# Power Analysis

The power analysis tool leverages the known mean and variance of a metric and the observed traffic volume to estimate the relationship between three variables:

- Minimum detectable effect (MDE): The smallest change in the metric that the experiment can detect. For example: An MDE of 1% means that if there's a true effect of 1% or larger on our metric, we expect the experiment will show a statistically significant result. If the effect is smaller than 1%, then it will likely fall inside the confidence intervals and not be statistically significant.
- Number of days or exposures: How long the experiment is active and the number of users enrolled in it. Longer running experiments typically have more observations, leading to tighter confidence intervals and smaller MDE. We use historical data to estimate the number of new users that would be eligible for the experiment each day.
- Allocation: The percentage of traffic that participates in the experiment. Larger allocation leads to smaller MDE, so it's often desirable to allocate as many users as possible to get faster or more sensitive results. When there's a risk of negative impact or a need for mutually exclusive experiments however, it's useful to know the smallest allocation that can achieve the desired MDE.

## Using the Tool

It can be accessed from the tools menu. It's also available on the experiment setup page.

Select the population used to determine the metric mean and variance and to estimate the number of exposures over time.

- Everyone: Analysis is based on the entire user base.
- Targeting gate: Analysis is scoped to the set of users that pass the selected feature gate, which has been active for at least 7 days. Choose this option when you plan to use a targeting gate for the experiment. Note: This will trigger an offline query, you'll be notified when results are ready.
- [Coming soon] Past experiment: Analysis is based on data collected from in a previous experiment. Use this option when the new experiment will impact a similar user base or part of the product as the previous one.

Select a metric of interest (or multiple metrics for a targeting gate analysis)

Select the type of analysis to perform:

- Fixed Allocation: You know the available allocation, the tool tells you the expected MDE for each duration
- Fixed MDE: You know the effect size you want to measure, the tool tells you the allocation and duration needed

Click on

**Start Calculation**to see the results

## Population Types

The population selected directly impacts the inputs of the analysis (mean, variance, number of users). To obtain reliable power analysis estimates, the metric values of the selected population should roughly match those of the users you'll be targeting in the experiment.

### Example

Say we want to test a change in the checkout flow and we want to know our expected MDE for total_purchases. Let's assume that only ~10% of our daily users reach the checkout page. If we use the *Everyone* population for our analysis, we're likely to:

- Overestimate the number of users that the experiment will get.
- Underestimate the mean value of the total_purchases metric. The 90% of user that don't reach the checkout page have a value of zero, but in practice they won't be in our experiment and won't contribute to the metric.
- Incorrectly estimate the variance in the total_purchases metric. The distribution of metric values is different if we include the 90% of users that have 0 purchases because they never reached the checkout page.

Thus, in cases when the experiment only includes a biased subset of users, it's possible the MDE and duration obtained by the power analysis won't be a good estimate.

One way to address this is to use data from a past experiment to estimate the power of a new, similar experiment (coming soon!). In our example, if we had a prior experiment that was also targeting the checkout page, we could use it to get better estimates of traffic volumes and metrics for this part of the product.

### Inputs by Population Type

This is how the various inputs for the power analysis are obtained from the different population types:

Population | Mean and Variance Calculation | Total Exposures by Week Estimate |
---|---|---|

Everyone | Mean and variance across all users, estimated for 1, 2, 3, and 4 week rollups | Total count of users seen in the past 1, 2, 3, and 4 weeks |

Targeting Gate | Mean and variance for users that pass the targeting gate, computed for 1, 2, 3, 4 week rollups | Total users that passed the targeting gate after 1, 2, 3, 4 weeks |

Past Experiment (coming soon) | Cumulative mean and variance for the control group at 1, 2, 3, and 4 weeks | Total experiment exposures after 1, 2, 3, and 4 weeks, adjusted according to the past experiment's allocation and the desired allocation for the new experiment. |

## Analysis Types

### Fixed Allocation Analysis

Choose this option to understand how the length of the experiment impacts the MDE. The example below shows how the MDE for a page load metric shrinks over time in an experiment with 100% allocation. After 1 week we expect 5200 users per group and an MDE of 21.6%, by week 4 the number of users per group should increase to ~48k and the MDE is reduced to 7%

### Fixed MDE Analysis

Choose this option if the smallest effect size that the experiment should detect is known. Enter the desired MDE as a percentage of the current metric value. For example: If a website currently gets 1,000 page loads per day, an MDE of 10% means we can detect a change of 100 or more page loads per day.

The results show the minimum number of weeks needed to reach this MDE for different allocation percentages. In the example below, the experiment should run for at least 2 weeks with 65% allocation or 4 weeks with 50% allocation. There's no way achieve the desired MDE in 1 week, as this would require more than 100% allocation (more users than we expect to see in one week).

## Advanced Options

Advanced settings to customize the analysis:

**One-sided or Two-sided test**: Toggle this setting to select the type of z-test to use for the analysis.**Number of Experiment Groups**: The total number of groups in the experiment, including control.**Test Group Size**: Default is 1, meaning the test and control groups are the same size. For different sized groups, enter the multiplier applied to the test group size. E.g.: 0.5 means the test group is half the size of the control group.**ID Type**: The Unit ID type that the experiment will be based on.**Custom Date Range**: The date range for past data used to obtain the metric mean, variance, and estimate of the total available traffic. By default, the most recent 7 days are used. Use this feature to exclude holidays or other events that are not representative of typical data trends expected during the experiment. A 7 day period is recommended to account for weekly seasonality.

## Calculation Details

The relative percentage MDE for a given metric *X* is computed using the following equation:

*X-bar*is the mean metric value across all users*var(X)*is the population variance of the metric*N*and_{test}*N*are the estimated number of users in the test and control group. These are based on historical active user data along with experiment allocation and group size._{control}*Z*is the standard Z-score for the selected power. Typically_{1-β}*1-β = 0.8*and*Z*_{1-β}= 0.84*Z*is the standard Z-score for the selected significance level in a 2-sided test. Typically_{1-α/2}*α = 0.05*and*Z*_{1-α/2}= 1.96

**Note:** This calculation relies on statistics computed across the entire user base of the project. It does not account for the fact that experiments targeting only a subset of users may have different summary statistics for their key metrics. For example, the metric mean and variance can be different in an experiment that targets only Android users or one that exposes users at the lower part of an acquisition funnel.