The
Mixed Model Power
process assists you in the planning of your experiments. Starting with an exemplary experimental design data set and parameter settings for a relevant
mixed model
, it enables you to calculate
power
curves for a range of Type 1 error probabilities (
alpha
). In other words, this process helps you decide how big an experiment you need to run in order to be reasonably assured that the true effects in the study (change in gene
expression
, for example) are deemed statistically significant. Conversely, this process also enables you to calculate the statistical power of an experiment, given a specified
sample size
. This process is typically run before you run your experiment, and it helps to have run a pilot study in order to determine reasonable values for
variance
components.
Mixed Model Power
computes the statistical power of a set of one-degree-of-freedom
hypothesis tests
arising from a mixed linear model. You specify an experimental design file, parameters for relevant PROC Mixed statements (including fixed values for the variance components and
ESTIMATE statements
), and ranges of values for
alpha
and effect sizes, and the process outputs a table of power values calculated using a noncentral
t
-
distribution
.
Two data sets are required to run
Mixed Model Power
. The first is the
Experimental Design Data Set (EDDS)
.
This data set provides information about the design, typically for one gene or protein, of the proposed experiment. It must include all relevant design
variables
of the experiment for which you want to compute power. The sample size equals the number of rows in this data set.
The second required file contains PROC MIXED ESTIMATE statements See
Estimate Builder
for more details. ESTIMATE statements are used to specify linear hypotheses of interest that are valid for each specified
fixed effects
model. Distinct power values are computed for each hypothesis test.
For detailed information about the files and data sets used or created by JMP Life Sciences software, see
Files and Data Sets
.
The output of the
Mixed Model Power
process includes one output data set listing the
t-statistics
and
Overlay Plot
s showing the associated power values for each multiplier and each level of
alpha
(not shown) and the associated power curves. This output is accessed from the tabbed
Results
window.
|
Examine the sample
overlay plot
shown below.
|
Effect sizes (
log
2
differences) are plotted along the x-axes. Power is plotted along the y-axis of each plot. The greater the power, the higher the probability of rejecting the
null hypothesis
(in this case, there is no difference in expression due to the experimental variable) when the observed difference is real. Note that, as might be expected, power increases for all effects as the effect size increases. In other words, the greater the difference due to the effect, the more likely you are to successfully conclude that the observed difference is real.
In all cases, we are also less likely to correctly reject the null at more stringent levels of
alpha.
Regardless of how you adjust the conditions, you should plan on rerunning this analysis using the new design. To compute power for a different design, use
DOE > Custom Design
to generate the design of interest, save the table as a SAS data set, and rerun
Mixed Model Power
using the new design as the EDDS.