Use the contents listing, or click on any active area in the accompanying map, to get an explanation. (If you do not see the contents or the image map, click here.)
An extended help page/tutorial is also available to provided for more details.
The options menu contains entries for the following:
The help menu contains an HTML link to this help page, as well as an additional link to the Effect Advisor and a small "About" box.
Enter the number of levels of each factor here. You can do this using either by typing in the number field or clicking on the bar-graph display.
When a "factor" is labeled "Within", its number of levels is simply the number of within-cell replications in the experiment. This number can be entered either by typing in the number field or clicking on the bar-graph display.
Use the radio buttons to set whether a factor's levels are fixed or random. When a factor has fixed levels, we are in a situation where each particular level of that factor is of interest -- for example, a factor named drug might have three fixed levels: placebo, standard, experimental. The statistical inference applies only to those fixed levels and cannot be extended to other drugs not tested in the experiment.
When a factor has random levels, we assume that its levels are instances of random sampling from some population, and we are interested in making an inference that applies to that whole population; for example, a factor named subject would generally be considered random, and often we would vary the number of subjects (i.e., levels of subject) as part of the power analysis. When a factor has random levels, its corresponding model term is modeled as a random effect, as are all interactions involving that factor.
It is conceptually impossible to have a fixed factor nested in one or more random factors, and the software enforces this constraint. Also, the "Within" factor, if present, is forced to stay random.
Effect size can be entered either by typing in the number field or clicking on the bar-graph display. Effect size is expressed as the standard deviation of the effects for the term in question. In the case of a random (or mixed) effect, this is the square root of the variance component for that term. In the case of a fixed effect, this is the "sample" or "bias-corrected" SD of the fixed effects. The Effect Advisor (available on the Options menu) may be useful for determining effect sizes for fixed effects. To determine effect SDs for random effects, you probably need to do a variance-component analysis on some pilot data.
The intent here, especially in the case of fixed effects, is to enter a hypothetical effect size that you wish to be able to detect in the experiment. The power will increase as the effect SD increases.
It is important to know that the SD you enter for a random effect will affect the powers of other tests, because random effects appear in their error terms. To see the error terms, use the "Show EMS" entry in the Options menu.
The power is displayed here, both numerically and graphically. You cannot change these values directly; they can be changed only by manipulating sample size, effect size, alpha, the number of levels of factors in the experiment, and whether factors are fixed or random.
Enter the significance level of the tests here. This value is used in determining the powers of all tests in the dialog.
This message (or something similar) is displayed by your browser to warn you that you are running a Java applet that is of uncertifiable content. There is a potential security risk in downloading and running an applet; you need to trust the site you are connected to. This applet was developed by Russ Lenth at the University of Iowa, and if you have run this by connecting directly to a URL at or below www.stat.uiowa.edu/~rlenth/, you should be ok.
Simply enter a number in the field. On most platforms, you can use arrow keys to move the cursor, the backspace key to delete backwards, and highlight the whole field or any portion thereof to replace what is there. When you hit the "Return" or "Enter" key, the number is entered and the powers are updated. An update also occurs automatically if you change the mouse focus (click it somewhere outside of the field).
An invalid entry causes all powers to be dispayed as "no test." Non-integer numbers of levels are converted to integers.
Each bar displays the current value entered in the number field to its left. A bar can also be used for inputting a value; simply click the mouse at the desired point along the center of the scale. Or you can drag the mouse along a bar to watch the power update continuously. (There are some heavy-duty calculations going on, however, and it is possible that the updates will lag behind.) The numerical scale for a set of bars can be altered if needed.
Each set of bars has a numerical scale below it. At any given time, this scale will accomodate all the values displayed by the bar set. It is possible to expand or contract the scale: simply click somewhere along the line where the numerical tick labels are, and drag to a new position. The scale value where you clicked will be moved to the point where you let go. For example, if you click on "1.0" and drag it to "0.4", the tick mark for 1.0 will appear where the old tick mark was for 0.4, and the maximum point on the scale will be about 1.0/0.4 = 2.5 times what it was. You are not allowed to make the scale maximum smaller than the current maximum value of the corresponding bar set.
The Effect Advisor is a dialog, available from either the Options or Help menu, that can help determine an appropriate value to use for the effect size of a fixed effect. The design is based on a two-way layout, but it can be used for one factor by simply using just the marginal means for rows or columns. Hypothetical cell means or marginal means can be entered in the dialog, or menu options are available for minimum-SD, maximum-SD, and uniformly spaced scenarios. It is also easy to rescale or recenter the hypothetical means, based on either the range or the SD.
Follow this link to obtain a tutorial and a deeper explanation of the methods.