William M Bolstad - Collected Quotes

"Data almost always contain uncertainty. This uncertainty may arise from selection of the items to be measured, or it may arise from variability of the measurement process. Drawing general conclusions from data is the basis for increasing knowledge about the world, and is the basis for all rational scientific inquiry. Statistical inference gives us methods and tools for doing this despite the uncertainty in the data. The methods used for analysis depend on the way the data were gathered. It is vitally important that there is a probability model explaining how the uncertainty gets into the data." (William M Bolstad & James M Curran, "Introduction to Bayesian Statistics" 3^rd Ed., 2017)

"Independence of two events is not a property of the events themselves, rather it is a property that comes from the probabilities of the events and their intersection. This is in contrast to mutually exclusive events, which have the property that they contain no elements in common. Two mutually exclusive events each with non-zero probability cannot be independent. Their intersection is the empty set, so it must have probability zero, which cannot equal the product of the probabilities of the two events!" (William M Bolstad & James M Curran, "Introduction to Bayesian Statistics" 3^rd Ed., 2017)

"Since we cannot completely eliminate uncertainty, we need to model it. In real life when we are faced with uncertainty, we use plausible reasoning. We adjust our belief about something, based on the occurrence or nonoccurrence of something else." (William M Bolstad & James M Curran, "Introduction to Bayesian Statistics" 3^rd Ed., 2017)

"Statistics is the science that relates data to specific questions of interest. This includes devising methods to gather data relevant to the question, methods to summarize and display the data to shed light on the question, and methods that enable us to draw answers to the question that are supported by the data." (William M Bolstad & James M Curran, "Introduction to Bayesian Statistics" 3^rd Ed., 2017)

"The lack of direct control means the outside factors will be affecting the data. There is a danger that the wrong conclusions could be drawn from the experiment due to these uncontrolled outside factors. The important statistical idea of randomization has been developed to deal with this possibility. The unidentified outside factors can be 'averaged out' by randomly assigning each unit to either treatment or control group. This contributes variability to the data. Statistical conclusions always have some uncertainty or error due to variability in the data. We can develop a probability model of the data variability based on the randomization used. Randomization not only reduces this uncertainty due to outside factors, it also allows us to measure the amount of uncertainty that remains using the probability model. Randomization lets us control the outside factors statistically, by averaging out their effects." (William M Bolstad & James M Curran, "Introduction to Bayesian Statistics" 3^rd Ed., 2017)

"The goal of scientific inquiry is to gain new knowledge about the cause-and-effect relationship between a factor and a response variable. We gather data to help us determine these relationships and to develop mathematical models to explain them." (William M Bolstad & James M Curran, "Introduction to Bayesian Statistics" 3^rd Ed., 2017)

"The scientific method searches for cause-and-effect relationships between an experimental variable and an outcome variable. In other words, how changing the experimental variable results in a change to the outcome variable. Scientific modeling develops mathematical models of these relationships. Both of them need to isolate the experiment from outside factors that could affect the experimental results. All outside factors that can be identified as possibly affecting the results must be controlled." (William M Bolstad & James M Curran, "Introduction to Bayesian Statistics" 3^rd Ed., 2017)

"Variability in data solely due to chance can be averaged out by increasing the sample size. Variability due to other causes cannot be." (William M Bolstad & James M Curran, "Introduction to Bayesian Statistics" 3^rd Ed., 2017)