# PHI

The PHI function returns the cumulative distribution function of a standard normal distribution. It calculates the probability that a random variable is less than or equal to a specified value in a normal distribution with a mean of 0 and a standard deviation of 1. This function is often used in statistical analysis to determine the probability of a certain event occurring based on a normal distribution.

## Usage

Use the `PHI` formula with the syntax shown below, it has 1 required parameter:

Parameters:
1. x (required):
The value at which to evaluate the cumulative distribution function.

## Examples

Here are a few example use cases that explain how to use the `PHI` formula in Google Sheets.

### Calculating the probability of a value in a normal distribution

By using the PHI function, you can calculate the probability that a random variable is less than or equal to a specified value in a normal distribution with a mean of 0 and a standard deviation of 1.

### Hypothesis testing

The PHI function is commonly used in hypothesis testing to determine the probability of observing a test statistic as extreme as the one calculated from a sample, assuming that the null hypothesis is true.

### Calculating z-scores

The PHI function can be used to calculate z-scores, which are a measure of how many standard deviations a data point is from the mean of a normal distribution.

## Common Mistakes

`PHI` not working? Here are some common mistakes people make when using the `PHI` Google Sheets Formula:

### Forgetting to convert the value to a z-score

The `PHI` function is used to calculate the cumulative distribution function of the standard normal distribution, so it expects a z-score as input. If you have a value that is not in z-score form, you need to convert it to a z-score before using the `PHI` function.

### Using the wrong sign for the input

The `PHI` function expects a z-score as input. It is important to use the correct sign for the input value, as this affects whether you are calculating the probability of being less than or greater than the value. For example, if you want to calculate the probability of being less than a certain value, you need to use a negative z-score as input.

The following functions are similar to `PHI` or are often used with it in a formula:

• `NORMDIST`

The `NORMDIST` function in Google Sheets calculates the normal distribution for a specified value, mean, and standard deviation. It returns the probability of a value occurring within a specified range of a normal distribution. It is commonly used in statistics, finance, and science to analyze data and make predictions.

• `NORMINV`

The `NORMINV` function returns the inverse of the normal cumulative distribution for a specified value, mean, and standard deviation. It is commonly used in statistics to find the value at which a given percentage of observations lie below that value.

• `NORMSDIST`

The `NORMSDIST` function returns the area under a normal distribution curve to the left of a specified value. This function is commonly used in statistics to calculate probabilities.

• `NORMSINV`

The `NORMSINV` function calculates the inverse of the standard normal cumulative distribution for a specified value of x. It is commonly used in statistical analysis to transform data from a normal distribution to a standard normal distribution with a mean of 0 and a standard deviation of 1.

You can learn more about the `PHI` Google Sheets function on Google Support.