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Introduction (PDF) Welcome to what I believe will be one of the most important sections of the Sources of Statistical Biases Series: Measurement. Besides the existence of confounders, I strongly believe that the measurement of a construct represents one of the largest sources of statistical bias in all scientific disciplines. This belief stems from theContinue reading “Statistical Biases and Measurement: Introduction”

Introduction (PDF & R-Code) The previous entries have focused on the biases that can exist when generating causal inferences through methodological and statistical approaches. I know it is considerably difficult for researchers trained in experimental methods – such as myself in criminology – to discern that causal inferences can be generated without randomly assigning participantsContinue reading “Entry 12: The Inclusion of Non-Causally Associated Constructs and Reverse Causal Specifications”

Introduction (PDF & R-Code) Generating causal inferences is a difficult process. We can run a true experiment (i.e., a randomized controlled trial), however that can be ethically concerning when randomizing certain treatments. Alternatively, we can develop a Directed Acyclic Graph (DAG) and reduce the influence of confounders and colliders on our association of interest. OrContinue reading “Entry 11: Instrumental Variables”

Introduction (PDF & R-Code) You might have the thought of: I know the constructs that can confound, mediate, or moderate the association I am interested in, and I am surely not going to include a collider as a covariate in my regression model! You also, like a great student of causal inference, have embraced theContinue reading “Entry 10: The Inclusion and Exclusion of Descendants”

PDF & R-Code A variety of techniques can be used to simulate linear associations between a continuous independent variable and a normal continuous dependent variable in R. I, however, rely on the lesser employed process of specifying linear directed equations. Briefly, a linear directed equation can be simply thought of as a regression formula but,Continue reading “Simulating Linear Associations with Normal Continuous Variables”

Introduction (PDF & R-Code) When I state “X is a cause of Y”, I am inherently implying that variation in X caused variation in Y. This statement, however, does not provide any indication of how X caused variation in Y. The how is just as important, if not more important, than knowing the causal association.Continue reading “Entry 9: The Inclusion and Exclusion of Mediating and Moderating Mechanisms”

Introduction (PDF & R-Code) You might be saying that Entry 7 provides good evidence for why we should include numerous variables in a statistical model and hope they adjust for confounder bias. I mean…  in some sense… climate change can confound the association between unemployment rates and crime rates. While it does suggest that, itContinue reading “Entry 8: The Inclusion of Colliders (Collider Bias)”

Introduction (PDF) A modifier is a value we identify – either systematically or randomly – that is used to specify the relationship between two variables. Alongside the distributional commands, we can not conduct a comprehensive data simulation without modifiers. We can simply save a value as a letter or use the value independent of aContinue reading “Modifiers”

The results of the looped simulations were updated on 04/04/21. An oversight occurred in the initial looped simulation where all of the sample sizes equaled 10,000 cases. The results did not change by permitting the sample size to vary between 100 and 1,000. The interpretations made when the association between X and Y was specifiedContinue reading “Entry 7: The Exclusion of Confounders (Confounder Bias)”

Introduction (PDF & R-Code) Consistent with the goals of the series, we will discuss how to specify data simulations satisfying the assumptions – rules – that we want to exist within the data. Nevertheless, before we being defining relationships and constructing dataframes, we must learn how to specify a vector of values (e.g, a variable)Continue reading “Simulating Distributions & Variables In R”