0.89468591
## E3.phosphate.buffers.and.carbonate..200uM.-E3..20uM..pH.6.5 -0.21135257
## E3.carbonate.200uM.-E3.Ca..200uM. -0.15874453
## E3.Mg..200uM.-E3.Ca..200uM. -0.90790624
## E3.Mg..200uM.p.H.6.5-E3.Ca..200uM. -0.75790624
## E3.pH6.5-E3.Ca..200uM. -0.14207786
## E3.phosphate.buffers..200uM.-E3.Ca..200uM. -0.87874453
## E3.phosphate.buffers.and.carbonate..200uM.-E3.Ca..200uM. -0.19541120
## E3.Mg..200uM.-E3.carbonate.200uM. -0.91874453
## E3.Mg..200uM.p.H.6.5-E3.carbonate.200uM. -0.76874453
## E3.pH6.5-E3.carbonate.200uM. -0.13800907
## E3.phosphate.buffers..200uM.-E3.carbonate.200uM. -0.87467574
## E3.phosphate.buffers.and.carbonate..200uM.-E3.carbonate.200uM. -0.19134241
## E3.Mg..200uM.p.H.6.5-E3.Mg..200uM. -0.11790624
## E3.pH6.5-E3.Mg..200uM. 0.49792214
## E3.phosphate.buffers..200uM.-E3.Mg..200uM. -0.23874453
## E3.phosphate.buffers.and.carbonate..200uM.-E3.Mg..200uM. 0.44458880
## E3.pH6.5-E3.Mg..200uM.p.H.6.5 0.34792214
## E3.phosphate.buffers..200uM.-E3.Mg..200uM.p.H.6.5 -0.38874453
## E3.phosphate.buffers.and.carbonate..200uM.-E3.Mg..200uM.p.H.6.5 0.29458880
## E3.phosphate.buffers..200uM.-E3.pH6.5 -0.89134241
## E3.phosphate.buffers.and.carbonate..200uM.-E3.pH6.5 -0.20800907
## E3.phosphate.buffers.and.carbonate..200uM.-E3.phosphate.buffers..200uM. 0.52865759
## upr
## E3..200uM.-E2 -0.66865759
## E3..200uM..pH.6.5-E2 -0.32199093
## E3..20uM.-E2 0.14728645
## E3..20uM..pH.6.5-E2 0.16801924
## E3.Ca..200uM.-E2 0.15207786
## E3.carbonate.200uM.-E2 0.14800907
## E3.Mg..200uM.-E2 -0.48792214
## E3.Mg..200uM.p.H.6.5-E2 -0.33792214
## E3.pH6.5-E2 0.16467574
## E3.phosphate.buffers..200uM.-E2 -0.57199093
## E3.phosphate.buffers.and.carbonate..200uM.-E2 0.11134241
## E3..200uM..pH.6.5-E3..200uM. 0.50134241
## E3..20uM.-E3..200uM. 0.97061979
## E3..20uM..pH.6.5-E3..200uM. 0.99135257
## E3.Ca..200uM.-E3..200uM. 0.97541120
## E3.carbonate.200uM.-E3..200uM. 0.97134241
## E3.Mg..200uM.-E3..200uM. 0.33541120
## E3.Mg..200uM.p.H.6.5-E3..200uM. 0.48541120
## E3.pH6.5-E3..200uM. 0.98800907
## E3.phosphate.buffers..200uM.-E3..200uM. 0.25134241
## E3.phosphate.buffers.and.carbonate..200uM.-E3..200uM. 0.93467574
## E3..20uM.-E3..200uM..pH.6.5 0.62395312
## E3..20uM..pH.6.5-E3..200uM..pH.6.5 0.64468591
## E3.Ca..200uM.-E3..200uM..pH.6.5 0.62874453
## E3.carbonate.200uM.-E3..200uM..pH.6.5 0.62467574
## E3.Mg..200uM.-E3..200uM..pH.6.5 -0.01125547
## E3.Mg..200uM.p.H.6.5-E3..200uM..pH.6.5 0.13874453
## E3.pH6.5-E3..200uM..pH.6.5 0.64134241
## E3.phosphate.buffers..200uM.-E3..200uM..pH.6.5 -0.09532426
## E3.phosphate.buffers.and.carbonate..200uM.