Lab 4
Izzy Simon
2024-09-26
Load Packages and Data
library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
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## filter, lag## The following objects are masked from 'package:base':
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## intersect, setdiff, setequal, unionlibrary(car)## Loading required package: carData##
## Attaching package: 'car'## The following object is masked from 'package:dplyr':
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## recodelibrary(ggplot2)
library(ggpubr)
library(rstatix)##
## Attaching package: 'rstatix'## The following object is masked from 'package:stats':
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## filterlibrary(EnvStats)##
## Attaching package: 'EnvStats'## The following object is masked from 'package:car':
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## qqPlot## The following objects are masked from 'package:stats':
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## predict, predict.lmwormSperm<-read.csv("~/Biostats 2024/Data/WormSperm.csv")
wormSperm## Sex SpermSize
## 1 hermaphrodite 10
## 2 hermaphrodite 10
## 3 hermaphrodite 10
## 4 hermaphrodite 10
## 5 hermaphrodite 10
## 6 hermaphrodite 10
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## 913 male 30blackBird<-read.csv("~/Biostats 2024/Data/BlackbirdTesto.csv")
blackBird## blackbird Antibody.production Treatment
## 1 1 105 Before
## 2 2 50 Before
## 3 3 136 Before
## 4 4 90 Before
## 5 5 122 Before
## 6 6 132 Before
## 7 7 131 Before
## 8 8 119 Before
## 9 9 145 Before
## 10 10 130 Before
## 11 11 116 Before
## 12 12 110 Before
## 13 13 138 Before
## 14 1 85 After
## 15 2 74 After
## 16 3 145 After
## 17 4 86 After
## 18 5 148 After
## 19 6 148 After
## 20 7 150 After
## 21 8 142 After
## 22 9 151 After
## 23 10 113 After
## 24 11 118 After
## 25 12 99 After
## 26 13 150 AfterblackBird2<-read.csv("~/Biostats 2024/Data/Blackbird2.csv")
blackBird2## blackbird Ant.Before Ant.After Ant.Diff
## 1 1 105 85 -20
## 2 2 50 74 24
## 3 3 136 145 9
## 4 4 90 86 -4
## 5 5 122 148 26
## 6 6 132 148 16
## 7 7 131 150 19
## 8 8 119 142 23
## 9 9 145 151 6
## 10 10 130 113 -17
## 11 11 116 118 2
## 12 12 110 99 -11
## 13 13 138 150 12carbon<-read.csv("~/Biostats 2024/Data/Carbon.csv")
carbon## Tree.Ht Treatment
## 1 325 L
## 2 257 L
## 3 303 L
## 4 315 L
## 5 380 L
## 6 153 L
## 7 263 L
## 8 242 L
## 9 206 L
## 10 344 L
## 11 258 L
## 12 368 H
## 13 390 H
## 14 379 H
## 15 260 H
## 16 404 H
## 17 318 H
## 18 352 H
## 19 359 H
## 20 216 H
## 21 222 H
## 22 283 H
## 23 332 Hstr(wormSperm)## 'data.frame': 913 obs. of 2 variables:
## $ Sex : chr "hermaphrodite" "hermaphrodite" "hermaphrodite" "hermaphrodite" ...
## $ SpermSize: int 10 10 10 10 10 10 10 10 10 10 ...str(blackBird)## 'data.frame': 26 obs. of 3 variables:
## $ blackbird : int 1 2 3 4 5 6 7 8 9 10 ...
## $ Antibody.production: int 105 50 136 90 122 132 131 119 145 130 ...
## $ Treatment : chr "Before" "Before" "Before" "Before" ...str(carbon)## 'data.frame': 23 obs. of 2 variables:
## $ Tree.Ht : int 325 257 303 315 380 153 263 242 206 344 ...
## $ Treatment: chr "L" "L" "L" "L" ...str(blackBird2)## 'data.frame': 13 obs. of 4 variables:
## $ blackbird : int 1 2 3 4 5 6 7 8 9 10 ...
## $ Ant.Before: int 105 50 136 90 122 132 131 119 145 130 ...
## $ Ant.After : int 85 74 145 86 148 148 150 142 151 113 ...
## $ Ant.Diff : int -20 24 9 -4 26 16 19 23 6 -17 ...Test Assumptions
Before<-filter(blackBird, Treatment == "Before")
Before## blackbird Antibody.production Treatment
## 1 1 105 Before
## 2 2 50 Before
## 3 3 136 Before
## 4 4 90 Before
## 5 5 122 Before
## 6 6 132 Before
## 7 7 131 Before
## 8 8 119 Before
## 9 9 145 Before
## 10 10 130 Before
## 11 11 116 Before
## 12 12 110 Before
## 13 13 138 BeforeAfter<-filter(blackBird, Treatment == "After")
After## blackbird Antibody.production Treatment
