1. What is the Cutoff Score Formula?

The cutoff score formula calculates a threshold value in a normal distribution based on the mean, standard deviation, and desired z-score. It's commonly used in statistics to determine acceptance criteria, pass/fail thresholds, or significance boundaries.

2. How Does the Calculator Work?

The calculator uses the cutoff score formula:

Where:

• \( \mu \) — Mean of the distribution
• \( z \) — Z-score (standard deviations from the mean)
• \( \sigma \) — Standard deviation of the distribution

Explanation: The formula calculates the raw score that corresponds to a specific number of standard deviations above or below the mean in a normal distribution.

3. Importance of Cutoff Scores

Details: Cutoff scores are essential in statistical analysis for determining significance thresholds, setting passing grades, establishing clinical diagnostic criteria, and creating inclusion/exclusion criteria for studies.

4. Using the Calculator

Tips: Enter the mean value, z-score (positive or negative), and standard deviation (must be positive). The calculator will compute the corresponding cutoff score.

5. Frequently Asked Questions (FAQ)

Q1: What does a positive vs. negative z-score mean?
A: A positive z-score indicates a cutoff above the mean, while a negative z-score indicates a cutoff below the mean.

Q2: How do I interpret the cutoff score?
A: The cutoff score represents the threshold value where a specified percentage of the distribution falls above or below this point.

Q3: What are common z-score values used for cutoffs?
A: Common values include ±1.96 (95% confidence), ±2.58 (99% confidence), or ±1.645 (90% confidence).

Q4: Can this be used for non-normal distributions?
A: The formula assumes a normal distribution. For non-normal distributions, other methods may be more appropriate.

Q5: How is this different from percentile calculation?
A: The z-score corresponds to specific percentiles in a normal distribution (e.g., z=1.96 ≈ 97.5th percentile).