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Cause and Effect
Cause and effect refers to a relationship between two phenomena in which one phenomenon is the reason behind the other. For example, eating too much fast food without any physical activity leads to weight gain. Here eating without any physical activity is the “cause” and weight gain is the “effect.” Another popular example in the discussion of cause and effect is that of smoking and lung cancer. A question that has surfaced in cancer research in the past several decades is, What is the effect of smoking on an individual's health? Also asked is the question, Does smoking cause lung cancer? Using data from observational studies, researchers have long established the relationship between smoking and the incidence of lung cancer; however, it took compelling evidence from several studies over several decades to establish smoking as a “cause” of lung cancer.
The term effect has been used frequently in scientific research. Most of the time, it can be seen that a statistically significant result from a linear regression or correlation analysis between two variables X and Y is explained as effect. Does X really cause Y or just relate to Y? The association (correlation) of two variables with each other in the statistical sense does not imply that one is the cause and the other is the effect. There needs to be a mechanism that explains the relationship in order for the association to be a causal one. For example, without the discovery of the substance nicotine in tobacco, it would have been difficult to establish the causal relationship between smoking and lung cancer. Tobacco companies have claimed that since there is not a single randomized controlled trial that establishes the differences in death from lung cancer between smokers and nonsmokers, there was no causal relationship. However, a cause-and-effect relationship is established by observing the same phenomenon in a wide variety of settings while controlling for other suspected mechanisms.
Statistical correlation (e.g., association) describes how the values of variable Y of a specific population are associated with the values of another variable X from the same population. For example, the death rate from lung cancer increases with increased age in the general population. The association or correlation describes the situation that there is a relationship between age and the death rate from lung cancer. Randomized prospective studies are often used as a tool to establish a causal effect. Time is a key element in causality because the cause must happen prior to the effect. Causes are often referred to as treatments or exposures in a study. Suppose a causal relationship between an investigational drug A and response Y needs to be established. Suppose YA represents the response when the participant is treated using A and Y0 is the response when the subject is treated with placebo under the same conditions. The causal effect of the investigational drug is defined as the population average δ = E(YA–Y0). However, a person cannot be treated with both placebo and Treatment A under the same conditions. Each participant in a randomized study will have, usually, equal potential of receiving Treatment A or the placebo. The responses from the treatment group and the placebo group are collected at a specific time after exposure to the treatment or placebo. Since participants are randomized to the two groups, it is expected that the conditions (represented by covariates) are balanced between the two groups. Therefore, randomization controls for other possible causes that can affect the response Y, and hence the difference between the average responses from the two groups, can be thought of an estimated causal effect of treatment A on Y.
Even though a randomized experiment is a powerful tool for establishing a causal relationship, a randomization study usually needs a lot of resources and time, and sometimes it cannot be implemented for ethical or practical reasons. Alternatively, an observational study may be a good tool for causal inference. In an observational study, the probability of receiving (or not receiving) treatment is assessed and accounted for. In the example of the effect of smoking on lung cancer, smoking and not smoking are the treatments. However, for ethical reasons, it is not practical to randomize subjects to treatments. Therefore, researchers had to rely on observational studies to establish the causal effect of smoking on lung cancer.
Causal inference plays a significant role in medicine, epidemiology, and social science. An issue about the average treatment effect is also worth mentioning. The average treatment effect, δ = E(Y1)–E(Y2), between two treatments is defined as the difference between two outcomes, but, as mentioned previously, a subject can receive only one of “rival” treatments. In other words, it is impossible for a subject to have two outcomes at the same time. Y1 and Y2 are called counterfactual outcomes. Therefore, the average treatment effect can never be observed. In the causal inference literature, several estimating methods of average treatment effect are proposed to deal with this obstacle. Also, for observational study, estimators for average treatment effect with confounders controlled have been proposed.
Further Readings
- Descriptive Statistics
- Distributions
- Graphical Displays of Data
- Hypothesis Testing
- p Value
- Alternative Hypotheses
- Beta
- Critical Value
- Decision Rule
- Hypothesis
- Nondirectional Hypotheses
- Nonsignificance
- Null Hypothesis
- One-Tailed Test
- Power
- Power Analysis
- Significance Level, Concept of
- Significance Level, Interpretation and Construction
- Significance, Statistical
- Two-Tailed Test
- Type I Error
- Type II Error
- Type III Error
- Important Publications
- “Coefficient Alpha and the Internal Structure of Tests”
- “Convergent and Discriminant Validation by the Multitrait–Multimethod Matrix”
- “Meta-Analysis of Psychotherapy Outcome Studies”
- “On the Theory of Scales of Measurement”
- “Probable Error of a Mean, The”
- “Psychometric Experiments”
- “Sequential Tests of Statistical Hypotheses”
- “Technique for the Measurement of Attitudes, A”
- “Validity”
- Aptitudes and Instructional Methods
- Doctrine of Chances, The
- Logic of Scientific Discovery, The
- Nonparametric Statistics for the Behavioral Sciences
- Probabilistic Models for Some Intelligence and Attainment Tests
- Statistical Power Analysis for the Behavioral Sciences
- Teoria Statistica Delle Classi e Calcolo Delle Probabilità
- Inferential Statistics
- Q-Statistic
- R2
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- Student's t Test
- Unbiased Estimator
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- Mathematical Concepts
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