## 1 1 85 After
## 2 2 74 After
## 3 3 145 After
## 4 4 86 After
## 5 5 148 After
## 6 6 148 After
## 7 7 150 After
## 8 8 142 After
## 9 9 151 After
## 10 10 113 After
## 11 11 118 After
## 12 12 99 After
## 13 13 150 AfterDiff<-Before$Antibody.production-After$Antibody.production
Diff## [1] 20 -24 -9 4 -26 -16 -19 -23 -6 17 -2 11 -12shapiro_test(Diff)## # A tibble: 1 × 3
## variable statistic p.value
## <chr> <dbl> <dbl>
## 1 Diff 0.931 0.356wormSperm %>%
group_by(Sex) %>%
shapiro_test(SpermSize)## # A tibble: 2 × 4
## Sex variable statistic p
## <chr> <chr> <dbl> <dbl>
## 1 hermaphrodite SpermSize 0.888 4.14e-12
## 2 male SpermSize 0.951 3.15e-14ggqqplot(wormSperm, x="SpermSize", facet.by="Sex")
ggplot(wormSperm, aes(sample=SpermSize, color=Sex)) + geom_qq() + stat_qq_line()
#2.3 the worm sperm data is currently not normally distributed (p<0.05 for both)
transformer<-mutate_(wormSperm, transformed = "log10(SpermSize)")## Warning: `mutate_()` was deprecated in dplyr 0.7.0.
## ℹ Please use `mutate()` instead.
## ℹ See vignette('programming') for more help
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.transformer %>%
group_by(Sex) %>%
shapiro_test(SpermSize)## # A tibble: 2 × 4
## Sex variable statistic p
## <chr> <chr> <dbl> <dbl>
## 1 hermaphrodite SpermSize 0.888 4.14e-12
## 2 male SpermSize 0.951 3.15e-14# 2.4 the transformation did not improve the normality of the distribution because the p values stayed the same, which means that we reject the null hypothesis of normality (p>0.05)
leveneTest(wormSperm$SpermSize, group=wormSperm$Sex)## Warning in leveneTest.default(wormSperm$SpermSize, group = wormSperm$Sex):
## wormSperm$Sex coerced to factor.## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 1 120.51 < 2.2e-16 ***
## 911
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#2.6 as previously stated, the wormSperm data does not pass the normality test (p>0.05) but now we also know that the data does not pass the homogeneity of variance test (p>0.05)Non-Parametric Alternative for t-tests
wilcox.test(SpermSize~Sex, data=transformer, var.equal=FALSE)##
## Wilcoxon rank sum test with continuity correction
##
## data: SpermSize by Sex
## W = 10297, p-value < 2.2e-16
## alternative hypothesis: true location shift is not equal to 0#3.1 it seems like we can reject the null hypothesis because the p value is less than 0.05 which, according to this test, means that the medians of the spermSize for male verus hermaphroditic worms are not equal
#3.2 the variance between the sperm size for male worms versus hermaphroditic worms are not equal (W=10297;p<0.002)Permutation Tests
carbon$Tree.Ht<-as.numeric(carbon$Tree.Ht)
carbon$Tree.Ht## [1] 325 257 303 315 380 153 263 242 206 344 258 368 390 379 260 404 318 352 359
## [20] 216 222 283 332before<-filter(carbon, Treatment=="L")
before## Tree.Ht Treatment
## 1 325 L
## 2 257 L
## 3 303 L
## 4 315 L
## 5 380 L
## 6 153 L
## 7 263 L
## 8 242 L
## 9 206 L
## 10 344 L
## 11 258 Lafter<-filter(carbon, Treatment=="H")
after## Tree.Ht Treatment
## 1 368 H
## 2 390 H
## 3 379 H
## 4 260 H
## 5 404 H
## 6 318 H
## 7 352 H
## 8 359 H
## 9 216 H
## 10 222 H
## 11 283 H
## 12 332 Hdifference<-before$Tree.Ht-after$Tree.Ht## Warning in before$Tree.Ht - after$Tree.Ht: longer object length is not a
## multiple of shorter object lengthdifference## [1] -43 -133 -76 55 -24 -165 -89 -117 -10 122 -25 -7shapiro_test(difference)## # A tibble: 1 × 3
## variable statistic p.value
## <chr> <dbl> <dbl>
## 1 difference 0.969 0.901#the variables are normally distributed as the null hypothesis cannot be rejected (p=0.9). A permutation test is necessary because there is a very small sample size.
