The PHI function in Google Sheets is a powerful statistical tool used to calculate the cumulative distribution function for a standard normal variable. It plays a significant role in statistical analysis, particularly when working with probabilities related to normally distributed data.

Syntax

PHI(z)

• z: This parameter represents the value for which you want to calculate the cumulative distribution function, effectively measuring how many standard deviations the value is away from the mean.

Example #1

PHI(1.96)

This function call calculates the cumulative distribution up to 1.96 standard deviations from the mean. The expected result is approximately 0.975, indicating a 97.5% probability of a value being less than or equal to 1.96 in a standard normal distribution.

Example #2

PHI(-1)

Here, the function computes the cumulative distribution at -1 standard deviation from the mean. The result should be around 0.1587, reflecting that about 15.87% of the data lies below this value in a standard normal distribution.

Example #3

PHI(0)

This function assesses the cumulative distribution at the mean (0 standard deviations). The anticipated output is 0.5, indicating that 50% of the values fall below the mean in a standard normal distribution.

Error handling

• NUM!: This error arises when the input value is not a valid number. Ensure that the parameter is a numerical value.
• VALUE!: This message indicates that the input type is incorrect, often caused by supplying non-numeric characters. Always use numeric values in the PHI function.

Conclusion

In summary, the PHI function in Google Sheets is a crucial resource for statistical calculations related to normally distributed data. Its ability to compute the cumulative distribution function makes it invaluable for researchers, analysts, and anyone needing precise statistical insights. By understanding its syntax and possible errors, users can effectively leverage this function for reliable results.