Summary of Scientific Reasoning: Correlation and Causation
Scientific Reasoning: Understanding Correlation and Causation
Introduction
Drawing valid scientific conclusions is the final step of an investigation. It means stating only what your data actually show, explaining how the data support (or do not support) your hypothesis, and being careful about claims of cause and effect.
Definition: A conclusion is a statement that summarises what the data show and whether they support the original hypothesis.
1. What a Good Conclusion Includes
Match the data
- State the pattern or relationship you observed between the dependent and independent variables. Use specific values from your results to justify the claim.
- Example: The reaction rate with catalyst B was higher than with catalyst A.
Definition: Evidence is the specific data or measurements used to support a conclusion.
Refer back to the hypothesis
- Say whether the data support the hypothesis. If the hypothesis was that catalyst B makes the reaction faster than catalyst A, explicitly say the data support or contradict that hypothesis.
Give quantitative justification
- Always quote numbers or calculated differences to back your claim. For example: "The rate with catalyst B was $19.5,\mathrm{cm^2/s}$ compared with $13.5,\mathrm{cm^2/s}$ with catalyst A, a difference of $6,\mathrm{cm^2/s}$."
2. Limit the Scope of Your Conclusion
- Only claim what your experiment directly tested. Do not generalise beyond the conditions and variables you measured.
- Example: From the table below you can only conclude how these catalysts affected this particular reaction under the conditions used.
| Catalyst | Rate of reaction (cm^2/s) |
|---|---|
| A | $13.5$ |
| B | $19.5$ |
| No catalyst | $5.5$ |
- Correct conclusion: "Catalyst B made this reaction go faster than catalyst A under the tested conditions."
- Incorrect extension: "Catalyst B will speed up all reactions more than catalyst A."
3. Correlation versus Causation
- A correlation is a relationship between two variables. Correlation does not automatically mean one variable causes the other.
Definition: Correlation is a consistent relationship between two variables; causation means one variable changes because of another.
Three reasons for a correlation
- Chance
- Measurements can sometimes align by coincidence. Replication helps check for flukes.
- Example: One study finds hair colour correlates with frisbee skill; other studies find no effect.
- Linked by a third variable
- A hidden variable may cause both observed changes.
- Example: Water temperature and shark attacks correlate because both increase when more people swim; the third variable is the number of swimmers.
- Cause
- You can conclude causation only when you have controlled or accounted for other possible influencing variables.
- Example: The link between smoking and lung cancer was concluded causal after controlling for age, occupational exposures, and other risk factors.
4. How to Strengthen Causal Claims
- Control variables: keep all other variables constant except the independent variable.
- Use randomisation and replication to reduce bias and the impact of chance.
- Use appropriate comparisons (controls, placebos) where possible.
- Report limitations: state which variables were not controlled and how that affects the conclusion.
Table: Correlation vs Causation (comparison)
| Aspect | Correlation | Causation |
|---|---|---|
| Meaning | Two variables show a relationship | One variable produces a change in another |
| Evidence required | Repeated observation of a pattern | Controlled experiments or strong causal inference |
| Risk | Misleading conclusions from third variables or chance | Requires ruling out alternative explanations |
Practical examples and real-world applications
- Laboratory experiment: measuring reaction rates with and without catalysts. Use measured rates and differences to draw conclusions limited to the tested reaction and conditions.
- Epidemiology: large observational studies can sho
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Scientific Conclusions
Klíčové pojmy: State conclusions that match only the data collected, Support conclusions with specific numerical evidence, Refer explicitly to the original hypothesis, Do not generalise beyond tested conditions, Correlation does not imply causation, Consider chance, third variables, or true cause for correlations, Control variables and use replication to infer causation, Report limitations and suggest follow-up experiments, Use appropriate controls to rule out alternative explanations, Quantify differences when comparing treatments, Repeat experiments to check for flukes, Use randomisation to reduce bias
## Introduction
Drawing valid scientific conclusions is the final step of an investigation. It means stating only what your data actually show, explaining how the data support (or do not support) your hypothesis, and being careful about claims of cause and effect.
> Definition: A conclusion is a statement that summarises what the data show and whether they support the original hypothesis.
## 1. What a Good Conclusion Includes
### Match the data
- State the pattern or relationship you observed between the dependent and independent variables. Use specific values from your results to justify the claim.
- Example: The reaction rate with catalyst B was higher than with catalyst A.
> Definition: Evidence is the specific data or measurements used to support a conclusion.
### Refer back to the hypothesis
- Say whether the data support the hypothesis. If the hypothesis was that catalyst B makes the reaction faster than catalyst A, explicitly say the data support or contradict that hypothesis.
### Give quantitative justification
- Always quote numbers or calculated differences to back your claim. For example: "The rate with catalyst B was $19.5\,\mathrm{cm^2/s}$ compared with $13.5\,\mathrm{cm^2/s}$ with catalyst A, a difference of $6\,\mathrm{cm^2/s}$."
## 2. Limit the Scope of Your Conclusion
- Only claim what your experiment directly tested. Do not generalise beyond the conditions and variables you measured.
- Example: From the table below you can only conclude how these catalysts affected this particular reaction under the conditions used.
| Catalyst | Rate of reaction (cm^2/s) |
| --- | --- |
| A | $13.5$ |
| B | $19.5$ |
| No catalyst | $5.5$ |
- Correct conclusion: "Catalyst B made this reaction go faster than catalyst A under the tested conditions."
- Incorrect extension: "Catalyst B will speed up all reactions more than catalyst A."
## 3. Correlation versus Causation
- A correlation is a relationship between two variables. Correlation does not automatically mean one variable causes the other.
> Definition: Correlation is a consistent relationship between two variables; causation means one variable changes because of another.
### Three reasons for a correlation
1. Chance
- Measurements can sometimes align by coincidence. Replication helps check for flukes.
- Example: One study finds hair colour correlates with frisbee skill; other studies find no effect.
2. Linked by a third variable
- A hidden variable may cause both observed changes.
- Example: Water temperature and shark attacks correlate because both increase when more people swim; the third variable is the number of swimmers.
3. Cause
- You can conclude causation only when you have controlled or accounted for other possible influencing variables.
- Example: The link between smoking and lung cancer was concluded causal after controlling for age, occupational exposures, and other risk factors.
## 4. How to Strengthen Causal Claims
- Control variables: keep all other variables constant except the independent variable.
- Use randomisation and replication to reduce bias and the impact of chance.
- Use appropriate comparisons (controls, placebos) where possible.
- Report limitations: state which variables were not controlled and how that affects the conclusion.
## Table: Correlation vs Causation (comparison)
| Aspect | Correlation | Causation |
| --- | --- | --- |
| Meaning | Two variables show a relationship | One variable produces a change in another |
| Evidence required | Repeated observation of a pattern | Controlled experiments or strong causal inference |
| Risk | Misleading conclusions from third variables or chance | Requires ruling out alternative explanations |
## Practical examples and real-world applications
- Laboratory experiment: measuring reaction rates with and without catalysts. Use measured rates and differences to draw conclusions limited to the tested reaction and conditions.
- Epidemiology: large observational studies can sho