A combination of hypothesis testing and confidence interval construction is often used in social and behavioral science studies. Sometimes confidence intervals are computed or reported only if a null hypothesis is rejected, perhaps to see whether the range of values is of practical importance. Sometimes they are constructed or reported only if a null hypothesis is accepted, in order to assess the range of plausible nonnull values due to inadequate power to detect them. Even if always computed, they are interpreted differently, depending on whether the null value is or is not included. Furthermore, many studies in which the null hypothesis is not rejected are never published (the “file drawer” problem). This article discusses the coverage probability of nominal 1− α confidence intervals when examining intervals that do or do not cover some specified null value, usually zero. A briefer treatment considers interval coverage when undesirable results are suppressed. The coverage probability of such conditional confidence intervals may be very far from the nominal value. The magnitude of the effect of selection on interval coverage probability and possible resultant biases in inference are illustrated, and discussed in relation to effect sizes of importance in social and behavioral science research and to estimation of effect sizes.