📊 Interpreting Statistics
Introduction
Correctly interpreting statistical results is an essential skill for making data-driven decisions. This practical tutorial teaches how to understand p-values, identify spurious correlations, avoid common pitfalls and extract valid insights from statistical analyses.
Understanding the p-value
The p-value is one of the most important measures in statistics, but also one of the most misinterpreted. Let's understand what it really means:
What is p-value?
The p-value is the probability of obtaining a result equal to or more extreme than the one observed, assuming that the null hypothesis (H₀) is true.
Important: The p-value is NOT the probability that the hypothesis is true or false.
Interpreting p-values
- p < 0.05: Generally considered statistically significant. We reject H₀ at the 5% significance level.
- p < 0.01: Highly significant. Strong evidence against H₀.
- p ≥ 0.05: We do not reject H₀. This does NOT mean that H₀ is true, only that we do not have sufficient evidence to reject it.
Common Interpretation Pitfalls
1. Confusing Correlation with Causality
One of the most common pitfalls is assuming that correlation implies causality. Two variables can be correlated without one causing the other.
Classic example: Ice cream sales and drowning numbers are correlated, but this does not mean ice cream causes drownings. Both variables are influenced by a third: temperature.
Solution: Always question whether there may be a hidden variable (confounder) explaining the correlation.
2. P-hacking (Data Torturing)
P-hacking occurs when multiple tests are performed and only significant results are reported, falsely increasing the discovery rate.
How to avoid: Define your hypotheses and analysis methods BEFORE collecting data. Use corrections for multiple comparisons when necessary.
3. Statistical Significance vs. Practical Significance
A result can be statistically significant but have little practical significance, especially with large samples.
Example: In a very large sample, a difference of 0.001% may be statistically significant, but probably has no practical relevance.
Solution: Beyond the p-value, always consider the effect size and the practical relevance of the results.
Interpreting Confidence Intervals
Confidence intervals provide a range of values within which the population parameter is likely to be, at a given confidence level.
Correct Interpretation
A 95% confidence interval means: "If we repeated the study 100 times, in 95 of them the interval would contain the true parameter value."
Does NOT mean: "There is a 95% chance that the parameter is in this interval."
Spurious Correlations
Spurious correlations are statistical relationships that appear significant, but are actually coincidences or caused by confounding variables.
How to Identify:
- • Check for confounding variables: Could there be a third variable explaining both?
- • Consider the theoretical context: Does the correlation make sense from a logical standpoint?
- • Analyze sample size: Correlations in small samples can be unstable.
- • Test robustness: Does the correlation hold in subgroups of the sample?
Step by Step: Interpreting Results
- 1. Examine the p-value: Is it lower than your significance level (usually 0.05)?
- 2. Check the effect size: Even if significant, is the effect large enough to be relevant?
- 3. Consider confidence intervals: They provide a range of plausible values for the parameter.
- 4. Evaluate context: Do the results make theoretical and practical sense?
- 5. Verify assumptions: Do the data meet the assumptions of the test used?
- 6. Consider limitations: Are there factors that may have affected the results?
Practical Example: Interpreting a Correlation
Suppose an analysis finds a correlation of r = 0.65 between the frequency of appearance of a number and the probability of being drawn in the next draw, with p < 0.001.
How to Interpret:
- Correlation (r = 0.65): Indicates a moderate to strong positive correlation.
- p < 0.001: The correlation is statistically significant.
- But attention: In fair lotteries, each number has equal probability. A correlation like this is probably spurious or the result of a temporary pattern that will not hold in the future.
Interpretation Checklist
Before concluding anything from a statistical result, ask yourself:
- ✓ Is the p-value below the significance level?
- ✓ Is the effect size practically relevant?
- ✓ Do the data meet the assumptions of the test?
- ✓ Are there uncontrolled confounding variables?
- ✓ Does the result make theoretical sense?
- ✓ Is the sample representative and adequate?
- ✓ Were multiple tests done without correction?
Conclusion
Correctly interpreting statistics requires not only technical knowledge, but also critical thinking and healthy skepticism. Always question results, consider context and evaluate practical relevance beyond statistical significance.
Next steps: Explore our articles on Hypothesis Testing and Correlations to deepen your knowledge.