Description Usage Arguments Details Value Calculation Author(s) References See Also Examples
Calculate Slater distance.
1  distanceSlater(x, trim = 20, index = TRUE)

x 

trim 
The number of characters a construct or element is trimmed to (default is

index 
Whether to print the number of the construct or element
in front of the name (default is 
The euclidean distance is often used as a measure of similarity between
elements (see distance
. A drawback of this measure is that it
depends on the range of the rating scale and the number of constructs used,
i. e. on the size of a grid.
An approach to standardize the euclidean distance to make it independent from
size and range of ratings and was proposed by Slater (1977, pp. 94). The
'Slater distance' is the Euclidean distance divided by the expected distance.
Slater distances bigger than 1 are greater than expected, lesser than 1 are
smaller than expected. The minimum value is 0 and values bigger than 2 are
rarely found. Slater distances have been be used to compare interelement
distances between different grids, where the grids do not need to have the
same constructs or elements. Hartmann (1992) showed that Slater distance is
not independent of grid size. Also the distribution of the Slater distances
is asymmetric. Hence, the upper and lower limit to infer 'significance' of
distance is not symmetric. The practical relevance of Hartmann's findings
have been demonstrated by Schoeneich and Klapp (1998). To calculate
Hartmann's version of the standardized distances see
distanceHartmann
A matrix with Slater distances.
The Slater distance is calculated as follows.
For a derivation see Slater (1977, p.94).
Let matrix D contain the row centered ratings. Then
P = D^TD
and
S = tr(P)
The expected 'unit of expected distance' results as
U = (2S/(m1))^.5
where m denotes the number of elements of the grid. The standardized Slater distances is the matrix of Euclidean distances E devided by the expected distance U.
E/U
Mark Heckmann
Hartmann, A. (1992). Element comparisons in repertory grid technique: Results and consequences of a Monte Carlo study. International Journal of Personal Construct Psychology, 5(1), 4156.
Schoeneich, F., & Klapp, B. F. (1998). Standardization of interelement distances in repertory grid technique and its consequences for psychological interpretation of selfidentity plots: An empirical study. Journal of Constructivist Psychology, 11(1), 4958.
Slater, P. (1977). The measurement of intrapersonal space by Grid technique. Vol. II. London: Wiley.
1 2 3 4 5 6 7 8 9  distanceSlater(bell2010)
distanceSlater(bell2010, trim=40)
d < distanceSlater(bell2010)
print(d)
print(d, digits=4)
# using Norris and MakhloufNorris (problematic) cutoffs
print(d, cutoffs=c(.8, 1.2))

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