The author's intention in presenting this thesis is to develop new and simple to apply analytic methods to robustly estimate and compare Willingness to Pay (WTP) estimates and particularly to develop tests for statistical significance in these differences by estimating sampling variance appropriate to the method, taking into account the correlation between estimates incorporating the CV methods and or sampling designs. In particular I am interested in testing differences in estimated valuation statistics, such as Median WTP and thus overcoming aspects of non independence in the welfare estimates due to the design of the survey methodology e.g. in Double Bounded Dichotomous choices the estimate of the Double Bounded welfare estimate is not independent of the Single Bounded estimate because of the nature of the DB method. The use of replication here refers specifically to resampling methods that are used to provide variances of differences by simulating the sampling distribution by randomly resampling and thus quantifying the sampling variation. Here 3 of the 4 papers presented use either the bootstrap or jac1dmife method to produce the sampling variation of difference. The fourth paper uses a split sample approach to test individual WTP differences with a pooled Benefit Transfer estimate. The thesis presents four papers from 4 separate stated preference studies using different Contingent Valuation question formats which are used to evaluate WTP for: Improvement to Animal Welfare, Child safety on farms, Values of Forest recreation and Renewable Electricity generation in Chile. The theme of the thesis is to test for differences in estimates in WTP estimates between various within sample and across samples designs. These tests are used in 2 papers to test for the occurrences of inconsistency between SB and DB estimates and to test for anchoring of the second bid in relation to the level of the first bid offered amount in DBDC and thus to test for respondent behavioural effects such as Learning on inconsistency and anchoring.