national multiple family submetering and allocation billing program ...

confidence interval ranged from 49.9 to 53.3 kgal. This means that in 95 of 100 samples are
drawn this way, the actual annual water use per unit would be found within a range similarly
constructed.
Bivariate analyses. In order to examine the association of property characteristics with
water use, two types of bivariate analyses were performed. Using ANOVA (analysis of
variance), the relationship between water use and “categorical” variables such as the designation
of a property as a senior citizen/retirement community (“yes,” “no” or “don’t know”) was
examined. This test examines whether differences in the levels of the variable (water use in this
example) are different in the specified subgroups. Factors with p-values less than 0.05 were
considered “statistically significant,” meaning that if there were no difference, the probability of
seeing a result as or more extreme than that seen in the sample was less than 5%.
The relationship of continuous variables, such as average bedroom size or average rent,
with water use were examined using Pearson correlations. A correlation statistic is produced
which ranges from -1 to +1. Correlations of 0 indicate there is not a relationship between the
two variables, while those close to -1 or +1 indicate strong negative or positive relationships. A
p-value is shown, and in general, the 0.05 level is chosen to indicate statistical significance.
In addition, differences in characteristics among properties based on the water billing
method used (a categorical variable, designated as “in-rent or HOA,” “submetered,” “RUBS,”
“hot water hybrid,” or “other”) were examined using ANOVA for continuous variables and chisquare
for categorical variables. The chi-square test examines whether proportions are different
between two groups; for example, whether a similar or different proportion of properties are
considered retirement communities among the different billing types. A p-value is produced,
and factors with p-values of less than 0.05 were considered “statistically significant,” meaning
that if there were no difference, the probability of seeing a result as or more extreme than that
seen in the sample was less than 5%.
T-tests were used to test differences between water use estimates by billing method or by
survey source (e.g., comparing water use estimates of postcard survey respondents to manager
survey respondents). P-values are also produced for these tests.
Multivariate analyses. There were differences in the characteristics of in-rent properties
compared to the impact properties; for example, submetered properties were more likely to be
newer (41% were built after 1994 compared to 7% of in-rent properties), while RUBS properties
were more likely to be larger complexes (71% had 100 or more units, compared to 32% of in-
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