# Presentation of the Data

# Presentation of the Data

From the 1994/1995 ISE Year Book group 86 provided the initial list of quoted real estate companies. Group 86 is comprised of companies in the real estate business whose income from unrelated business amounts to no more than 60% of profits. This list was then modified on three grounds so as to include only those companies:

- listed on the ISE before 1
^{st}February, 1983 for inclusion in the ten year study, or before 1^{st}February, 1988 for the five year study; - in Group 86 throughout the period; and
- for which a clean price series was available.

Seventy companies complied with the criteria for the five year study, of which 44 had been in the list since 1^{st} February, 1983. A list of these companies is contained in tables B.1, and B.2. Real estate companies which failed to meet all the criteria are listed in tables B.3, and B.4.

Adjusted and unadjusted share price data was obtained from Datastream. This was then modified to include dividends, for which data was provided by Extel.

### Test Statistics

Three statistical methods of assessing the correlation of ranked series were used, namely the Kendall *τ*, Spearman's R and Gamma. Spearman's R is the least restrictive of the three, assuming only that the series under consideration were measured on an ordinal (rank order) scale i. e. that the individual observations could be sorted into two ranked series.

The Kendall *τ* is equivalent to Spearman's R as to underlying assumption. It is also comparable in terms of its statistical power. However, the Kendall *τ* and Spearman's R are not usually identical in magnitude, as their underlying logic - as well as their method of computation - is markedly different. Siegel and Castellan [1988] express the relationship of the two measures in terms of the inequality:

-1 ≤ 3 Kendall *τ *- 2 Spearman R ≤ 1

More importantly, the Kendall *τ* and Spearman's R are interpreted differently. Kendall's *τ* represents a probability. That is, it represents the difference between the probability of the two variables in the observed data being in the same order, and the probability that the two variables are in different orders. Spearman's R can be thought of as the regular Pearson product moment correlation coefficient. It is similarly measured in terms of the proportion of variability accounted for, except that Spearman's R is computed from ranks.

The Gamma statistic is preferable to either the Kendall *τ* or Spearman's R when the data contains many tied observations. Gamma's underlying assumptions are equivalent to both the Kendall *τ* and Spearman's R. However, in terms of its interpretation and computation it is more akin to the Kendall *τ* than Spearman's R. Gamma is also a probability. Specifically, it is computed as the difference between the probability of the rank ordering of the two variables agreeing and the probability of them disagreeing, divided by 1 minus the probability of ties. Thus, Gamma is basically equivalent to Kendall *τ*, except that ties are explicitly taken into account.