Question 1178478
Absolutely! Let's break down how to calculate accuracy with percentages and then apply it to your confusion matrices and the skewed population scenario.

**Understanding Accuracy and Confusion Matrices**

* **Accuracy:** The overall correctness of a model. It's calculated as (True Positives + True Negatives) / Total Predictions.
* **Confusion Matrix:** A table that visualizes the performance of a classification model. It typically looks like this:

    ```
    |                | Predicted Positive | Predicted Negative |
    |----------------|--------------------|--------------------|
    | Actual Positive | True Positive (TP) | False Negative (FN) |
    | Actual Negative | False Positive (FP) | True Negative (TN) |
    ```

**Calculating Accuracy from a Confusion Matrix**

1.  **Sum the Diagonals:** Add the True Positives (TP) and True Negatives (TN).
2.  **Sum All Cells:** Add all the values in the matrix (TP + FP + FN + TN). This is the total number of predictions.
3.  **Divide:** Divide the sum of the diagonals by the sum of all cells.

**Applying It to Your Models**

* **Model A:**
    * Confusion Matrix:
        ```
        [500 200]
        [0   300]
        ```
    * TP = 500, TN = 300, FP = 200, FN = 0
    * Accuracy = (500 + 300) / (500 + 200 + 0 + 300) = 800 / 1000 = 0.8 or 80%

* **Model B:**
    * Confusion Matrix:
        ```
        [300 0]
        [200 500]
        ```
    * TP = 300, TN = 500, FP = 0, FN = 200
    * Accuracy = (300 + 500) / (300 + 0 + 200 + 500) = 800 / 1000 = 0.8 or 80%

**The Unbalanced Population (64% and 96%)**

You've mentioned that the accuracies change to 64% and 96% on the "true unbalanced population." This means the original confusion matrices, while based on a balanced dataset, are being evaluated against a new dataset that is unbalanced.

**The Highly Skewed Population (5% Positive, 95% Negative)**

Now, let's calculate the accuracies for the even more skewed population.

1.  **Assume a Total Population:** Since you have a 1,000 training population, for simplicity, let's assume we are still working with a population of 1000.
2.  **Calculate Positive and Negative Counts:**
    * Positive: 1000 * 0.05 = 50
    * Negative: 1000 * 0.95 = 950
3.  **Adjust the Confusion Matrices Based on the Proportions:**
    * Since the original confusion matrix totals are 1000, we will keep the ratios of the True positives, false positives, false negatives and true negatives.
    * Model A:
        * TP: 500/700 * 50 = 35.71, round to 36.
        * FP: 200/500 * 950 = 380.
        * FN: 0.
        * TN: 300/500 * 950 = 570.
    * Model B:
        * TP: 300/500 * 50 = 30.
        * FP: 0
        * FN: 200/500 * 50 = 20.
        * TN: 500/500 * 950 = 950.
4.  **Calculate Accuracies:**
    * Model A:
        * Accuracy = (36 + 570) / 1000 = 606 / 1000 = 0.606 or 60.6%
    * Model B:
        * Accuracy = (30 + 950) / 1000 = 980 / 1000 = 0.98 or 98%

**Therefore:**

* For the 5% positive, 95% negative population:
    * Model A's accuracy is approximately 60.6%.
    * Model B's accuracy is 98%.

**Key Takeaway:**

* When dealing with unbalanced datasets, accuracy can be misleading. Model B appears to perform much better in the skewed population.
* It is critical to be aware of the underlying population distribution when evaluating the model.