# Z-Score for Anomaly Detection

## What is the Z-Score for Anomaly Detection?

The z-score method is a statistical measure that has proven to be an effective tool for detecting anomalies in a range of applications.

Anomaly detection is a mechanism that identifies any unusual patterns. Industries ranging from cybersecurity to finance can use z-scores to enhance security, detect fraud, and provide better services.

The z-score quantifies standard behavior and, from there, sets the criteria for what should be considered an anomaly. The result allows for a more effective way to identify outliers, which can then be used in various ways.

## The Theory Behind Z-Scores

Let’s quickly discuss the foundational concept of z-scores. A z-score standardizes the dataset, making every data point relative to the mean. Understanding the z-score is crucial for datasets where the scale of measurements often varies significantly.

Engineers can use the z-score for outliers based on its relative to the mean of the dataset. We’ll explore more about the specific numbers below, but for now, it’s important to understand that what makes an ideal z-score varies based on the specific use case.

## How is a Z-Score Calculated?

Ultimately, z-scores help developers and data scientists implement anomaly detection in their systems, which includes a wide range of possible uses, such as machine learning models or fraud prevention. The first step is learning how to know a z-score and understanding how it’s calculated.

The overall process for a z-score calculator can be broken down into three steps:

• Computing the mean: Sum up all the data points and divide by the number of data points. This simple calculation results in the mean value of the dataset.
• Calculating standard deviation: The next step is to compute the average of the squared differences from the mean and then take the square root. The result is the standard deviation.
• Determine the z-score: The final step is subtracting the mean and dividing by the standard deviation for everything within the dataset. Once done, you’ll have the z-score for each item to identify any outliers or anomalies.

## What is a Good Z-Score?

The concept of a “good” z-score varies by use case. Regardless of implementation, a z-score tells you how many standard deviations a data point is from the mean. Generally speaking, we can break down what z-scores represent:

• Z-score of 0: This means the data point’s value is precisely the same as the mean value of the data set.
• Z-score of 1.0: This value indicates one standard deviation above the mean.
• Z-score of -1.0: Similarly, a value of -1 indicates the data point is one standard deviation below the mean.
• Z-score greater than 1.0 or less than -1.0: The data point is considered unusual or farther from the mean. The greater the absolute value of the z-score, the more unusual the data point is.

The z-score table above gives you a rough idea of what might constitute a good z-score. However, a “good” z-score varies based on the use case. Let’s go over a few examples:

• Performance metrics: If you’re measuring performance, a higher z-score indicates a value above average. For example, if we use a basic example of a classroom setting, a student’s test score with a z-score of 2.0 is significantly above the class average.
• Quality control: In manufacturing or quality control contexts, a “good” z-score might be one close to 0, indicating that a product or process is operating on target. Conversely, z-scores far from 0 might indicate a defect or flaw that needs to be addressed.
• Anomaly detection: Extremely high or low z-scores, like +/- 3, typically indicate an anomaly to trigger an alarm, block a financial transaction, or prevent a cyber attack.

Z-scores are increasingly popular in data analysis and statistics as they offer plenty of benefits over alternative methods like the Interquartile Range (IQR). Let’s explore some of these benefits to demonstrate the value of z-scores.

### Data Standardization

One of the main advantages of z-cores is the capability for data standardization. Z-scores transform datasets with a mean of 0 and a standard deviation of 1.

As a result, it’s possible to compare datasets sourced from different scales and units. This capability can be extremely useful for machine-learning algorithms. Many machine-learning algorithms perform better when features are on a standardized scale.

Other use cases also benefit from standardization, as it allows varying metrics to be evaluated more precisely. For example, fraud detection depends on evaluating data such as purchase amount, past behavior, and IP location compared to billing address. A z-score makes it easier to evaluate these different items more effectively.

### Sensitivity to Outliers

Z-scores shine when it comes to spotting outliers in datasets, especially when we use the commonly cited +3 and -3 thresholds for high and low z-scores. This sensitivity enables quicker identification of data points that stand out from the majority. This advantage of z-scores is versatile and finds a wide variety of use cases, from biology to finance.

### Enhances Data Visualization

When data is standardized using z-scores, visualizations like histograms or box plots provide more intuitive insights into the data distribution and outliers. Data visualization based on z-scores combines the above benefits into a widely helpful tool. From there, it’s easier for other systems or human analysts to reach valuable conclusions and actionable insights.