This procedure does not support case weights or split files. They will be ignored with a warning. Cases with missing data will be excluded listwise. Variable measurement levels are used to provide appropriate handling for categorical and continuous (scale) variables, so be sure that these are set correctly. The dialog box generates syntax for the STATS PERM extension command.
STATS PERM
DEPVAR = Dependent Variable*
INDVARS list of independent variables
INTERACTIONSA group of variables
INTERACTIONSB group of variables
INTERACTIONSC group of variables
ORDERA highest degree of interactions for INTERACTIONSA
ORDERB highest degree of interactions for INTERACTIONSB
ORDERC highest degree of interactions for INTERACTIONSC
IDVAR = ID variable, required if saving residuals or predicted values
RESVAR = name for new variable for residuals
PREDVAR = name for new variable for predicted values
/OPTIONS
NPERM= number of permutations to create
METHOD = method for generating permutations
PLOTCOEF = NO** or YES
/HELP
STATS PERM /HELP displays this information and does nothing else.
* Required
** Default
STATS PERM DEPVAR=salary INDVARS=gender jobtime
INTERACTIONSA = minority jobcat RESVAR=resids PREDVAR=preds IDVAR=id
/OPTIONS NPERM=10000 METHOD=FREEDMAN_LANE
/DISPLAY PLOTCOEF=no.
DEPVAR specifies a scale dependent variable.
INDVARS specifies independent variables to enter additively.
INTERACTIONSA Specifies independent variables to enter as interactions.
For a two group t test or anova model, specify the group variable (simple t test) or variables (anova and regression). Variables with a categorical measurement level will be converted to dummy variables. Variables in the INDVARS list will be additive, and variables in the INTERACTIONSA list will be multiplicative with all combinations included. For example, if there are three interaction variables, x, y, and z the model will include x, y, z, x*y, x*z, y*z, and x*y*z. Both categorical and scale variables can be used.
INTERACTIONSB and INTERACTIONSC allow for two additional groups of interaction variables.
ORDERA, ORDERB, and ORDERC specify the highest degree of the corresponding INTERACTIONS variable. By default, that is determined by the number of variables in the INTERACTIONS list, but you can limit it. In the previous example, specifying all two-way would include x, y, z, x*y, x*z, and y*z but not x*y*z. Since main effects for interaction variables are automatically included, you do not need to also list those variables in the Independent Variables box.
IDVAR, RESVAR, and PREDVAR specify an ID variable and names for new variables to hold the residuals and predicted values. The ID variable is required if either RESVAR or PREDVAR is specified. The ID values must be unique, and the input must be in ascending sort order.
NPERM specifies the number of permutations to generate. The default value is 5000.
METHOD specifies how to generate the permutations. There are seven choices. freedman_lane is the default.
When there are multiple independent variables involved, such as typical for anova and regression, for each test, one variable is selected at a time, and all the others are considered nuisance variables, Permutation tests assume exchangeability under the null hypothesis, but the nuisance variables violate this assumption, so the data are transformed in order to reduce the effect of the nuisance variables before performing the tests. The output shows all the estimated coefficients, each computed with the effect of the other variables removed.
The first reference below explains the seven methods available. Here is an extract from that documentation. y is the dependent variable, D is the matrix of nuisance variables, and X is the variable of interest.
The freedman_lane method works as follows: we first fit the “small” model which only uses the nuisance variables D as predictors. Then, we permute its residuals and add them to the fitted values. Theses steps produce the permuted response variable which constitutes the “new sample”. It is fitted using the unchanged design D and X. In this procedure, only the residuals are permuted and they are supposed to share the same expectation (of zero) under the null hypothesis. For each permutation, the effect of nuisance variables is hence reduced.
The manly method simply permutes the response (this method is sometimes called raw permutations). Even if this method does not take into account the nuisance variables, it still has good asymptotic properties when using studentized statistics.
draper_stoneman permutes the design of interest (note that without nuisance variables permuting the design is equivalent to permuting the response variable). However, this method ignores the correlation between D and X that is typically present in regressions or unbalanced designs.
For the dekker method, we first orthogonalize X with respect to D, then we permute the design of interest. This transformation reduces the influence of the correlation between D and X and is more appropriate for unbalanced design.
The kennedy method orthogonalizes all of the elements (y, D and X) with respect to the nuisance variables, removing the nuisance variables in the equation, and then permutes the obtained response. Doing so, all the design matrices lie in the span of X, a sub-space of observed design X and D. However this projection modifies the distribution of the residuals that lose exchangeability for original IID data).
The huh_jhun method is similar to kennedy but it applies a second transformation to the data to ensure exchangeability (up to the second moment. It implies that the P’s matrices for the huh_jhun method have smaller dimensions.
The terBraak method is similar to freedman_lane but uses the residuals of the full model. This permutation method creates a new response variable y∗ which assumes that the observed value of the estimate ˆ β|y is the true value of β. Computing the statistic using y*, X, D would not produce a permutation distribution under the null hypothesis. To circumvent this issue, the method changes the null hypothesis when computing the statistics at each permutation to H0 : β = ˆ β|y = (X⊤RDX)−1X⊤RDy|y. The right part of this new hypothesis corresponds to the observed estimate of the parameters of interest under the full model, and implicitly uses a pivotal assumption. Note that terBraak is the only method where the statistic computed with the identity permutation is different from the observed statistic. The notation RD,X means that the residuals matrix is based on the concatenation of the matrices D and X. See Section 5.2 for advises on the choice of the method.
PLOTCOEF specifies whether to plot the coefficient distributions. If there are many variables, it may be necessary to stretch out the plot in the SPSS Viewer window.
This procedure uses the R permuco package by Frossard J. Renaud from CRAN.Frossard J, Renaud O (2021). “Permutation Tests for Regression, ANOVA, and Comparison of Signals: The permuco Package.” Journal of Statistical Software, 99(15), 1–32. doi:10.18637/jss.v099.i15. permuco
© Copyright Jon K Peck 2025