This exercise involves investigating the water holding capacity of soil in three different woodland areas by analyzing soil samples. The data provided includes the water holding capacity (in milliliters per gram) for each sample from Woodland A, B, and C. The task is to carry out a suitable analysis, such as calculating basic statistics (mean, standard deviation) and performing a one-way ANOVA to determine if there are significant differences between the three areas. The analysis will require making assumptions about the normality of data distribution, homogeneity of variance, and the independence of samples. The goal is to conclude whether the differences in water holding capacity between the woodland areas are statistically significant.

Experimental Design Exercise in Julia

A study was undertaken to investigate the water holding capacity of the soil in three different areas of woodland. In each area, a number of soil samples were collected randomly and sent to the same laboratory for analysis. The following table gives the water holding capacity (in millilitres per gram) of the soil samples collected in each area.

Woodland A Woodland B Woodland C
72 35 54
51 33 62
38 29 88
87 50 65
77 44 80
65 17 53
70 47
66 58
64
74

Carry out a suitable analysis of these data, stating the assumptions you have made and explaining what you conclude as a result of your analysis.

Solution

Let’s start by organizing the data in Julia and then carry out the analysis.

Step 1: Organize Data

# Define the data for each woodland area
woodland_a = [72, 51, 38, 87, 77, 65, 70, 66, 64, 74]
woodland_b = [35, 33, 29, 50, 44, 17, 47, 58]
woodland_c = [54, 62, 88, 65, 80, 53]

# Print the data for verification
println("Woodland A: ", woodland_a)
println("Woodland B: ", woodland_b)
println("Woodland C: ", woodland_c)

Step 2: Basic Statistics

Next, we will calculate basic statistics such as the mean and standard deviation for each woodland area.

using Statistics

# Calculate mean and standard deviation
mean_a = mean(woodland_a)
mean_b = mean(woodland_b)
mean_c = mean(woodland_c)

std_a = std(woodland_a)
std_b = std(woodland_b)
std_c = std(woodland_c)

# Print the results
println("Woodland A - Mean: ", mean_a, " Std Dev: ", std_a)
println("Woodland B - Mean: ", mean_b, " Std Dev: ", std_b)
println("Woodland C - Mean: ", mean_c, " Std Dev: ", std_c)

Step 3: Statistical Analysis

Let’s perform a one-way ANOVA to determine if there are statistically significant differences between the mean water holding capacities of the soil samples from the three different woodland areas.

using HypothesisTests

# Combine data into a single array and create a corresponding group array
data = vcat(woodland_a, woodland_b, woodland_c)
group = repeat(["A", "B", "C"], [length(woodland_a), length(woodland_b), length(woodland_c)])

# Perform ANOVA
anova_result = fit(OneWayANOVA, data, group)

# Print the results
println(anova_result)

Step 4: Conclusion

Based on the ANOVA results, we will determine if there are significant differences in the water holding capacities.

p_value = pvalue(anova_result)
println("P-Value: ", p_value)

if p_value < 0.05
    println("There is a significant difference in the water holding capacities between the woodland areas.")
else
    println("There is no significant difference in the water holding capacities between the woodland areas.")
end

Assumptions

  1. The data is normally distributed within each woodland area.
  2. The variance of water holding capacity is equal across woodland areas (homogeneity of variance).
  3. The samples are randomly collected and independent of each other.

Conclusion

If the p-value from the ANOVA test is less than 0.05, we reject the null hypothesis and conclude that there is a significant difference in the water holding capacities between the woodland areas. If the p-value is greater than 0.05, we fail to reject the null hypothesis and conclude that there is no significant difference in the water holding capacities.

This should give you a good starting point for analyzing the water holding capacity data in Julia.