This report contains many statistics. Some are numbers, such as the number of housing, food, and other programs in the United States. Others are simple percentages, such as the percentage of clients who are male. Still others are comparisons between two groups.

Confidence Intervals

A 90 percent criterion has been used for confidence intervals in this report.

• For numbers: Ninety percent confidence intervals are given for all estimates of numbers. A 90 percent confidence interval of ±400 means that if the reported number of soup kitchens is 4,000, 4,000 is the estimate of the number of soup kitchens and the probability is 90 percent that the number falls between 3,600 and 4,400.

• For percentages: Almost all simple percentages reported in the text have a 90 percent confidence interval of no more than ±4 percentage points. A 90 percent confidence interval of ±4 percentage points means that if the reported percent is 60, 60 is the best point estimate and the probability is 90 percent that the true percent falls between 56 and 64 percent. In the few instances when the confidence interval exceeds ±4 percentage points, the actual confidence interval is reported in a footnote with the following notation: 90% C.I. = X percentage points.

Statistical Significance of Comparisons

Comparisons are the other important way that information is presented in this report. When one reports that currently homeless clients include higher proportions of men than do formerly homeless clients, one is making a comparison. A statistical test is used to determine whether the difference between two percentages from different groups is "significant" in the statistical sense. As with confidence intervals, these tests can be calculated for different levels of statistical significance.

A 90 percent criterion has been used for all comparisons in this report. Thus, all comparisons discussed in the text are statistically significant at p = .10 or better, meaning that there is only a 10 percent chance that the difference is not a true difference.

Risk of False Positives

The reader should note that when one conducts a very large number of statistical significance tests, some of them are going to produce false positives, meaning that a difference between two numbers really is not significant, although the test says it is. Thousands of tests for statistical significance were performed on the data contained in this report. The reader is cautioned not to make too much of statistically significant but relatively small differences between populations. Rather, attention is best directed to serious or sizable differences between populations that are most likely to be stable and reliable, and also may have a chance to be important for policy purposes.

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