10 Common Statistical Mistakes (And How to Avoid Them)
Learn about the most common statistical errors made by students and researchers, from confusing correlation with causation to misinterpreting p-values.
Statistics is a powerful tool for understanding data, but it’s easy to make mistakes that can lead to incorrect conclusions. Whether you’re a student, researcher, or data analyst, avoiding these common pitfalls will improve the quality of your work.
1. Confusing Correlation with Causation
The Mistake: Assuming that because two variables are correlated, one must cause the other.
Example: Ice cream sales and drowning deaths are positively correlated. Does ice cream cause drowning? No! Both increase in summer due to hot weather.
How to Avoid:
- Always consider lurking variables (third factors)
- Remember: correlation shows association, not causation
- To establish causation, you need controlled experiments or strong causal inference methods
- Ask: “Could there be another explanation?“
2. Cherry-Picking Data
The Mistake: Selecting only data that supports your hypothesis while ignoring contradictory evidence.
Example: A company highlights only its successful products in a report, ignoring the failures.
How to Avoid:
- Use complete datasets whenever possible
- Report all analyses conducted, not just significant ones
- Pre-register your hypotheses before data collection
- Be transparent about data exclusions and explain why
3. Misunderstanding P-Values
The Mistake: Thinking p-value is the probability that the null hypothesis is true, or that your results are due to chance.
Reality: The p-value is the probability of seeing results at least this extreme if the null hypothesis were true.
How to Avoid:
- p < 0.05 doesn’t mean “proof” — it means evidence against H₀
- A p-value is not the probability that your hypothesis is correct
- Consider effect sizes alongside p-values
- Remember: statistical significance ≠ practical importance
4. Ignoring Sample Size
The Mistake: Drawing strong conclusions from tiny samples or not recognizing the limitations of small studies.
Why It Matters:
- Small samples have high variability
- Confidence intervals are wide with small n
- Easy to miss real effects (low statistical power)
- More susceptible to outliers
How to Avoid:
- Always report sample size
- Use power analysis to determine adequate sample size
- Be cautious with conclusions from small samples
- Consider conducting pilot studies first
5. Using the Wrong Test
The Mistake: Applying a statistical test without checking its assumptions or using it in inappropriate situations.
Common Examples:
- Using a t-test when data is highly skewed
- Applying parametric tests to ordinal data
- Using chi-square when expected frequencies are too small
How to Avoid:
- Check assumptions before running tests (normality, independence, homogeneity of variance)
- Visualize your data first
- Learn when to use non-parametric alternatives
- Consult statistical references or experts when unsure
6. Multiple Comparisons Problem
The Mistake: Running many hypothesis tests without adjusting for multiple comparisons, inflating the chance of false positives.
Why It Happens: If you test 20 hypotheses at α = 0.05, you’d expect 1 false positive by chance alone!
How to Avoid:
- Use Bonferroni correction: divide α by number of tests
- Apply False Discovery Rate (FDR) methods
- Use omnibus tests (like ANOVA) before pairwise comparisons
- Limit the number of exploratory analyses
7. Extrapolating Beyond the Data
The Mistake: Making predictions far outside the range of your observed data.
Example: A regression model fit to heights of children aged 5-10 shouldn’t be used to predict adult heights.
How to Avoid:
- Only make predictions within the range of your data
- Be extremely cautious about extrapolation
- Clearly state the limitations of your model
- Consider whether relationships remain linear beyond your data range
8. Ignoring Outliers
The Mistake: Either blindly removing outliers or ignoring their influence on your analysis.
The Problem: Outliers can:
- Drastically affect means and correlation coefficients
- Violate assumptions of statistical tests
- Sometimes represent important real phenomena
How to Avoid:
- Investigate outliers — are they errors or genuine extreme values?
- Report analyses with and without outliers
- Use robust methods less affected by outliers (median, IQR, Spearman’s correlation)
- Never delete outliers without justification
9. Overfitting Models
The Mistake: Creating overly complex models that fit your specific sample perfectly but fail to generalize.
Signs of Overfitting:
- Model has too many parameters relative to sample size
- Perfect fit to training data but poor predictions on new data
- Unrealistically complex relationships
How to Avoid:
- Use cross-validation to test generalization
- Apply regularization techniques
- Follow parsimony: simpler models are often better
- Split data into training and testing sets
10. Misinterpreting Confidence Intervals
The Mistake: Thinking a 95% CI means “there’s a 95% probability the true value is in this range.”
Reality: If we repeated the study many times, 95% of constructed intervals would contain the true parameter. The parameter is fixed; the interval is what’s random.
Other Mistakes:
- Thinking non-overlapping CIs always mean significant differences
- Confusing CIs with prediction intervals
- Forgetting that wider intervals mean more uncertainty
How to Avoid:
- Learn the correct interpretation of confidence intervals
- Remember: CIs are about the long-run performance of the method
- Report CIs alongside point estimates
- Consider the width of the interval when making decisions
Bonus Tips for Avoiding Statistical Mistakes
1. Visualize Your Data First
Before running any test, create plots:
- Scatter plots for relationships
- Histograms for distributions
- Box plots for comparing groups
2. Report Effect Sizes
P-values tell you if there’s an effect; effect sizes tell you how large it is.
3. Be Transparent
- Report all analyses conducted
- Acknowledge limitations
- Share your data and code when possible
4. Get a Second Opinion
- Have a colleague review your analysis
- Consult with a statistician for complex analyses
- Use peer review to catch errors
5. Keep Learning
Statistics is complex and constantly evolving:
- Stay updated on best practices
- Take advanced courses
- Read methodological papers in your field
Conclusion
Statistical mistakes are common, but they’re also avoidable. By understanding these pitfalls and taking steps to prevent them, you’ll produce more reliable, trustworthy analyses.
Key Takeaways:
- Correlation ≠ Causation
- Understand what p-values actually mean
- Check assumptions before applying tests
- Consider sample size and power
- Correct for multiple comparisons
- Visualize your data
- Report effect sizes and confidence intervals
- Be transparent about your methods and limitations
Remember: good statistical practice is about honesty, rigor, and clear communication of uncertainty.