-E3..200uM..pH.6.5 0.58800907
## E3..20uM..pH.6.5-E3..20uM. 0.13228191
## E3.Ca..200uM.-E3..20uM. 0.12461677
## E3.carbonate.200uM.-E3..20uM. 0.11395312
## E3.Mg..200uM.-E3..20uM. -0.51538323
## E3.Mg..200uM.p.H.6.5-E3..20uM. -0.36538323
## E3.pH6.5-E3..20uM. 0.13061979
## E3.phosphate.buffers..200uM.-E3..20uM. -0.60604688
## E3.phosphate.buffers.and.carbonate..200uM.-E3..20uM. 0.07728645
## E3.Ca..200uM.-E3..20uM..pH.6.5 0.12179848
## E3.carbonate.200uM.-E3..20uM..pH.6.5 0.11468591
## E3.Mg..200uM.-E3..20uM..pH.6.5 -0.51820152
## E3.Mg..200uM.p.H.6.5-E3..20uM..pH.6.5 -0.36820152
## E3.pH6.5-E3..20uM..pH.6.5 0.13135257
## E3.phosphate.buffers..200uM.-E3..20uM..pH.6.5 -0.60531409
## E3.phosphate.buffers.and.carbonate..200uM.-E3..20uM..pH.6.5 0.07801924
## E3.carbonate.200uM.-E3.Ca..200uM. 0.27874453
## E3.Mg..200uM.-E3.Ca..200uM. -0.37209376
## E3.Mg..200uM.p.H.6.5-E3.Ca..200uM. -0.22209376
## E3.pH6.5-E3.Ca..200uM. 0.29541120
## E3.phosphate.buffers..200uM.-E3.Ca..200uM. -0.44125547
## E3.phosphate.buffers.and.carbonate..200uM.-E3.Ca..200uM. 0.24207786
## E3.Mg..200uM.-E3.carbonate.200uM. -0.48125547
## E3.Mg..200uM.p.H.6.5-E3.carbonate.200uM. -0.33125547
## E3.pH6.5-E3.carbonate.200uM. 0.17134241
## E3.phosphate.buffers..200uM.-E3.carbonate.200uM. -0.56532426
## E3.phosphate.buffers.and.carbonate..200uM.-E3.carbonate.200uM. 0.11800907
## E3.Mg..200uM.p.H.6.5-E3.Mg..200uM. 0.41790624
## E3.pH6.5-E3.Mg..200uM. 0.93541120
## E3.phosphate.buffers..200uM.-E3.Mg..200uM. 0.19874453
## E3.phosphate.buffers.and.carbonate..200uM.-E3.Mg..200uM. 0.88207786
## E3.pH6.5-E3.Mg..200uM.p.H.6.5 0.78541120
## E3.phosphate.buffers..200uM.-E3.Mg..200uM.p.H.6.5 0.04874453
## E3.phosphate.buffers.and.carbonate..200uM.-E3.Mg..200uM.p.H.6.5 0.73207786
## E3.phosphate.buffers..200uM.-E3.pH6.5 -0.58199093
## E3.phosphate.buffers.and.carbonate..200uM.-E3.pH6.5 0.10134241
## E3.phosphate.buffers.and.carbonate..200uM.-E3.phosphate.buffers..200uM. 0.83800907
## p adj
## E3..200uM.-E2 0.0000000
## E3..200uM..pH.6.5-E2 0.0000000
## E3..20uM.-E2 0.9999998
## E3..20uM..pH.6.5-E2 0.9999716
## E3.Ca..200uM.-E2 0.9908970
## E3.carbonate.200uM.-E2 1.0000000
## E3.Mg..200uM.-E2 0.0000000
## E3.Mg..200uM.p.H.6.5-E2 0.0000003
## E3.pH6.5-E2 1.0000000
## E3.phosphate.buffers..200uM.-E2 0.0000000
## E3.phosphate.buffers.and.carbonate..200uM.-E2 0.9953726
## E3..200uM..pH.6.5-E3..200uM. 0.0000024
## E3..20uM.-E3..200uM. 0.0000000
## E3..20uM..pH.6.5-E3..200uM. 0.0000000
## E3.Ca..200uM.-E3..200uM. 0.0000000
## E3.carbonate.200uM.-E3..200uM. 0.0000000
## E3.Mg..200uM.