"Statisticians can calculate the probability that such random samples represent the population; this is usually expressed in terms of sampling error [...]. The real problem is that few samples are random. Even when researchers know the nature of the population, it can be time-consuming and expensive to draw a random sample; all too often, it is impossible to draw a true random sample because the population cannot be defined. This is particularly true for studies of social problems. [...] The best samples are those that come as close as possible to being random." (Joel Best, "Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists", 2001)
"[...] it is while doing mathematical research that one truly comes to see the beauty of mathematics. It faces you in those moments when the underlying simplicity of a question appears and its meaningless complications can be forgotten. In those moments a piece of a colossal logical structure is illuminated, and some of the meaning hidden in the nature of things is finally revealed." (David Ruelle, "The Mathematician's Brain", 2007)
"Under normal conditions the research scientist is not an innovator but a solver of puzzles, and the puzzles upon which he concentrates are just those which he believes can be both stated and solved within the existing scientific tradition." (Thomas S Kuhn, "The Essential Tension: Selected Studies in Scientific Tradition and Change", 2011)
"Meta-analytic thinking is the consideration of any result in relation to previous results on the same or similar questions, and awareness that combination with future results is likely to be valuable. Meta-analytic thinking is the application of estimation thinking to more than a single study. It prompts us to seek meta-analysis of previous related studies at the planning stage of research, then to report our results in a way that makes it easy to include them in future meta-analyses. Meta-analytic thinking is a type of estimation thinking, because it, too, focuses on estimates and uncertainty." (Geoff Cumming, "Understanding the New Statistics", 2012)
"Statistical cognition is concerned with obtaining cognitive evidence about various statistical techniques and ways to present data. It’s certainly important to choose an appropriate statistical model, use the correct formulas, and carry out accurate calculations. It’s also important, however, to focus on understanding, and to consider statistics as communication between researchers and readers."
"Another way to secure statistical significance is to use the data to discover a theory. Statistical tests assume that the researcher starts with a theory, collects data to test the theory, and reports the results - whether statistically significant or not. Many people work in the other direction, scrutinizing the data until they find a pattern and then making up a theory that fits the pattern."
"How can we tell the difference between a good theory and quackery? There are two effective antidotes: common sense and fresh data. If it is a ridiculous theory, we shouldn’t be persuaded by anything less than overwhelming evidence, and even then be skeptical. Extraordinary claims require extraordinary evidence. Unfortunately, common sense is an uncommon commodity these days, and many silly theories have been seriously promoted by honest researchers."
"These practices - selective reporting and data pillaging - are known as data grubbing. The discovery of statistical significance by data grubbing shows little other than the researcher’s endurance. We cannot tell whether a data grubbing marathon demonstrates the validity of a useful theory or the perseverance of a determined researcher until independent tests confirm or refute the finding. But more often than not, the tests stop there. After all, you won’t become a star by confirming other people’s research, so why not spend your time discovering new theories? The data-grubbed theory consequently sits out there, untested and unchallenged."
"A conceptual model is a framework that is initially used in research to outline the possible courses of action or to present an idea or thought. When a conceptual model is developed in a logical manner, it will provide a rigor to the research process." (N Elangovan & R Rajendran, "Conceptual Model: A Framework for Institutionalizing the Vigor in Business Research", 2015)
"Even properly done statistics can’t be trusted. The plethora of available statistical techniques and analyses grants researchers an enormous amount of freedom when analyzing their data, and it is trivially easy to ‘torture the data until it confesses’." (Alex Reinhart, "Statistics Done Wrong: The Woefully Complete Guide", 2015)
"The correlational technique known as multiple regression is used frequently in medical and social science research. This technique essentially correlates many independent (or predictor) variables simultaneously with a given dependent variable (outcome or output). It asks, 'Net of the effects of all the other variables, what is the effect of variable A on the dependent variable?' Despite its popularity, the technique is inherently weak and often yields misleading results. The problem is due to self-selection. If we don’t assign cases to a particular treatment, the cases may differ in any number of ways that could be causing them to differ along some dimension related to the dependent variable. We can know that the answer given by a multiple regression analysis is wrong because randomized control experiments, frequently referred to as the gold standard of research techniques, may give answers that are quite different from those obtained by multiple regression analysis." (Richard E Nisbett, "Mindware: Tools for Smart Thinking", 2015)
"Collecting data through sampling therefore becomes a never-ending battle to avoid sources of bias. [...] While trying to obtain a random sample, researchers sometimes make errors in judgment about whether every person or thing is equally likely to be sampled."
"Samples give us estimates of something, and they will almost always deviate from the true number by some amount, large or small, and that is the margin of error. […] The margin of error does not address underlying flaws in the research, only the degree of error in the sampling procedure. But ignoring those deeper possible flaws for the moment, there is another measurement or statistic that accompanies any rigorously defined sample: the confidence interval."
"The job of the statistician is to formulate an inventory of all those things that matter in order to obtain a representative sample. Researchers have to avoid the tendency to capture variables that are easy to identify or collect data on - sometimes the things that matter are not obvious or are difficult to measure."
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