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minor tweaks + additional glossary term
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docs/source/design_notation.md

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$O_1$ | $O_2$ | X | $O_3$ |
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This would allow us to estimate how the group was changing over time before the treatment was introduced. This could be used to make a stronger causal claim about the impact of the treatment.
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This would allow us to estimate how the group was changing over time before the treatment was introduced. This could be used to make a stronger causal claim about the impact of the treatment. We could use {term}`interrupted time series<ITS>` analysis to help here.
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## Nonequivalent group designs
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| $O_1$ | $O_2$ | $O_3$ | $O_4$ | X | $O_5$ | $O_6$ | $O_7$ | $O_8$ |
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You can see that this is an example of a pretest-posttest design with multiple pre and posttest measures.
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## Comparative interrupted time series designs
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The {term}`comparative interrupted time-series<CITS>` design incorporates aspects of **interrupted time series** (with only a treatment group), and **nonequivalent group designs** (with a treatment and control group). This design can be used to estimate the causal impact of a treatment by comparing the trajectory of the outcome variable before and after the treatment in the treatment group, and comparing this to the trajectory of the outcome variable in the control group. See p226 of {cite:t}`reichardt2019quasi`.
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## Regression discontinuity designs
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The design notation for {term}`regression discontinuity designs<RDD>` are different from the others and take a bit of getting used to. We have two groups, but allocation to the groups are determined by a units' relation to a cutoff point `C` along a running variable. Also, $O_1$ now represents the value of the running variable, and $O_2$ represents the outcome variable. See p169 of {cite:t}`reichardt2019quasi`. This will make more sense if you consider the design notation alongside one of the example notebooks.
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The design notation for {term}`regression discontinuity designs<RDD>` are different from the others and take a bit of getting used to. We have two groups, but allocation to the groups are determined by a units' relation to a cutoff point `C` along a {term}`running variable`. Also, $O_1$ now represents the value of the running variable, and $O_2$ represents the outcome variable. See p169 of {cite:t}`reichardt2019quasi`. This will make more sense if you consider the design notation alongside one of the example notebooks.
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docs/source/glossary.rst

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Regression kink design
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A quasi-experimental research design that estimates treatment effects by analyzing the impact of a treatment or intervention precisely at a defined threshold or "kink" point in a quantitative assignment variable (running variable). Unlike traditional regression discontinuity designs, regression kink design looks for a change in the slope of an outcome variable at the kink, instead of a discontinuity. This is useful when the assignment variable is not discrete, jumping from 0 to 1 at a threshold. Instead, regression kink designs are appropriate when there is a change in the first derivative of the assignment function at the kink point.
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Running variable
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In regression discontinuity designs, the running variable is the variable that determines the assignment of units to treatment or control conditions. This is typically a continuous variable. Examples could include a test score, age, income, or spatial location. But the running variable would not be time, which is the case in interrupted time series designs.
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Sharp regression discontinuity design
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A Regression discontinuity design where allocation to treatment or control is determined by a sharp threshold / step function.
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