causality

Examples of causality in the following topics:

• Correlation is Not Causation

  • The conventional dictum "correlation does not imply causation" means that correlation cannot be used to infer a causal relationship between variables.
  • This dictum does not imply that correlations cannot indicate the potential existence of causal relations.
  • Consequently, establishing a correlation between two variables is not a sufficient condition to establish a causal relationship (in either direction).
  • A few go further and calculate the likelihood of a true causal relationship.
  • Examples include the Granger causality test and convergent cross mapping.

• Overview of data collection principles exercises

  • Also comment on whether or not the results of the study can be generalized to the population and if the findings of the study can be used to establish causal relationships.
  • Also comment on whether or not the results of the study can be generalized to the population and if the findings of the study can be used to establish causal relationships.
  • However, since the study is observational, the findings do not imply causal relationships.
  • However, since the study is an experiment, the findings can be used to establish causal relationships.
  • (d) Since this is an observational study, a causal relationship is not implied.

• Introducing observational studies and experiments

  • In general, observational studies can provide evidence of a naturally occurring association between variables, but they cannot by themselves show a causal connection.
  • When researchers want to investigate the possibility of a causal connection, they conduct an experiment.
  • To check if there really is a causal connection between the explanatory variable and the response, researchers will collect a sample of individuals and split them into groups.

• Statistical Literacy

  • What experimental design involving niacin would test whether the relationship between HDL and heart disease is causal?
  • A finding that niacin increased HDL without decreasing heart disease would cast doubt on the causal relationship.

• Observational studies

  • Making causal conclusions based on experiments is often reasonable.
  • However, making the same causal conclusions based on observational data can be treacherous and is not recommended.
  • While one method to justify making causal conclusions from observational studies is to exhaust the search for confounding variables, there is no guarantee that all confounding variables can be examined or measured.
  • In the same way, the county data set is an observational study with confounding variables, and its data cannot easily be used to make causal conclusions.
  • However, it is unreasonable to conclude that there is a causal relationship between the two variables.

• What are Observational Studies?

  • A common goal in statistical research is to investigate causality, which is the relationship between an event (the cause) and a second event (the effect), where the second event is understood as a consequence of the first.
  • There are two major types of causal statistical studies: experimental studies and observational studies.
  • A randomized experiment would violate ethical standards: Suppose one wanted to investigate the abortion – breast cancer hypothesis, which postulates a causal link between induced abortion and the incidence of breast cancer.
  • Observational studies can never identify causal relationships because even though two variables are related both might be caused by a third, unseen, variable.
  • Since the underlying laws of nature are assumed to be causal laws, observational findings are generally regarded as less compelling than experimental findings.

• Causation

  • An obvious obstacle to inferring causality is that there are many unmeasured variables that affect how many hours someone sleeps.
  • Does the possibility of a third-variable problem make it impossible to draw causal inferences without doing an experiment?
  • However, be aware that the assumption of no third-variable problem may be hidden behind a complex causal model that contains sophisticated and elegant mathematics.
  • A second problem is determining the direction of causality.

• Interpreting regression line parameter estimates

  • We must be cautious in this interpretation: while there is a real association, we cannot interpret a causal connection between the variables because these data are observational.
  • (It would be reasonable to contact the college and ask if the relationship is causal, i.e. if Elmhurst College's aid decisions are partially based on students' family income. ) The estimated intercept b0 = 24.3 (in $1000s) describes the average aid if a student's family had no income.

• An Intuitive Approach to Relationships

  • In this example, there is a causal relationship, because extreme weather causes people to use more electricity for heating or cooling; however, statistical dependence is not sufficient to demonstrate the presence of such a causal relationship (i.e., correlation does not imply causation).

• When the success-failure condition is not met

  • The claim is that there is a causal connection, but the data are observational.
  • While it is not possible to assess this causal claim, it is still possible to test for an association using these data.