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**TOOLS>STATISTICS>COMPARE AGGREGATE PROXIMITY MATRICES>OVERLAPPING GROUPS**

**PURPOSE **Use a permutation test to compare proximity matrices aggregated from a cognitive social structure into two groups which may overlap.

**DESCRIPTION **To compare aggregated proximity matrices from a partition of the respondents into two possibly overlapping groups Eg Smokers and Drinkers, we begin by correlating the two matrices (or computing a dissimilarity measure). This is our observed test statistic. Then we go back to the individual level data and divide the respondents into two groups at random. We then aggregate the matrices separately for each group, obtaining an aggregate proximity matrix for each group. Next, we correlate these matrices (or compute dissimilarity measure) and store the result. This process is repeated thousands of times to generate a distribution of (dis)similarities under the null hypothesis of independence (i.e., judged proximities are independent of gender). We then count the proportion of correlations (or dissimilarity measures) that are as small (or as large) as the observed measure. The proportion of correlations as small as the observed (or, equally, the proportion of dissimilarity coefficients as large as the observed) gives the p-value: the likelihood that the difference we see could be obtained by chance. Note that the aggregation is simply the mean of the matrices.

**PARAMETERS** **Input Dataset**

** **Name of dataset containing the cognitive social structure.

Data type: Valued graph, multirelational.

** **

** Utilize diagonal values **(Default=No)

If YES diagonal values are included

**Data are symmetric **(Default = No)

**Group Indicator Matrix**

** **The name of an Ucinet dataset. This dataset must contain a row for each actor and two columns representing the two groups. The (i,j)th entry is a 1 if actor i is in group j (j= 1 or 2) and zero otherwise. The matrix is simply a standard incidence matrix with two columns.

**No. of permutations **(Default =2000)

Number of Permutations used in the permutation test.

**Output Dataset **(Default = 'agprox')

Name of file that will contain the mean of the matrices corresponding to each group. Two files will be produced one for each group and they will be called agprox1 and agprox2. These are not displayed in the logfile.

** **

**LOG FILE **A listing of the partitions used in the aggregation procedure, followed by the sizes of the two groups, the number of observations and the number of permutations used in the test. The observed correlation and Euclidean distance are the values calculated between the two aggregated matrices. This is followed by the average correlation and Euclidean distance over all the random permutations. Finally the number of times the correlation and regression were as high or higher and as low or lower are given as a probability. These values are used to determine the significance of the observed values.

**TIMING **O(N^2)

**COMMENTS **None

**REFERENCES** Borgatti, S.P. () A Statistical Method for Comparing Aggregate Data Across a Priori Groups