You need to answer several questions before selecting the right statistics for your Ph.D. dissertation. What kind of data have you collected? Does the data fit the normal or the Gaussian distribution? What kind of comparisons would you make in your dissertation? The decisions taken based on these answers will pave the way for choosing the right statistics for your dissertation.
The parameters for choosing the statistics
One decision that needs to be made is based on whether or not to use parametric tests. If you have sampled your data from a Gaussian distribution, you may use parametric tests such as the ANOVA (analysis of variance) or the T-test. If you have collected data in the form of rankings or categories, then you may use non-parametric tests such as Mann-Whitney, chi square, or Kruskal-Wallis tests. Another major factor that would influence the choice of statistics in your dissertation would be the problem or the question your dissertation addresses. You would probably begin with a description of the data you have collected already. What are the average or the mean values of your distributions? What are the spread of scores? What was the mode as seen in the standard deviation?
The other parameters
How many independent variables were there in the study? How many dependent variables have you collected the data for? This will help you to clarify what kind of comparisons you are making. Are you comparing a group of things to another? Are you comparing a single variable with another? Are you trying to make predictions in your research? The answers that you give to these questions will help you determine exactly what statistical method to choose for your dissertation or what would be right for your dissertation. You can eventually determine whether to use a parametric or a non-parametric statistical method for your research.