mean(before$Tree.Ht)## [1] 276.9091mean(after$Tree.Ht)## [1] 323.5833#these means are where the numbers come from in the code you gave us in 4.4
dStat<-abs(323.5833-276.9091)
dStat## [1] 46.6742set.seed(1973)
perm.carbon <- twoSamplePermutationTestLocation(carbon$Tree.Ht[carbon$Treatment == "H"], carbon$Tree.Ht[carbon$Treatment == "L"], fcn= "mean", alternative = "two.sided", (mul.minus.mu2 = 0), paired = FALSE, exact=FALSE, n.permutations = 1000, seed = 123)
#p value increases when the number of permutations decrease but does not change a lot when it is increased
perm.carbon##
## Results of Hypothesis Test
## --------------------------
##
## Null Hypothesis: mu.x-mu.y = 0
##
## Alternative Hypothesis: True mu.x-mu.y is not equal to 0
##
## Test Name: Two-Sample Permutation Test
## Based on Differences in Means
## (Based on Sampling
## Permutation Distribution
## 1000 Times)
##
## Estimated Parameter(s): mean of x = 323.5833
## mean of y = 276.9091
##
## Data: x = carbon$Tree.Ht[carbon$Treatment == "H"]
## y = carbon$Tree.Ht[carbon$Treatment == "L"]
##
## Sample Sizes: nx = 12
## ny = 11
##
## Test Statistic: |mean.x - mean.y| = 46.67424
##
## P-value: 0.104plot(perm.carbon)
perm.carbon2 <- twoSamplePermutationTestLocation(carbon$Tree.Ht[carbon$Treatment == "H"], carbon$Tree.Ht[carbon$Treatment == "L"], fcn= "median", alternative = "two.sided", (mul.minus.mu2 = 0), paired = FALSE, exact=FALSE, n.permutations = 1000, seed = 123)
perm.carbon2##
## Results of Hypothesis Test
## --------------------------
##
## Null Hypothesis: mu.x-mu.y = 0
##
## Alternative Hypothesis: True mu.x-mu.y is not equal to 0
##
## Test Name: Two-Sample Permutation Test
## Based on Differences in Medians
## (Based on Sampling
## Permutation Distribution
## 1000 Times)
##
## Estimated Parameter(s): median of x = 342
## median of y = 263
##
## Data: x = carbon$Tree.Ht[carbon$Treatment == "H"]
## y = carbon$Tree.Ht[carbon$Treatment == "L"]
##
## Sample Sizes: nx = 12
## ny = 11
##
## Test Statistic: |median.x - median.y| = 79
##
## P-value: 0.051plot(perm.carbon2)
# Army Ants
army<-read.csv("~/Biostats 2024/Data/ArmyAnts.csv")
army## treatment aggressionScore
## 1 Control 0.04
## 2 Control 0.00
## 3 Control 0.22
## 4 Control 0.10
## 5 Control 0.11
## 6 Control 0.54
## 7 Isolated 0.25
## 8 Isolated 1.00
## 9 Isolated 1.00
## 10 Isolated 0.42
## 11 Isolated 0.50
## 12 Isolated 1.00
## 13 Isolated 1.00
## 14 Isolated 1.00#shapiro test
beFore<-filter(army, treatment == "Control")
beFore## treatment aggressionScore
## 1 Control 0.04
## 2 Control 0.00
## 3 Control 0.22
## 4 Control 0.10
## 5 Control 0.11
## 6 Control 0.54aFter<-filter(army, treatment == "Isolated")
aFter## treatment aggressionScore
