"A statistical index has all the potential pitfalls of any descriptive statistic - plus the distortions introduced by combining multiple indicators into a single number. By definition, any index is going to be sensitive to how it is constructed; it will be affected both by what measures go into the index and by how each of those measures is weighted." (Charles Wheelan, "Naked Statistics: Stripping the Dread from the Data", 2012)
"Correlation measures the degree to which two phenomena are related to one another. [...] Two variables are positively correlated if a change in one is associated with a change in the other in the same direction, such as the relationship between height and weight. [...] A correlation is negative if a positive change in one variable is associated with a negative change in the other, such as the relationship between exercise and weight." (Charles Wheelan, "Naked Statistics: Stripping the Dread from the Data", 2012)
"Descriptive statistics give us insight into phenomena that we care about. […] Although the field of statistics is rooted in mathematics, and mathematics is exact, the use of statistics to describe complex phenomena is not exact. That leaves plenty of room for shading the truth." (Charles Wheelan, "Naked Statistics: Stripping the Dread from the Data", 2012)
"Even if you have a solid indicator of what you are trying to measure and manage, the challenges are not over. The good news is that 'managing by statistics' can change the underlying behavior of the person or institution being managed for the better. If you can measure the proportion of defective products coming off an assembly line, and if those defects are a function of things happening at the plant, then some kind of bonus for workers that is tied to a reduction in defective products would presumably change behavior in the right kinds of ways. Each of us responds to incentives (even if it is just praise or a better parking spot). Statistics measure the outcomes that matter; incentives give us a reason to improve those outcomes." (Charles Wheelan, "Naked Statistics: Stripping the Dread from the Data", 2012)
"Even in the best of circumstances, statistical analysis rarely unveils “the truth.” We are usually building a circumstantial case based on imperfect data. As a result, there are numerous reasons that intellectually honest individuals may disagree about statistical results or their implications. At the most basic level, we may disagree on the question that is being answered." (Charles Wheelan, "Naked Statistics: Stripping the Dread from the Data", 2012)
"If the distance from the mean for one variable tends to be broadly consistent with distance from the mean for the other variable (e.g., people who are far from the mean for height in either direction tend also to be far from the mean in the same direction for weight), then we would expect a strong positive correlation. If distance from the mean for one variable tends to correspond to a similar distance from the mean for the second variable in the other direction (e.g., people who are far above the mean in terms of exercise tend to be far below the mean in terms of weight), then we would expect a strong negative correlation. If two variables do not tend to deviate from the mean in any meaningful pattern (e.g., shoe size and exercise) then we would expect little or no correlation." (Charles Wheelan, "Naked Statistics: Stripping the Dread from the Data", 2012)
"Once these different measures of performance are consolidated into a single number, that statistic can be used to make comparisons […] The advantage of any index is that it consolidates lots of complex information into a single number. We can then rank things that otherwise defy simple comparison […] Any index is highly sensitive to the descriptive statistics that are cobbled together to build it, and to the weight given to each of those components. As a result, indices range from useful but imperfect tools to complete charades." (Charles Wheelan, "Naked Statistics: Stripping the Dread from the Data", 2012)
"Probability is the study of events and outcomes involving an element of uncertainty." (Charles Wheelan, "Naked Statistics: Stripping the Dread from the Data", 2012)
"Regression analysis, like all forms of statistical inference, is designed to offer us insights into the world around us. We seek patterns that will hold true for the larger population. However, our results are valid only for a population that is similar to the sample on which the analysis has been done." (Charles Wheelan, "Naked Statistics: Stripping the Dread from the Data", 2012)
"Statistics cannot be any smarter than the people who use them. And in some cases, they can make smart people do dumb things." (Charles Wheelan, "Naked Statistics: Stripping the Dread from the Data", 2012)
"The correlation coefficient has two fabulously attractive characteristics. First, for math reasons that have been relegated to the appendix, it is a single number ranging from –1 to 1. A correlation of 1, often described as perfect correlation, means that every change in one variable is associated with an equivalent change in the other variable in the same direction. A correlation of –1, or perfect negative correlation, means that every change in one variable is associated with an equivalent change in the other variable in the opposite direction. The closer the correlation is to 1 or –1, the stronger the association. […] The second attractive feature of the correlation coefficient is that it has no units attached to it. […] The correlation coefficient does a seemingly miraculous thing: It collapses a complex mess of data measured in different units (like our scatter plots of height and weight) into a single, elegant descriptive statistic." (Charles Wheelan, "Naked Statistics: Stripping the Dread from the Data", 2012)
"The problem is that the mechanics of regression analysis are not the hard part; the hard part is determining which variables ought to be considered in the analysis and how that can best be done. Regression analysis is like one of those fancy power tools. It is relatively easy to use, but hard to use well - and potentially dangerous when used improperly." (Charles Wheelan, "Naked Statistics: Stripping the Dread from the Data", 2012)
"There are limits on the data we can gather and the kinds of experiments we can perform."(Charles Wheelan, "Naked Statistics: Stripping the Dread from the Data", 2012)
"While the main point of statistics is to present a meaningful picture of things we care about, in many cases we also hope to act on these numbers." (Charles Wheelan, "Naked Statistics: Stripping the Dread from the Data", 2012)
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