This article helps you:
Understand the different kinds of formula metrics supported by the Experiment Results chart
Understand how Amplitude calculates statistical significance for formula metrics
In an Experiment Results chart, using a formula metric offers you greater flexibility when performing analyses. A formula metric is a metric that consists of:
If you've used custom formulas in Event Segmentation, this should be familiar to you. If not, take review that article before proceeding.
You can also view this metric in the object management center.
Experiment Results supports the formula functions listed here:
Syntax: UNIQUES(event)
Syntax: TOTALS(event)
Syntax: PROPSUM(event)
This function only works when grouping by a numerical property on the event. If grouping by multiple properties, the formula runs the calculation with the first group-by clause.
Returns the sum of the property values you're grouping the specified event by.
Syntax: PROPAVG(event)
This function only works when grouping by a numerical property on the event. If grouping by multiple properties, the formula runs the calculation with the first group-by clause.
Returns the average of the property values you're grouping by. This function is the same as PROPSUM(event)/TOTALS(event)
. Learn more about how Amplitude calculates PROPAVG and PROPSUM in this article
Syntax: PROPCOUNTAVG(event)
For example, imagine you're interested in the average number of song genres your music app subscribers listen to. Every time a user plays a song, a Play Song or Video event triggers; each played song also captures a Genre_Type event property. Running PROPCOUNTAVG on Play Song or Video grouped by Genre_Type gives you the average number of unique Genre_Type values users who fire PlaySong or Video have.
PROPCOUNTAVG
supports only numeric event properties in Experiment.
Syntax: PROPMAX(event)
Syntax: PROPMIN(event)
Syntax: PROPCOUNT(event)
Returns the number of distinct property values for the property by which the event is grouped. In this setup, the formula retrieves the number of different departments covering all the items for which details were viewed:
PROPCOUNT
is an estimate of distinct property values. This estimate comes from a HyperLogLog algorithm, and its accuracy depends on amount of data it has to work with. Expect a relative error in the range of 0.1% for less than 12,000 unique values and up to 0.5% for more than 12,000 unique property values, depending on the cardinality of the property.
PROPCOUNT
supports only numeric event properties in Experiment.
Syntax: $:REVENUETOTAL(event)
Returns the aggregate sum of the property, formatted as a currency. It's the same as PROPSUM(event)
. The $:
prefix is optional. Its presence ensures the output format is a currency.
In your formulas, refer to events selected in the Events Module by their corresponding letter. The functions and the parameters aren't case-sensitive. You can also perform the following arithmetic operations:
Before getting into how calculations of formula metrics work with experiment data, it’s important to understand the Experiment Analysis view, which provides details for your experiment.
For formula metrics, Amplitude computes the results for each function independently to find the mean and variance of each one. It then applies the arithmetic operators to the results of these individual functions.
For example: You've defined a formula metric as TOTALS(A) + TOTALS(B)
. Amplitude calculates the variances and means of both components of this metric, as well as the covariance.
If you set X equal to TOTALS(A) and Y equal to TOTALS(B), the following statements hold:
V[X]
= Variance of X
E[X]
= Mean of X
V[Y]
= Variance of Y
E[Y]
= Mean of Y
Cov[X, Y]
= Covariance of X and Y, assumed to be zero for all mathematical operations.
Addition:
Variance: V[X + Y] = nV[X] + nV[Y]
Mean: E[X + Y] = E[X] + E[Y]
Subtraction:
Variance: V[X - Y] = nV[X] + nV[Y]
Mean: E[X - Y] = E[X] - E[Y]
Multiplication:
Variance: V[X * Y] = n^3 mu_y^2 sigma_x^2 + n^3 sigma_y^2 mu_x^2 + n^2 sigma_x^2 sigma_y^2
Mean: E[X * Y] = E[X] * E[Y]
Division:
Variance:
Mean:
E[X / Y] = E[X] / E[Y]
After you have the mean and variance of the formula metric, you can calculate the confidence interval chart and the p-values.
Formula / Metric: TOTALS(A) / TOTALS(B)
November 14th, 2024
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