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Correlation is a fundamental concept within statistics that, once understood, provides insight into more complex statistical models and ideas. From a conceptual standpoint, correlation summarizes the measured association between variables, meaning the extent to which one variable is affected by the other. Put another way, correlation is simply a measure of association.The term measured association carries a lot of meaning here, so let's unpack it. To calculate the correlation between variables, we first have to measure those variables. The term measured association rather than simply association is a hedge against the possibility that those measures could be inaccurate, and not truly reflect the thing we intend to measure. Science is cautious; and the terms we use reflect that caution. The word association refers to how the data points between variables trend relative to each other. If one goes up does the other go up as well? Or maybe it goes down? Or maybe the change in one does not systematically affect the the other. Of course, this means that we need multiple data points across variables to determine correlation; but more on that in a minute.Association as a concept is a singular thing, but correlation as a measurement is multiple things. There are a variety of way to calculate correlation; and each is responsive to two important data characteristics. The first characteristic is the type of data being analyzed. All data is not created equal. It comes in levels of measurement that are categorized from least to most detailed as: nominal, ordinal, interval, ratio. Nominal is often something like a discrete category (e.g., Democrat, Republican, Libertarian, Independent) and ratio is a continuous measurement where zero represents an absence of the variable (e.g., height, age). Ordinal and interval are somewhere between. The second characteristic is the trend within the data. Data comes in different types of distributions. Imagine having a list of test scores, placing them in order from lowest to highest, plotting them on a graph, and fitting a line that summarizes the trend of the data. That line may be straight (i.e., linear) or curved (non-linear). Correlation is calculated differently based on this trend within the data begin analyzed. When the data we have is at the interval or ratio level of measurement, and we expect the trend of the data to be essentially linear, correlation is measured with a statistic known as Pearson's r, or sometimes simply r. It is measured on a continuous decimal scale from -1 to 1 (Figure 1). The number we arrive upon, called a correlation coefficient, tells us the magnitude (i.e., strength) of the association between the measured variables and the direction (i.e., positive or negative) of that association.

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LaTeX is a powerful free and open-source academic writing system; however, it does come with a learning curve. This curve can be especially steep when trying to incorporate bibliographic references and formatting a document to the current writing style of the field - APA 6th edition. Anyone who has submitted a manuscript for publication is familiar with the trials and tribulations of formatting and citing sources. Any tool to help with this process is a welcome one. Although LaTeX comes close to APA compatibility natively, it doesn't quite nail it. This post describes how to set-up and integrate a powerful (and free) LaTeX editor with a powerful (and free) citation manager to assist with formatting and citing. To get started, you will need to download and install two programs. Texmaker: LaTeX editorZotero: citation managerThen download two files that will run on these programs.APA 6th File: LaTeX document formatting codeBetter BibTex: program for generating cite keysThese programs and files are compatible with the major operating systems. Installation with Windows and macOS is largely a matter of point and click. Installation on Linux requires a bit more know-how of course; and it's assumed that those using a Linux distribution are familiar with the processes for installing programs and various file extensions. If you are already familiar with the terminology of LaTeX and citation managers then read on. If not, it would be helpful to first review the key terms listed at the end of this post. Zotero Set-upZotero can be used separately as a reference manager, but its real utility comes from its ability to generate a bibliographic reference file (i.e., .bib file) that contains cite keys for each of your references. These cite keys are entered into a LaTeX document to generate citations. Although Zotero has a great deal of native functionality, some set-up is required for fluid integration with LaTeX. First, you need to install Better BibTex, a program for generating those cite keys.From the Zotero toolbar, navigate to: Tools > Add-ons > Extensions.Select the gear icon in the top-right corner and select ‘Install Add-on From File…’ Navigate to the folder where you saved the Better Bibtex file and install it. At this point you will need to restart Zotero to complete the install and auto-update to the most recent version of Better Bibtex. Navigate back to Extensions and make sure Better Bibtex is now listed. You may see an option for preferences. Don't worry about setting-up the Better BibTex preferences yet; that will be done in a moment.