1.2: A "Geek Out" Explanation of Variation
- Page ID
- 48869
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)When something varies, we observe that the “it,” or the construct, is different across contexts. What are the ways that the “it” is different? There are only two ways things vary: by type and amount. By type, that means that whatever this “it” is one thing versus another thing. If we identify an “it” as gender (assuming the binary for the moment, and we will acknowledge the continuum of gender identity), we have two types: female and male (and in this world, females are first, most definitely they should be first, 😊). The number of “types” for it does vary according to one’s perspective. Race varies by type (assuming the U.S. government’s definition for the moment), and we have five types: White, Black, Latinx, Asian, and Middle Eastern.
For now, we will assume that “type” means sorting entities into one or another group, and there is no overlap between the groups. Honestly, the number of true “types,” or one thing is exclusively one type versus another, is mainly in the eye of the beholder. Yes, race can be subdivided further into additional types. There are different types of “Whites,” “Blacks,” “Latinos, Latina,” and so forth. Gender is now rightfully thought of as more than two types. Does it matter how many types there are? Yes, and it depends on how you conceptualize your research or curiosity. Save this placeholder for future discussions when we discuss variables.
First, things vary by type; second, they vary by amount. The amount is thought of in two ways. First, the amount can vary by counting or frequency, which ranges from more to less. A given classroom has more males than females. Someone is taller than another person. Someone has more money than another person. Someone drank more beer than another person. What is interesting about counting is that, ostensibly, counting is something that can be readily observed in the physical sense. You can observe more males than females; you can observe that someone is taller than the other; you can observe that someone has more money in their bank account than someone else; and you can observe that someone is drinking more glasses of beer than another person. For now, amounts that vary by counting are based on observing the physical characteristics of something.
And yes, things get interesting when you are trying to count something that is not readily observable or something that not everyone agrees should be counted. Is going one mile over the speed limit an observed count of speeding that warrants a ticket? Is going one degree over your body temperature an observed count that warrants you staying home from class and calling in sick? It gets interesting, so let’s take that ponderance for now.
The second way that an amount can vary is by intensity. What is interesting about intensity is that it is a perceived experience. Sometimes, you observe it directly; other times, you observe a manifestation of it. Take temperature. You can’t readily observe the temperature. However, you can feel it. One day it is hot, the other day it is not so hot. One day, you can observe a gentle, romantic rain; the other day, it is a raging lightning thunderstorm. No one would doubt that there is a difference in the temperature and in the rain because the experience of these “it’s”, or constructs, or phenomenon, varies.
Yes, we should acknowledge here that these issues all get interesting when applied to psychology topics. Take anxiety. Are there different types of anxiety? Generalized anxiety, social anxiety, and performance anxiety. Are there different amounts of anxiety that vary by amount in terms of counts? Number of anxious days in a week, increased heart rate when experiencing an anxious event, number of minutes per panic attack? Are there different amounts of anxiety that vary by amount in terms of intensity? Feeling scared to the point of avoidance, a feeling of anxiety that could be considered common, such as feeling anxious when giving a speech in front of a group, or feeling anxious about your safety at night? What about racism? Are there different types of racism, different amounts of racism that occur, different intensities of racism per event? Statistics and research can sort through these questions, but importantly, the theme of learning statistics and research rests on this premise. Your conceptualization of the issue you are curious about will drive the answer to these questions. The sorting and calibrating of the variation depends on whether the sorting and calibration system serves your purpose. This is another issue we will put in our pockets for now.


