Here’s the data: Units u:	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
Coder A	*	*	*	*	*	3	4	1	2	1	1	3	3	*	3
Coder B	1	*	2	1	3	3	4	3	*	*	*	*	*	*	*
Coder C	*	*	2	1	3	4	4	*	2	1	1	3

Thank you for providing the data. From this, we need to derive the values for \( V \), \( o_{vv'} \), \( n \), \( n_v \), and \( \delta_{\text{metric}}(v, v') \). Here's the step-by-step breakdown of the information required:

1. **Number of elements (\( V \))**: This is the total number of units, which is 15.

2. **Observed metric values (\( o_{vv'} \))**: These are the agreement or disagreement scores between each pair of units for the given coders. We'll need to process the data to generate these values.

3. **Total number of observations (\( n \))**: This is the number of coders, which is 3.

4. **Number of occurrences (\( n_v \))**: This is the count of valid (non-*) observations for each unit.

5. **Metric distances (\( \delta_{\text{metric}}(v, v') \))**: This can be derived based on the agreement or disagreement between the coders for each pair of units.

Let's start by organizing the provided data into a more manageable format:

| Unit   | Coder A | Coder B | Coder C |
|--------|---------|---------|---------|
| 1      | *       | 1       | *       |
| 2      | *       | *       | *       |
| 3      | *       | 2       | 2       |
| 4      | *       | 1       | 1       |
| 5      | *       | 3       | 3       |
| 6      | 3       | 3       | 4       |
| 7      | 4       | 4       | 4       |
| 8      | 1       | 3       | *       |
| 9      | 2       | *       | 2       |
| 10     | 1       | *       | 1       |
| 11     | 1       | *       | 1       |
| 12     | 3       | *       | 3       |
| 13     | 3       | *       | *       |
| 14     | *       | *       | *       |
| 15     | 3       | *       | *       |

To proceed, we need to compute:

1. The number of valid observations (\( n_v \)) for each unit.
2. The agreement metric values (\( o_{vv'} \)) based on coder agreements.
3. The metric distances (\( \delta_{\text{metric}}(v, v') \)) which can be defined as 1 if coders agree and 0 otherwise.

Let's begin with computing \( n_v \) for each unit.

\[
n_v = \text{number of non-* values for each unit}
\]

Next, we need to construct the observed agreement matrix \( o_{vv'} \).

Here's a simplified way to compute these matrices:

1. Compute \( n_v \):

| Unit   | \( n_v \) |
|--------|-----------|
| 1      | 1         |
| 2      | 0         |
| 3      | 2         |
| 4      | 2         |
| 5      | 2         |
| 6      | 3         |
| 7      | 3         |
| 8      | 2         |
| 9      | 2         |
| 10     | 2         |
| 11     | 2         |
| 12     | 2         |
| 13     | 1         |
| 14     | 0         |
| 15     | 1         |

2. Construct the \( o_{vv'} \) matrix by checking coder agreements:

For simplicity, let's consider the Krippendorff's alpha metric with a simple agreement (1 if coders agree, 0 otherwise).

Using these values, we can then substitute into the equation to compute \(\alpha_{\text{metric}}\).

Let's now process these steps to compute the desired metric values.

Would you like me to proceed with these calculations?

Learn how to compute agreement metrics using Krippendorff's alpha with a detailed step-by-step breakdown. This problem involves analyzing agreement between coders based on given data, focusing on non-* values and constructing observed agreement matrices. Suitable for advanced learners and researchers.

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