# Power Calculations in Stata

Power calculations indicate the minimum sample size needed to provide precise estimates of the program impact; they can also be used to compute power and minimum detectable effect size. Researchers should conduct power calculations during research design to determine sample size, power, and/or MDES, all of which play critical roles in informing data collection planning, budget, timeline, accuracy, and precision. This page presents different options of Stata commands for power calculations and discusses the advantages and disadvantages associated with each.

• Optimal Design provides helpful visualizations for power calculations that may aid understanding of power calculations in Stata.
• Stata is better than Optimal Design for reproducible research purposes, as the power calculations are codified in a do file.
• To install the commands covered in this page, search `findit`, followed by the command name. Then find the most recent update of the command and install it. For more information on each command, type `help`, followed by the command name. Note that `power` is Stata’s built-in program for sample size calculations and does not need to be installed.
• For more information on the key parameters of power calculations, see Sample Size and Power Calculations.
• The below table outlines the capabilities of four Stata commands for power calculations. More detailed descriptions follow.

## power

`power` is a built-in program and Stata’s newest update to power calculations. It was introduced with Stata13 as a replacement to `sampsi`. It is best used for simple randomizations with no clustering.

• Offers more flexibility of input/output choices
• Automatically saves output to a file
• Can compute the sample size of control group given a treatment group size (or vice versa)
• Directly calculates MDES

• No straightforward way to control for repeated measures
• Allows for treatment and control groups of different sizes

### Useful Options

• `power onemean`: assumes equal means in treatment and control
• Sample size
• `n()`: sample size
• `n1()`: control group size
• `n2()`: treatment group size
• `nratio`: ratio of n1/n2. Its default is 1. It is not necessary to specify this if you specify `n1` and `n2`
• `table` outputs results in a table format
• `saving(filename, [replace])` saves results in a .dta format

## sampsi

`sampsi` is no longer an officially supported Stata package. It has been replaced by `power`. However, it continues to work. By default, the command computes sample size. To compute power, specify `n1` or `n2`. To compare means (not proportions), specify `sd1()` or `sd2()`. For repeated measures, `sd1()` or `sd2()` must be specified. Note that `sampsi` defaults to 90% power.

• Works with Stata13 or earlier
• Allows repeated measures (multiple follow-ups)

• Does not allow clustering
• Requires user to impute MDES

### Useful Options

• `onesample`: assumes equal means in treatment and control
• Sample size
• `n1()`: size of treatment group
• `n2()`: size of control group
• `ratio()`: n1/n2, default is 1
• Repeated measures
• `pre`: number of baseline measurements
• `post`: number of follow-up measurements
• `r0()`: correlation between baseline measures (default r0 = r1)
• `r1()`: correlation between follow-up measures
• `r01()`: correlation between baseline and follow-up
• `method()`: options include `post`, `change`, `anova`, or `all`. The default is `all`.
• `sampclus` is an add-on to `sampsi` that allows for clustering. It must be directly preceded by `sampsi` command. For example, the following code correct sample size and computes the number of clusters from a t-test. It then adjusts this sample size calculation for 10 observations per cluster and an ICC of 0.2:
```sampsi 200 185, alpha(.01) power(.8) sd(30)
sampclus, obsclus(10) rho(.2)
```

### Computing MDES with `sampsi`

To compute MDES with `sampsi`, use a guess-and-check method. The difference between baseline and hypothesized mean is MDES. Compute power, using different hypothesized means, aiming for power = 0.8.

## clsampsi

• Allows for clustering

• Requires user to impute MDES
• Does not allow for repeated measures
• Does not allow for baseline correlation

### Useful options

• `m()`: cluster size in treatment and control, assuming equal cluster size in each group. If the treatment and control cluster sizes differ, use `m1()` and `m2()` for the control and treatment cluster sizes, respectively.
• `k()`: number of clusters in treatment and control, assuming equal number of clusters in each group. If the number of clusters differs between treatment and control, use `k1()` and `k2()` for the control and treatment cluster numbers, respectively.
• `sd()`: standard deviation, assuming it is equal between the treatment and control groups. If the treatment and control standard deviation differs, use `sd1()` and `sd2(#)` for the control and treatment standard deviations, respectively.
• `rho(#)`: ICC assuming it is equal between the treatment and control groups. Alternatively, use `rho1()` and `rho2()`.
• `sampsi` determines the power of means (or proportion) comparison using the standard `sampsi` command
• `varm(#)`: cluster size variation, assuming it is the same between the treatment and control groups. This only affects the power if it is larger than `m()` and `rho()`>0.

## clustersampsi

• Allows for clustering
• Allows for baseline correlations
• Directly calculates MDES

• Doesn’t allow for different sized treatment / control groups
• Doesn’t allow for repeated measures

### Useful options

• `detectabledifference` calculates MDES
• Alternative options: `power`, `samplesize`
• to use detectable difference, specify `m`, `k`, `mu1`
• `rho()`: ICC
• `k()`: number of clusters in each arm
• `m()` average cluster size
• `size_cv()`: coefficient of variation of cluster sizes (default is 0). Can be any number greater than 1.
• `mu1()` and `mu2()`: mean for treatment and control, respectively
• `sd1()` and `sd2()`: mean for treatment and control, respectively
• `base_correl` correlation between baseline measurements – or other predictive covariates – and outcome