Although Wald tests form one of the major classes of hypothesis tests, they suffer from the well-known major drawback that they are not invariant under reparameterisation. This thesis uses the differential-geometric concept of a yoke to introduce one-parameter families of geometric Wald statistics, which are parameterisation-invariant statistics in the spirit of the traditional Wald statistics. Both the geometric Wald statistics based on the expected likelihood yokes and those based on the observed likelihood yokes are investigated. Bartlett-type adjustments of the geometric Wald statistics are obtained, in order to improve the accuracy of the chi-squared approximations to their distributions under the null hypothesis.