We construct Wald-type tests for hypothesis testing based on treatment assignments by adaptive designs. Asymptotic distributions of the Wald-type statistics are also derived. When the trial involves two treatments and a single covariate, we show that the choice of an adaptive design influences the statistical power of the test via the following quantities: (i) the target allocation proportion, (ii) the bias of the randomization procedure from the target, and (iii) the variability induced by the randomization process (design variability). Furthermore, we show that as design variability decreases, the statistical power increases. In this study, the efficiency of statistical inference is measured by the power of the tests and the ethics of the clinical trial or well-being of participating patients by the success rate of treatments. We conduct an intensive simulation study to compare these measures of efficiency and ethics under three designs, namely, response-adaptive, covariate-adjusted response-adaptive, and completely randomized designs.