Correlation Analysis using Julia

class: center, middle, inverse, title-slide

.title[
# Correlation Analysis using Julia
]
.subtitle[
## Julia Workshop
]

---

## Correlation Analysis using Julia.

Here we'll explore how to calculate correlation coefficients, visualize correlations, and interpret the results. Here's a step-by-step tutorial to get you started.

### Step 1: Install Julia and Packages
First, you'll need to have Julia installed on your machine. You can download it from the [official Julia website](https://julialang.org/downloads/).

Next, let's install some essential packages for data manipulation and visualization:

```julia
using Pkg
Pkg.add("DataFrames")
Pkg.add("CSV")
Pkg.add("Plots")
Pkg.add("Statistics")
```

---

### Step 2: Load the Data
For this tutorial, we'll use a sample CSV file containing some data. Let's load the data into a DataFrame:

```julia
using DataFrames
using CSV

# Load the data
data = CSV.read("path_to_your_data.csv", DataFrame)
```

---

### Step 3: Calculate Correlation Coefficient
The correlation coefficient measures the strength and direction of the linear relationship between two variables. We'll use the `cor` function from the `Statistics` package:

```julia
using Statistics

# Calculate the correlation coefficient
x = data[:, :column1]
y = data[:, :column2]
correlation_coefficient = cor(x, y)
println("Correlation Coefficient: ", correlation_coefficient)
```
---

### Step 4: Visualize Correlation
Let's visualize the correlation using a scatter plot:

```julia
using Plots

# Create scatter plot
scatter(x, y, title="Scatter Plot", xlabel="Column 1", ylabel="Column 2", legend=false)

# Save the plot
savefig("scatter_plot.png")
```

---

### Step 5: Interpret the Results
The correlation coefficient ranges from -1 to 1:
- **1** indicates a perfect positive correlation.
- **-1** indicates a perfect negative correlation.
- **0** indicates no correlation.

Values closer to 1 or -1 signify a stronger correlation, while values closer to 0 signify a weaker correlation.

---

Here's a quick guide to interpreting correlation coefficients:
- **0.7 to 1.0** (or **-0.7 to -1.0**): Strong positive (or negative) correlation
- **0.4 to 0.69** (or **-0.4 to -0.69**): Moderate positive (or negative) correlation
- **0.1 to 0.39** (or **-0.1 to -0.39**): Weak positive (or negative) correlation
- **0.0 to 0.09** (or **-0.0 to -0.09**): No correlation

---

Let's extend our correlation analysis tutorial to include the Spearman and Kendall correlation coefficients.

---

### Spearman Correlation

The Spearman correlation measures the rank correlation between two variables. Here's how you can compute it:

1. **Install the necessary package:**

```julia
using Pkg
Pkg.add("StatsBase")
```

---

2. **Load the data and compute the Spearman correlation:**

```julia
using DataFrames
using CSV
using StatsBase

# Load the data
data = CSV.read("path_to_your_data.csv", DataFrame)

# Extract the columns
x = data[:, :column1]
y = data[:, :column2]

# Compute the Spearman correlation
spearman_correlation = cor(x, y, method=:spearman)
println("Spearman Correlation: ", spearman_correlation)
```

---

### Kendall Correlation

The Kendall correlation measures the ordinal association between two variables. Here's how you can compute it:

1. **Load the necessary package:**

```julia
using Pkg
Pkg.add("HypothesisTests")
```

---

2. **Load the data and compute the Kendall correlation:**

```julia
using DataFrames
using CSV
using HypothesisTests

# Load the data
data = CSV.read("path_to_your_data.csv", DataFrame)

# Extract the columns
x = data[:, :column1]
y = data[:, :column2]

# Compute the Kendall correlation
kendall_correlation = cor(x, y, method=:kendall)
println("Kendall Correlation: ", kendall_correlation)
```

---

### Interpreting the Results

Both Spearman and Kendall correlation coefficients range from -1 to 1:
- **1** indicates a perfect positive correlation.
- **-1** indicates a perfect negative correlation.
- **0** indicates no correlation.

Values closer to 1 or -1 signify a stronger correlation, while values closer to 0 signify a weaker correlation.

- **Spearman correlation** is useful for data that is not normally distributed or has outliers.
- **Kendall correlation** is useful for measuring ordinal associations and is robust against non-linear relationships.

---

### Complete Example

Here's the complete code in one place for easy reference:

```julia
using Pkg
Pkg.add("DataFrames")
Pkg.add("CSV")
Pkg.add("Plots")
Pkg.add("Statistics")

using DataFrames
using CSV
using Plots
using Statistics

# Load the data
data = CSV.read("path_to_your_data.csv", DataFrame)

# Calculate the correlation coefficient
x = data[:, :column1]
y = data[:, :column2]
correlation_coefficient = cor(x, y)
println("Correlation Coefficient: ", correlation_coefficient)

# Create scatter plot
scatter(x, y, title="Scatter Plot", xlabel="Column 1", ylabel="Column 2", legend=false)

# Save the plot
savefig("scatter_plot.png")
```

---

### Complete Example

Here's the complete code for both Spearman and Kendall correlation calculations:

```julia
using Pkg
Pkg.add("DataFrames")
Pkg.add("CSV")
Pkg.add("Plots")
Pkg.add("Statistics")
Pkg.add("StatsBase")
Pkg.add("HypothesisTests")

using DataFrames
using CSV
using StatsBase
using HypothesisTests

# Load the data
data = CSV.read("path_to_your_data.csv", DataFrame)

# Extract the columns
x = data[:, :column1]
y = data[:, :column2]

# Compute the Spearman correlation
spearman_correlation = cor(x, y, method=:spearman)
println("Spearman Correlation: ", spearman_correlation)

# Compute the Kendall correlation
kendall_correlation = cor(x, y, method=:kendall)
println("Kendall Correlation: ", kendall_correlation)
```