### Abstract

This study uses a within study comparison design (WSC) to conduct a novel test of how much causal bias results when researchers use a nonequivalent comparison group design type (NECGD) that combines: (a) a comparison group local to the treatment group; (b) a pretest measure of the study outcome; and (c) a rich set of 19 other multidimensional covariates. Most prior WSCs have dealt with the bias consequences of only 1 of these, revealing that each routinely reduces bias but does not necessarily eliminate it. Thus, a need exists to identify NECGDs that more robustly eliminate bias. This study is the first to examine how combining the 3 bias-control mechanisms above affects bias. The intervention we examine is a prekindergarten mathematics curriculum, for which a randomized control trial (RCT) produces a positive 1-year math effect. Final bias in the NECGD is assessed as the difference between its impact and that of the RCT when each design has the same intervention, outcome, and estimand. Over the many specifications we explore, NECGD bias is less than .10 standard deviations, indicating that minimal bias results when an NECGD combines all 3 design elements. The factorial design we use in this study also tests the bias associated with seven other NECGD types. Comparing the total pattern of results shows that the minimal bias when all 3 elements are combined is uniquely attributable to the locally chosen comparison group and not the availability of a pretest or other covariates. In actual research practice, it is impossible to predict in advance which design elements will affect bias by how much in any given application. So further research is needed to probe whether the simultaneous use of all three design elements achieves minimal bias dependably across diverse applications and not just in the preschool math context examined here.

Original language | English (US) |
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Journal | Psychological methods |

DOIs | |

State | Accepted/In press - Jan 1 2020 |

### Keywords

- Bias after local comparison group choice
- Causation, observational studies
- Use of pretest and of a rich set of other covariates
- Within-study comparison

### ASJC Scopus subject areas

- Psychology (miscellaneous)

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## Cite this

*Psychological methods*. https://doi.org/10.1037/met0000260