- 1. not only for the total 1. not only for the total median values of the gammas for FA are greater than those for SC set of 36 coefficients but also for each of the three sub-categories ( Mono-Media/Hetero- and However, with Function, Hetero-Media/Mono-Function, Hetero-Media/Hetero-Function). respect to (as reflected by the corresponding values of , the reverse ordering dispersion range) holds. The range or spread between the maximum and minimum gammas for the SC ratings exceeds than for FA ratings, overall and for each of the 3 sub-categories.
- Such a pattern of difference in the levels and dispersions of the pairwise association would arise if informants were more discriminating in the making assessments of SC than of FA. To investigate this possibility, we analyzed the extent to which the rankings of the pairwise case A coefficients varied across the 3 ( ).The gamma mono-media/hetero-functions triangles coefficients within each triangle were for the same set of 3 different pairs of the same 3 functions while the media condition was different for each triangle. A similar analysis was made of the case B consistency of the ranking for the 3 comprising . hetero-media/mono-media diagonals
- In Table B3, we report the value of Kendall coefficient of concordance (W), a non-parametric measure of the degree of agreement among m(m>2) sets of rankings of k objects that varies from 0 to +1 (Kendall and Babington Smith 1939, Teles 2012). W=1 when there is perfect agreement among the msets of rankings, if there are no ties. Wcan take the minimum value of zero when there is no agreement, only if m(k+1) is even (Teles 2012, p.751). The latter condition is satisfied case A here since k=3=m for both the mono-method/hetero-functions triangles ( ) and the hetero- case B media/mono-media diagonals Following Marozzi's (2014) recommendation for small ( ). sized samples, we test the null hypothesis that rankings are independent of one another and report p-value derived from the exact distribution of the test statistic (W) by permuting the k ranks in all possible ways, as discussed in Kendall and Babington Smith (1937, pp.277-278.) In the present case where m=k=3, this test is equivalent to testing that the population value of W=0.
- Referring to the p values shown in Table B3, we find that for both the FA and SA ratings, the null hypothesis of no agreement (W=0) cannot be rejected at conventional levels of significance in either case A or case B. In all four cases, the associated p values (one tail test) exceeded levels that might suggest even marginal significance; the smallest p value being 0.194. Thus, these results do not indicate that informants' ratings of FA and SC differed with respect to discriminant validity.
- 2. The levels of the median values for these Gammas shown in the Hetero-Media/ Hetero-Function Table B3 are .615 and .538 for the 'Frequency' and 'Similarity' ratings, respectively. What accounts for this substantial level of association across this set of seemingly unrelated if not independent pairings of media/function conditions? Variations across firms attributable to differences among firms with respect to the latent construct (i.e., FA or SC), or to differences among informants with respect to some source of systematic or random measurement error?
- We are unable to assess this issue directly with the data available from the study we conducted, which represented a single method/multi-construct design. However, the problem could be addressed by a study that employed a full-scale multi-method/multi construct design that would allow both convergent and discriminant validity to be assessed and enable comparisons to be made between the influence on pairwise associations of systematic and/or random measurement error components present in the ratings vs. that attributable to covariation between the 'true' values of the underlying constructs.