expand on "equivalent"

Author: drbenvincent

docs/source/design_notation.md

@@ -22,9 +22,11 @@ This would allow us to estimate how the group was changing over time before the
 
 ## Nonequivalent group designs
 
-In randomized experiments, with large enough groups, the randomization process should ensure that the treatment and control groups are equivalent. However, in quasi-experimental designs, with non-random (`NR`) allocation, we could expect there to be differences between the treatment and control groups. This poses some challenges in making strong causal claims about the impact of the treatment.
+In randomized experiments, with large enough groups, the randomization process should ensure that the treatment and control groups are approximately equivalent in terms of their attributes. This is positive for causal inference as we can be more sure that differences between control and test groups are due to treatment exposure, not because of differences in attributes of the groups.
 
-For example, in the simplest {term}`nonequivalent group design<NEGD>`, we have two groups, one treated and one not treated, and just one posttest. See p114 of {cite:t}`reichardt2019quasi`.
+However, in quasi-experimental designs, with non-random (`NR`) allocation, we could expect there to be differences between the treatment and control groups' attributes. This poses some challenges in making strong causal claims about the impact of the treatment - we can't be sure that differences between the groups at the posttest are due to the treatment, or due to pre-existing differences between the groups.
+
+In the simplest {term}`nonequivalent group design<NEGD>`, we have two groups, one treated and one not treated, and just one posttest. See p114 of {cite:t}`reichardt2019quasi`.
 
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docs/source/glossary.rst

@@ -48,7 +48,7 @@ Glossary
 
    Non-equivalent group designs
    NEGD
-      A quasi-experimental design where units are assigned to conditions non-randomly, and not according to a running variable (see Regression discontinuity design).
+      A quasi-experimental design where units are assigned to conditions non-randomly, and not according to a running variable (see Regression discontinuity design). This can be problematic when assigning causal influence of the treatment - differences in outcomes between groups could be due to the treatment or due to differences in the group attributes themselves.
 
    One-group posttest-only design
       A design where a single group is exposed to a treatment and assessed on an outcome measure. There is no pretest measure or comparison group.