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Contents
  1. About this book
  2. 1. Foreword
Planning a Study
  1. 2. A Few Words About Causality
  2. 3. Variance and Error
  3. 4. Design
  4. 5. Effect Size and Power
  5. 6. Sample Size
Describing and Preparing Data
  1. 7. Describing Data
  2. 8. Assumptions and Outliers
  3. 9. Normalization, Standardization, and Data Transformation
Comparing Groups
  1. 10. t-Tests and Their Rank-Based Alternatives
  2. 11. Equivalence Testing
  3. 12. ANOVA: Analysis of Variance
  4. 13. Factorial ANOVA and Interactions
  5. 14. ANCOVA: Analysis of Covariance
  6. 15. MANOVA: Multiple Analysis of Variance
Repeated Measures
  1. 16. Repeated-Measures ANOVA
  2. 17. Mixed Designs
Relationships Between Variables
  1. 18. Correlations
  2. 19. Chi-Square Test
  3. 20. Simple Linear Regression
  4. 21. Multiple Linear Regression Analysis
  5. 22. Categorical Predictors
  6. 23. Multiple Logistic Regression
  7. 24. Mediation Analysis
  8. 25. Path Analysis
  1. References

2 A Few Words About Causality

Causality is pervasive and ubiquitous. It helps build intellectual understanding, supports deliberations, is involved in planning, in technology, and even in language11 Words like break or move can serve as indicators of causal relationships or events. . It is part of everyday decisions, requiring implications and consequences to be considered in the process of evaluation and judgment. Causality is also a construct of intelligence. In Wesley C Salmon’s words (Salmon 1998):

1 Words like break or move can serve as indicators of causal relationships or events.

“If there had never been any human or other intelligent beings, there never would have been causes and effects - that is to say, there never would have been causal relations - in the physical universe the events would occur, but the causal relations would not exist.” (p. 8)

The understanding of causality is critical to the understanding of scientific research and everything that comes with it: research design, analysis, interpretations. This is because the drive to understand causality is deeply rooted in people’s need to make sense of the world around them, or to come to terms with it.

More commonly understood, causality represents the relationship between two or more entities where the behavior of one or more of them determines the behavior of the other(s). Fundamentally, causality arises from the empirical relations of:

Conjunctive plurality, which states that an effect is rarely the result of a single cause, was later added as another important attribute to emphasize the complexity of real-life processes which are the target of many research studies.

Another way of looking at the fundamental conditions for a causal relation to exist is that causal relations are durable. They always (or most of the time) hold true. That is, they are stable, consistent, and reliable and remain true across time and space and across instances of the same system (Sloman 2005). Considering that our lives as intelligent beings are predicated on the ability to predict, we have to be selective22 Most facts and information are useless for a specific decision. Taking everything possible into consideration overloads our minds and slows us down. Therefore, selectivity means that only those things that carry relevant information for the task or decision are to be considered to make the process fast and efficient. and attend to what is stable33 Stability, or invariance, is fundamental to the process of prediction because it highlights the variables that behave constantly across time and space and therefore make it easy to infer their future values or behavior from their current values or state.. Finding these durable relations is, in essence, the purpose of scientific inquiry.

2 Most facts and information are useless for a specific decision. Taking everything possible into consideration overloads our minds and slows us down. Therefore, selectivity means that only those things that carry relevant information for the task or decision are to be considered to make the process fast and efficient.

3 Stability, or invariance, is fundamental to the process of prediction because it highlights the variables that behave constantly across time and space and therefore make it easy to infer their future values or behavior from their current values or state.

When reasoning about causality it may be helpful to think of it as two intersecting processes in space and time (Salmon 1998). The intersection, while not a causal construct or concept in itself, can help distinguish causal phenomena from non-causal ones. At that intersection we can expect two major types of events: causal interactions and non-causal intersections. If both processes exit the intersection in a changed state and that changed state persists beyond the place/time of intersection we have a causal interaction44 For example, when a bullet hits a target, both the bullet and the target are affected at the point of intersection and in the future. The target ends up with a whole and the bullet loses energy.. Alternatively, if either or none of the processes is changed, we are looking at a non-causal intersection55 Think of two beams of light that cross paths and intersect at a point. At that point they are just superimposed on each other, but neither affects the other. After they leave that point, they continue unaffected..

4 For example, when a bullet hits a target, both the bullet and the target are affected at the point of intersection and in the future. The target ends up with a whole and the bullet loses energy.

5 Think of two beams of light that cross paths and intersect at a point. At that point they are just superimposed on each other, but neither affects the other. After they leave that point, they continue unaffected.

While understanding causality is fundamental to both scientific and everyday reasoning there are many problems people have when dealing with causality and causally linked events. It is important for researchers to be aware that these issues and biases exist and to understand and make efforts to minimize their impact on a research study. For example, a few of these problems, relevant to designing research studies, are:

Understanding the concept of causality is valuable to the design of a research study, experimental or not. For example, for causality to exist, the cause and effect have to be observed (measured) many times (2 or 3 is not enough), proving that constant conjunction exists and therefore confirming the potential for the existence of a causal relationship. This is what, fundamentally, statistical analysis tries to do. Therefore, the study should be designed so that that is possible. The other attributes are helpful in guiding the design and interpretation. For example, temporal succession should guide not only the determination of which is the independent and which is the dependent variable, but also in the selection of the variables appropriate for the study. Contiguity is also helpful in the selection and definition of variables and can be used as a checkpoint in building the model to be tested. Conjunctive plurality helps by raising awareness about the fact that many events can participate in the onset of the effect and is useful in the selection and definition of the variables used to define the construct being studied.

For a causal relationship to be truly understood, one needs to answer three questions: what?, why?, how?. The what? questions is answered through statistical analysis and proves that constant conjunction happens while the other requirements for a causal relation to exist are met. The how? and why? questions provide an explanation of the mechanisms at work that underlie the causal relations as well as the reasoning for the purpose of the relationship and what it means for theory and practice.

Discovery, understanding, and documentation of causal relationships is, most of the time, the focus of most research studies that use quantitative approaches to understand concepts, constructs, and phenomena. This chapter just scratched the surface of a much larger conversation on causality as it relates to the scientific method reflected in quantitative research designs. Causality is both the starting point and the end goal of many statistical analysis methods and can be observed at work through the theory and practice of statistics. It is construct worth exploring and understanding and a conversation worth having as it will lead to better research designs, with higher quality findings. Do not stop here.

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