When we get into statistics, a major issue that we deal with is how well a model fits the data. We refer to this as “Goodness of fit” and what it represents is usually a summary of the differences between observed values and expected values. The reason for doing such tests is to gauge how well our model works to explain the observations.
This could be as simple as the relationship between the independent variable (the one which we control or change) and the dependent variable (the one on which the effect of changes in the independent variable is seen), to complex multivariate analyses which attempt to gauge the effect of multiple variables on a single variable.
Models are means to an end, they are the extension of a theory, and work to test how well that theory fits reality. They represent our hypothesis of cause and effect, based on the theory we have formulated about how something works. To give an example, if we wanted to know if there is a relationship between number of repetitions affect hypertrophy, we would formulate 2 hypotheses:
Null-hypothesis – There is no relationship between number of repetitions and muscle hypertrophy
Hypothesis 1 – There is a relationship between number of repetitions and muscle hypertrophy
We would then conduct an experiment where we take a sample, have them perform a given number of repetitions across a period of time at a frequency held constant, and then measure the change between the start of the experiment and the end of the experiment. From this we get an answer of whether the independent variable (number of repetitions) affects the dependent variable (hypertrophy). The results of this experiment could then be validated, replicated and serve as a foundation for future research into hypertrophy.
This research, and future research can then serve to guide us when we are aiming to gain more muscle so that we find the most efficient route between point A and point B. We began with a question “How does number of repetitions affect muscle hypertrophy“, we did our research, formulated a theory and then tested that theory in an experiment, the results of which are utilized to amend our model of reality, which can then be tested again.
This is how most research works, a researcher starts by wanting to answer a question, does research into the question, based on the question a theory is formulated, this theory is tested through observation or experiment, and the results of said experiments are then integrated into the theory.
Our goal when conducting research is to generate mind-independent information, meaning that human minds constantly generate cause and effect hypotheses, then test them against reality. However, we are also prone to many errors of reasoning that lead us to believing in false relationships, a prime example being the superstitions of various athletes or sports-teams.