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**TOOLS>STATISTICS>COMPARE AGGREGATE PROXIMITY MATRICES>PARTITION**

**PURPOSE **Use a permutation test to compare proximity matrices aggregated from a cognitive social structure into two mutually exclusive groups.

**DESCRIPTION **To compare aggregated proximity matrices from a partition of the respondents into two mutually exclusive groups Eg male and female, 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)

**Partition Vector**

** **The name of an Ucinet dataset.To partition the matrices of the data matrix into groups, specify a blocking vector by giving the dataset name, a dimension and an integer value. For example, to use the second row of a dataset called ATTRIB, enter "ATTRIB ROW 2". The program will then read the second row of ATTRIB and use that information to sort the matrices. All matrices with identical values on the criterion vector (i.e. the second row of attrib) will be placed in the same group. There should only be two groups and so the vector should only contain two different values. The partition can also be typed in directly so that 1 1 2 1 2 2 2 places matrices 1,2 and 4 in one group and matrices 3,5,6 and 7 in the other group.

**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