## 1 Isolated 0.25
## 2 Isolated 1.00
## 3 Isolated 1.00
## 4 Isolated 0.42
## 5 Isolated 0.50
## 6 Isolated 1.00
## 7 Isolated 1.00
## 8 Isolated 1.00diFFerence<-beFore$aggressionScore-aFter$aggressionScore## Warning in beFore$aggressionScore - aFter$aggressionScore: longer object length
## is not a multiple of shorter object lengthdiFFerence## [1] -0.21 -1.00 -0.78 -0.32 -0.39 -0.46 -0.96 -1.00shapiro_test(diFFerence)## # A tibble: 1 × 3
## variable statistic p.value
## <chr> <dbl> <dbl>
## 1 diFFerence 0.862 0.124#the variables are normally distributed because the null hypothesis cannot be rejected (p=0.124)
#qq plot
ggqqplot(army, x="aggressionScore", facet.by="treatment")
#histogram
ggplot(data=army, aes(x=aggressionScore)) + geom_histogram(bins=12,color="black",fill="white") + xlab("Aggression Score")
#equal variance test
leveneTest(army$aggressionScore, group=army$treatment)## Warning in leveneTest.default(army$aggressionScore, group = army$treatment):
## army$treatment coerced to factor.## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 1 0.5491 0.4729
## 12#Mann-Whitney U test
wilcox.test(aggressionScore~treatment, data=army, var.equal=FALSE)## Warning in wilcox.test.default(x = DATA[[1L]], y = DATA[[2L]], ...): cannot
## compute exact p-value with ties##
## Wilcoxon rank sum test with continuity correction
##
## data: aggressionScore by treatment
## W = 3, p-value = 0.006796
## alternative hypothesis: true location shift is not equal to 0#permutation test
beFore.mean<-mean(beFore$aggressionScore)
beFore.mean## [1] 0.1683333aFter.mean<-mean(aFter$aggressionScore)
aFter.mean## [1] 0.77125DStat<-abs(aFter.mean-beFore.mean)
DStat## [1] 0.6029167set.seed(1973)
perm.army <- twoSamplePermutationTestLocation(army$aggressionScore[army$treatment == "Control"], army$aggressionScore[army$treatment == "Isolated"], fcn= "mean", alternative = "two.sided", (mul.minus.mu2 = 0), paired = FALSE, exact=FALSE, n.permutations = 1000, seed = 123)
perm.army##
## Results of Hypothesis Test
## --------------------------
##
## Null Hypothesis: mu.x-mu.y = 0
##
## Alternative Hypothesis: True mu.x-mu.y is not equal to 0
##
## Test Name: Two-Sample Permutation Test
## Based on Differences in Means
## (Based on Sampling
## Permutation Distribution
## 1000 Times)
##
## Estimated Parameter(s): mean of x = 0.1683333
## mean of y = 0.7712500
##
## Data: x = army$aggressionScore[army$treatment == "Control"]
## y = army$aggressionScore[army$treatment == "Isolated"]
##
## Sample Sizes: nx = 6
## ny = 8
##
## Test Statistic: |mean.x - mean.y| = 0.6029167
##
## P-value: 0.006plot(perm.army)
#4.6 the results of the mann-whitney u test shows that we have evidence to reject the null hypothesis, that the medians for the control and isolated silverfish populations are not the same (w=3, p=0.0067). the results of the permutation test show something similar - the means of both variables are not the same (p=0.006)