Statistical data analysis can be subdivided into descriptive statistics and inferential statistics.
Descriptive statistics is concerned with exporing, visualising, and summarizing data but without fitting the data to any models. This kind of analysis is used to explore the data in the initial stages of data analysis. Since no models are involved, it can not be used to test hypotheses or to make testable predictions. Nevertheless, it is a very important part of analysis that can reveal many interesting features in the data.
Inferential statistics is the next stage in data analysis and involves the identification of a suitable model. The data is then fit to the model to obtain an optimal estimation of the model's parameters. The model then undergoes validation by testing either predictions or hypotheses of the model. Models based on a unique sample of data can be used to infer generalities about features of the whole population.
Much of climate analysis is still at the descriptive stage, and this often misleads climate researchers into thinking that statistical results are not as testable or as useful as physical ideas. This is not the case and statistical thinking and inference could be exploited to much greater benefit to make sense of the complex climate system.