power2x2 Power for testing two independent proportions power2x2

# Visualizing Categorical Data: power2x2

\$Version: 1.1 (19 Aug 1999)
Michael Friendly
York University

## The power2x2 macro ( get power2x2.sas)

### Power for testing two independent proportions

The POWER2X2 macro computes the power of a test comparing proportions from two, equal-sized, independent samples. Power is given for various sizes of the total sample, or required sample size is given for various power values, allowing you to pick the sample size that achieves the desired power.

## Usage

The POWER2X2 macro takes 9 keyword arguments. You must supply the DIFF= parameter. By default the macro computes power for a range of sample sizes (given by NMIN= and NMAX=). Alternatively, you may specify a range of power values (given by POWER=) for which the required sample size is calculated.

### Parameters

P1=
Specifies an estimate of the ``success'' rate in one group, the baseline group. [Default: P1=.50]
DIFF=
Specifies the difference in the proportions that you want to detect. This is the specification of the alternative hypothesis at which power is computed. The difference MUST be specified; there is NO default. You may specify a list of values separated by commas, a range of the form `x TO y BY z`, or a combination of these. However, you must surround the DIFF= value with `%STR()` if any commas appear in it. For example,
```        diff=.10 to .30 by .05
diff=%str(.10, .13, .20)
```
ALPHA=
Specifies the significance level or size of the test. It is a decimal value less that 1. For example, `ALPHA=.05` sets the probability of a Type 1 error at 0.05. You may specify a single value, or a list of values separated by commas, or a range of the form `x TO y by z`. [Default: `ALPHA=.05`]
POWER=
Values of power for sample size calculation. You may specify a list of values separated by commas, a range of the form `x TO y BY z`, or a combination of these, as in a `DO` statement. However, you must surround the POWER= value with `%STR()` if any commas appear in it.
NMIN=
Specifies the minimum total sample size at which power will be computed. [Default: `NMIN=10`]
NMAX=200
Specifies the minimum total sample size at which power will be computed. [Default: `NMAX=200`] To get power for a single total sample size, set NMIN and NMAX to half of the total sample size.
PLOT=
is a specification for plotting the results, in the form `Y * X` or `Y * X = Z`, where X, Y, and Z may be any of the variables N, DIFF, P2, POWER or OR. No plots are produced if PLOT= is blank. [Default: `PLOT=POWER `* `N=DIFF`]
PLOTBY=
is another variable in the OUT= data set. Separate plots are drawn for each level of the PLOTBY= variable.
OUT=
The name of the output data set. [Default: `OUT=_POWER_`]

## Details

Hypotheses in the test are:
```       H0: p1 = p2
Ha: p1 ne p2
```

where p1 and p2 are the success probabilities in the two populations. The Pearson chi-square statistic tests the null hypothesis (H0) against the alternative hypothesis (Ha) and is available in the FREQ procedure when the CHISQ option is specified on the TABLES statement.

The power is the probability of rejecting H0 and is a function of the true difference in proportions. Power is often computed assuming many different settings of the true proportions. The type 2 error rate (denoted beta) is the probability of accepting H0 for some non-zero true difference and is equal to 1-power. The power and beta are computed for a range of total sample sizes at a particular alternative hypothesis that you specify. It is assumed that the total sample size will be split equally between the two samples.

### Example

```%include vcd(power2x2);        *-- or include in an autocall library;
%power2x2( p1=.6,  diff=.10 to .20 by .05,  nmin=50);
```

With the settings above, the expected baseline success rate is 60%. Power for detecting a difference of 10-20% in the two proportions will be computed for a .05 level test and for sample sizes ranging from 50 to 200.