DAX

Dax Function: NORM.S.INV

Q: What does the NORM.S.INV function do in Power BI?

It calculates the z-score corresponding to a given cumulative probability in the standard normal distribution.

Q: What is the range of probabilities allowed in NORM.S.INV?

Probabilities must be between 0 and 1 (exclusive).

Q: How is NORM.S.INV different from NORM.S.DIST?

NORM.S.INV calculates the inverse cumulative probability (z-score), while NORM.S.DIST calculates the cumulative probability or density for a given z-score.

Q: Can I use NORM.S.INV for non-standard distributions?

No, it is designed specifically for the standard normal distribution. Use NORM.INV for custom distributions.

Q: How do I handle errors with out-of-range probabilities?

Use error-handling techniques like IF statements or validation checks to ensure probabilities are within the valid range.

Category: Statistical Functions

The NORM.S.INV function in Power BI is a DAX function used to calculate the inverse of the standard normal cumulative distribution function (CDF). Given a probability, it returns the corresponding z-score for a standard normal distribution (mean = 0, standard deviation = 1).

Purpose of the Function

Determine the z-score corresponding to a given cumulative probability.

Type of Calculations

Computes the inverse cumulative distribution.

Practical Use Cases

Finding critical z-scores in hypothesis testing.
Calculating cutoff values in control charts.
Estimating thresholds for risk assessment.


NORM.S.INV(<probability>)</probability>

Parameter	Type	Description
`<Probability>`	Scalar	A numeric value representing the cumulative probability. Must be between 0 and 1 (exclusive).

How Does NORM.S.INV Dax Works

Mathematical Principle

The function inverts the cumulative distribution function (CDF) of the standard normal distribution:

Input: A probability p, where 0 < p < 1.
Output: A z-score that satisfies:
F(z)=p
Where F(z) is the cumulative distribution function of the standard normal distribution.

For example:

If p = 0.5, z = 0 (the median of the standard normal distribution).
If p = 0.025, z = −1.96 (common in 95% confidence intervals).

What Does It Return?

The NORM.S.INV function returns:

A numeric value representing the z-score corresponding to the cumulative probability.
The returned z-score can range from −∞ to , depending on the input probability.

When Should We Use It?

Critical Values: Identify zz-scores for statistical tests (e.g., significance levels in t-tests or z-tests).
Threshold Analysis: Calculate cutoff values for specific probabilities.
Quantile Calculations: Find percentiles in standardized datasets.

Examples

Basic Usage :

Find the z-score for a cumulative probability of 0.975:


NORM.S.INV(0.975)

Output: Approximately 1.96.

Column Usage

Compute z-scores for a column of cumulative probabilities:


ADDCOLUMNS(
Probabilities,
"ZScore",
NORM.S.INV(Probabilities[Probability])
)

Use Case: Add a column of z-scores corresponding to the cumulative probabilities.

Advanced Usage

Combine with other DAX functions to compute critical zz-scores for varying confidence levels:


NORM.S.INV(1 - (1 - ConfidenceLevel) / 2)

Use Case: Calculate two-tailed critical values for different confidence levels dynamically.

Tips and Tricks

Valid Input Range: Ensure probabilities are strictly between 0 and 1; values outside this range will result in errors.
Standard Normal Assumption: The function assumes a mean of 0 and standard deviation of 1. Use NORM.INV for non-standard distributions.
Error Handling: Wrap the function in an error-checking mechanism for dynamic datasets to handle out-of-range probabilities.

Performance Impact of NORM.S.INV DAX Function:

Efficient for individual calculations.
For large datasets, consider precomputing critical values for common probabilities.

Related Functions You Might Need

NORM.DIST: Calculates cumulative probability or density for a normal distribution with a given mean and standard deviation.
NORM.INV: Finds the value for a given probability in a normal distribution with a specified mean and standard deviation.
NORM.S.DIST: Computes the cumulative or density function for the standard normal distribution.

Want to Learn More?
For more information, check out the official Microsoft documentation for NORM.S.INV You can also experiment with this function in your Power BI reports to explore its capabilities.

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1. What does the NORM.S.INV function do in Power BI?

It calculates the -score corresponding to a given cumulative probability in the standard normal distribution.

2. What is the range of probabilities allowed in NORM.S.INV?

Probabilities must be between 0 and 1 (exclusive).

3. How is NORM.S.INV different from NORM.S.DIST?

NORM.S.INV calculates the inverse cumulative probability (-score), while NORM.S.DIST calculates the cumulative probability or density for a given z-score.

4. Can I use NORM.S.INV for non-standard distributions?

No, it is designed specifically for the standard normal distribution. Use NORM.INV for custom distributions.

5. How do I handle errors with out-of-range probabilities?

Use error-handling techniques like IF statements or validation checks to ensure probabilities are within the valid range.

Dax Function: NORM.S.DIST

Dax Function: PERCENTILE.EXC