-E3..200uM. 0.7246083
## E3.Mg..200uM.p.H.6.5-E3..200uM. 0.0087291
## E3.pH6.5-E3..200uM. 0.0000000
## E3.phosphate.buffers..200uM.-E3..200uM. 0.5203161
## E3.phosphate.buffers.and.carbonate..200uM.-E3..200uM. 0.0000000
## E3..20uM.-E3..200uM..pH.6.5 0.0000000
## E3..20uM..pH.6.5-E3..200uM..pH.6.5 0.0000000
## E3.Ca..200uM.-E3..200uM..pH.6.5 0.0000395
## E3.carbonate.200uM.-E3..200uM..pH.6.5 0.0000000
## E3.Mg..200uM.-E3..200uM..pH.6.5 0.0336265
## E3.Mg..200uM.p.H.6.5-E3..200uM..pH.6.5 0.9653790
## E3.pH6.5-E3..200uM..pH.6.5 0.0000000
## E3.phosphate.buffers..200uM.-E3..200uM..pH.6.5 0.0003209
## E3.phosphate.buffers.and.carbonate..200uM.-E3..200uM..pH.6.5 0.0000000
## E3..20uM..pH.6.5-E3..20uM. 1.0000000
## E3.Ca..200uM.-E3..20uM. 0.9462790
## E3.carbonate.200uM.-E3..20uM. 0.9999869
## E3.Mg..200uM.-E3..20uM. 0.0000000
## E3.Mg..200uM.p.H.6.5-E3..20uM. 0.0000001
## E3.pH6.5-E3..20uM. 1.0000000
## E3.phosphate.buffers..200uM.-E3..20uM. 0.0000000
## E3.phosphate.buffers.and.carbonate..200uM.-E3..20uM. 0.9131338
## E3.Ca..200uM.-E3..20uM..pH.6.5 0.9108437
## E3.carbonate.200uM.-E3..20uM..pH.6.5 0.9996764
## E3.Mg..200uM.-E3..20uM..pH.6.5 0.0000000
## E3.Mg..200uM.p.H.6.5-E3..20uM..pH.6.5 0.0000001
## E3.pH6.5-E3..20uM..pH.6.5 0.9999999
## E3.phosphate.buffers..200uM.-E3..20uM..pH.6.5 0.0000000
## E3.phosphate.buffers.and.carbonate..200uM.-E3..20uM..pH.6.5 0.8607660
## E3.carbonate.200uM.-E3.Ca..200uM. 0.9961163
## E3.Mg..200uM.-E3.Ca..200uM. 0.0000008
## E3.Mg..200uM.p.H.6.5-E3.Ca..200uM. 0.0000568
## E3.pH6.5-E3.Ca..200uM. 0.9742147
## E3.phosphate.buffers..200uM.-E3.Ca..200uM. 0.0000000
## E3.phosphate.buffers.and.carbonate..200uM.-E3.Ca..200uM. 0.9999996
## E3.Mg..200uM.-E3.carbonate.200uM. 0.0000000
## E3.Mg..200uM.p.H.6.5-E3.carbonate.200uM. 0.0000003
## E3.pH6.5-E3.carbonate.200uM. 0.9999995
## E3.phosphate.buffers..200uM.-E3.carbonate.200uM. 0.0000000
## E3.phosphate.buffers.and.carbonate..200uM.-E3.carbonate.200uM. 0.9988984
## E3.Mg..200uM.p.H.6.5-E3.Mg..200uM. 0.6668388
## E3.pH6.5-E3.Mg..200uM. 0.0000000
## E3.phosphate.buffers..200uM.-E3.Mg..200uM. 0.9999999
## E3.phosphate.buffers.and.carbonate..200uM.-E3.Mg..200uM. 0.0000000
## E3.pH6.5-E3.Mg..200uM.p.H.6.5 0.0000002
## E3.phosphate.buffers..200uM.-E3.Mg..200uM.p.H.6.5 0.2345517
## E3.phosphate.buffers.and.carbonate..200uM.-E3.Mg..200uM.p.H.6.5 0.0000011
## E3.phosphate.buffers..200uM.-E3.pH6.5 0.0000000
## E3.phosphate.buffers.and.carbonate..200uM.-E3.pH6.5 0.9770382
## E3.phosphate.buffers.and.carbonate..200uM.-E3.phosphate.buffers..200uM. 0.0000000