Equine Research Formative

Data Analysis

eqsub <-read.table('~/Equine Summative NEW/eqsub.txt', header = TRUE, sep = "\t")
equine <-read.table('~/Equine Summative NEW/Equine.txt', header = TRUE, sep = "\t")

1. Is there a difference in compliance time between mares and geldings?

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Hypothesis

It is hypothesised there will be no significant difference in average compliance time based on the sex of the animal (mares and geldings)

Results

# Testing for normality shows to test the residuals for normality 

# Fitting a linear model
model <- lm (comp ~ sex, data = equine)

# Extract residuals
residuals <- residuals(model)

# Visual tests
hist(residuals, main = "Histogram of Residuals")

qqnorm(residuals)
qqline(residuals, col = "red")

# Formal test
shapiro.test(residuals)

    Shapiro-Wilk normality test

data:  residuals
W = 0.99738, p-value = 0.6242

# P > 0.05 therefore the residules are normally distributed

# Testing via Independent Two-Sample t-test based on normality testing

# Perform independent t-test comparing 'comp' by 'sex'
t_test_result <- t.test(comp ~ sex, data = equine)
 
# Print the result
print(t_test_result)

    Welch Two Sample t-test

data:  comp by sex
t = -2.8315, df = 494.83, p-value = 0.004821
alternative hypothesis: true difference in means between group Female and group Male is not equal to 0
95 percent confidence interval:
 -0.6105344 -0.1103336
sample estimates:
mean in group Female   mean in group Male 
            34.94452             35.30496 

# P < 0.05 therefore, there is a significant difference in compliance time between mares and geldings. This result rejects the hypothesis.

library(ggplot2)

ggplot(equine, aes(x = sex, y = comp, fill = sex)) + geom_boxplot(color = “black”) + # Keep the outline color black stat_summary(fun = mean, geom = “point”, size = 3, color = “red”, shape = 18) + # Add means labs(x = “Sex”, y = “Compliance Time”, title = “Compliance Time by Gender”) + theme_minimal() + scale_fill_manual(values = c(“Male” = “skyblue”, “Female” = “lightpink”)) # Custom colors for each sex

library(ggplot2)

ggplot(equine, aes(x = sex, y = comp, fill = sex)) + 
  geom_boxplot(color = "black") +  # Keep the outline color black
  stat_summary(fun = mean, geom = "point", size = 3, color = "red", shape = 18) +  # Add means
  labs(x = "Sex", y = "Compliance Time", title = "Compliance Time by Gender") + 
  theme_minimal() +
  scale_fill_manual(values = c("Male" = "skyblue", "Female" = "lightpink"))  # Custom colors for each sex

2. Are there significant correlations between compliance time and other variables (IRT, cortisol level and heart rate)

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Is there a significant difference between Thermographic Eye Temperature (Celcius) and Compliance Time (seconds)

Hypothesis

It is hypothesised there will be a difference between thermographic eye temperature and compliance time

Results

# Perform the Shapiro-Wilk normality test
shapiro.test(equine$irt)

    Shapiro-Wilk normality test

data:  equine$irt
W = 0.95889, p-value = 1.447e-10

shapiro.test(equine$comp)

    Shapiro-Wilk normality test

data:  equine$comp
W = 0.99692, p-value = 0.4695

# P < 0.05 therefore the data is not normally distributed

cor.test(equine$irt, equine$comp, method = "spearman")

    Spearman's rank correlation rho

data:  equine$irt and equine$comp
S = 21203514, p-value = 0.5028
alternative hypothesis: true rho is not equal to 0
sample estimates:
        rho 
-0.03008441 

# P > 0.05 therefore there is a not a significant correlation between compliance time and eye temperature. This result accepts the hypothesis.

# Add a linear regression line
library(ggplot2)
ggplot(equine, aes(x = irt, y = comp)) +
  geom_point() +  # Add points
  geom_smooth(method = "lm", se = FALSE, color = "blue") +  # Add linear regression line
  labs(title = "Scatterplot of Compliance Time vs. Thermographic Eye Temperature (IRT)",
       x = "IRT (Celcius)",
       y = "Compliance Time (seconds)")

`geom_smooth()` using formula = 'y ~ x'

Is there a significant difference between Blood Cortisol Levels (mcg/dL) and Compliance Time (seconds)

Hypothesis

It is hypothesised there will be a difference. When blood cortisol increases, the compliance time will increase.

Results

# Perform the Shapiro-Wilk normality test
shapiro.test(equine$cortisol)

    Shapiro-Wilk normality test

data:  equine$cortisol
W = 0.96362, p-value = 9.245e-10

shapiro.test(equine$comp)

    Shapiro-Wilk normality test

data:  equine$comp
W = 0.99692, p-value = 0.4695

# P < 0.05 therefore the data is not normally distributed

cor.test(equine$cortisol, equine$comp, method = "spearman")

    Spearman's rank correlation rho

data:  equine$cortisol and equine$comp
S = 21166080, p-value = 0.529
alternative hypothesis: true rho is not equal to 0
sample estimates:
        rho 
-0.02826584 

# P > 0.05 therefore there is a not a significant correlation between compliance time and blood lactate levels. This result rejects the hypothesis. 

