Examples of Granger causality test in the following topics:
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- 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.
- Many statistical tests calculate correlation between variables.
- A few go further and calculate the likelihood of a true causal relationship.
- Examples include the Granger causality test and convergent cross mapping.
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- 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.
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- 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.
- Write out hypotheses in both plain and statistical language to test for the association between the consultant's work and the true complication rate, p, for this consultant's clients.
- The p-value is computed based on the null distribution, which is the distribution of the test statistic if the null hypothesis is true.
- Supposing the null hypothesis is true, we can compute the p-value by identifying the chance of observing a test statistic that favors the alternative hypothesis at least as strongly as the observed test statistic.
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- 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.
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- No matter what a student scores on the original test, the best prediction of his score on the second test is 50.
- Some of the lucky students on the first test will be lucky again on the second test, but more of them will have (for them) average or below average scores.
- Therefore a student who was lucky on the first test is more likely to have a worse score on the second test than a better score.
- Similarly, students who score less than the mean on the first test will tend to see their scores increase on the second test.
- Statistical regression toward the mean is not a causal phenomenon.
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- Examples: Crash testing cars, medical testing for rare conditions.
- Causality: A relationship between two variables does not mean that one causes the other to occur.
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- Women tend to score lower on graduate admissions exams, such as the Graduate Record Exam (GRE) and the Graduate Management Admissions Test (GMAT).
- Representatives of the companies that publish these tests have hypothesized that greater number of female applicants taking these tests pull down women's average scores.
- Controlling for the number of people taking the test does not account for the scoring gap.
- This result is often encountered in social-science and medical-science statistics, and is particularly confounding when frequency data are unduly given causal interpretations.
- As to why and how a story, not data, should dictate choices, the answer is that it is the story which encodes the causal relationships among the variables.
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- ANCOVA can be used to compare regression lines by testing the effect of a categorial value on a dependent variable, controlling the continuous covariate.
- Researchers, such as those working in the field of biology, commonly wish to compare regressions and determine causal relationships between two variables.
- In order to understand this, it is necessary to understand the test used to evaluate differences between groups, the $F$-test.
- The $F$-test is computed by dividing the explained variance between groups (e.g., gender difference) by the unexplained variance within the groups.
- The slopes of the different regression lines should be equal (in our current context, this assumption is what will be tested).
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- Beyond these factors, researchers may not consider or have access to data on other causal factors.
- An individual might attempt to explain this correlation by inferring a causal relationship between the two variables (either that ice cream causes drowning, or that drowning causes ice cream consumption).
- Similarly, study replication can test for the robustness of findings from one study under alternative testing conditions or alternative analyses (e.g., controlling for potential confounds not identified in the initial study).
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- Just as we did for the normal case, we standardize the sample mean using the Z score to identify the test statistic.
- If the null hypothesis was true, the test statistic T would follow a t distribution with df = n − 1 = 29 degrees of freedom.
- 5.23: This is a one-sided test.H0: student scores do not improve by more than 100 after taking the company's course.µdiff = 100 (we always write the null hypothesis with an equality).
- 5.26: This is an observational study, so we cannot make this causal conclusion.
- For instance, maybe SAT test takers tend to improve their score over time even if they don't take a special SAT class, or perhaps only the most motivated students take such SAT courses.