# Add a linear regression line
library(ggplot2)
ggplot(equine, aes(x = cortisol, y = comp)) +
  geom_point() +  # Add points
  geom_smooth(method = "lm", se = FALSE, color = "blue") +  # Add linear regression line
  labs(title = "Scatterplot of Compliance Time vs. Cortisol",
       x = "Cortisol (mcg/dL)",
       y = "Compliance Time (seconds)")

`geom_smooth()` using formula = 'y ~ x'

Is there a significant difference between Heart Rate (bpm) and Compliance Time (seconds)?

Hypothesis

It is hypothesised there will be a difference. When heart rate increases, the compliance time will increase.

Results

# Testing each variable for normality 
# Perform the Shapiro-Wilk normality test
shapiro.test(equine$weight)

    Shapiro-Wilk normality test

data:  equine$weight
W = 0.94685, p-value = 2.229e-12

shapiro.test(equine$comp)

    Shapiro-Wilk normality test

data:  equine$comp
W = 0.99692, p-value = 0.4695

# P > 0.05 therefore the residules are normally distributed

# Testing significance of Pearson correlation
cor.test(equine$BPM, equine$comp)

    Pearson's product-moment correlation

data:  equine$BPM and equine$comp
t = 22.767, df = 496, p-value < 2.2e-16
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 0.6689964 0.7552703
sample estimates:
      cor 
0.7148428 

# P < 0.05 therefore there is a significant correlation between compliance time and heart rate. This result accepts the hypothesis. 

# Add a linear regression line
library(ggplot2)
ggplot(equine, aes(x = BPM, y = comp)) +
  geom_point() +  # Add points
  geom_smooth(method = "lm", se = FALSE, color = "blue") +  # Add linear regression line
  labs(title = "Scatterplot of Compliance Time vs. Heart Rate ",
       x = "Heart Rate (BPM)",
       y = "Compliance Time (seconds)")

`geom_smooth()` using formula = 'y ~ x'

3. Is there a correlation between IRT and Cortisol?

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Hypothesis

It is hypothesised there will be a correlation between IRT and cortisol. When IRT increases, cortisol will also increase.

Results

# Perform the Shapiro-Wilk normality test
shapiro.test(equine$irt)

    Shapiro-Wilk normality test

data:  equine$irt
W = 0.95889, p-value = 1.447e-10

shapiro.test(equine$cortisol)

    Shapiro-Wilk normality test

data:  equine$cortisol
W = 0.96362, p-value = 9.245e-10

# P < 0.05 therefore the data is not normally distributed 

cor.test(equine$irt, equine$cortisol, method = "spearman")

    Spearman's rank correlation rho

data:  equine$irt and equine$cortisol
S = 17878766, p-value = 0.00332
alternative hypothesis: true rho is not equal to 0
sample estimates:
      rho 
0.1314346 

# P < 0.05 therefore there is a a significant correlation between eye temperature and blood lactate levels. This result accepts the hypothesis.

# Perform a paired t-test
result <- t.test(equine$cortisol, equine$irt, paired = TRUE)

# Print the result
print(result)

    Paired t-test

data:  equine$cortisol and equine$irt
t = 59.819, df = 497, p-value < 2.2e-16
alternative hypothesis: true mean difference is not equal to 0
95 percent confidence interval:
 44.93358 47.98550
sample estimates:
mean difference 
       46.45954 

# Calculate correlation between IRT and cortisol
correlation_result <- cor(equine$irt, equine$cortisol, use = "complete.obs")
correlation_result

[1] 0.1286011

# Create a scatter plot
ggplot(equine, aes(x = irt, y = cortisol)) +
  geom_point() +
  labs(title = "Correlation between IRT and Cortisol Levels",
       x = "Thermographic Eye Temperature (Celsius)",
       y = "Blood Cortisol Levels (mcg/dl)") +
  theme_minimal() +
  geom_smooth(method = "lm", se = FALSE, color = "blue")

`geom_smooth()` using formula = 'y ~ x'

4. Does the application of the calming spray have an effect on compliance time?

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Hypothesis

# It is hypothesised there will difference. When the claming spray is applied, compliance time will decrease.

Results

#Testing for normality shows to test the residuals for normality 

# Fitting a linear model
model <- lm (comp ~ comp2, data = eqsub)

# Extract residuals
residuals <- residuals(model)

# Visual tests
hist(residuals, main = "Histogram of Residuals")

qqnorm(residuals)
qqline(residuals, col = "red")

# Formal test
shapiro.test(residuals)

    Shapiro-Wilk normality test

data:  residuals
W = 0.48102, p-value < 2.2e-16

# P < 0.05 therefore the residuals are not normally distributed

# Perform the Wilcoxon signed-rank test
wilcox_test <- wilcox.test(eqsub$comp, eqsub$comp2, paired = TRUE)

# Print the results
print(wilcox_test)

    Wilcoxon signed rank test with continuity correction

data:  eqsub$comp and eqsub$comp2
V = 124251, p-value < 2.2e-16
alternative hypothesis: true location shift is not equal to 0

# P < 0.05 therefore there is a significant difference between compliance time before the calming spray and after the application of the calming spray. This result accepts the hypothesis.