Pearson vs. Spearman: The Likert Scale Dilemma
If you are using PSPP or SPSS to analyze 5-point Likert scale data, you have likely run into a common statistical crossroads: Pearson’s Correlation or Spearman’s Rho?
While both coefficients measure the strength and direction of a relationship between two variables, choosing the wrong one can lead to misleading conclusions. Let’s break down which one is better for your survey data and what those mysterious symbols in PSPP actually mean.
1. Pearson’s Correlation (r)
Pearson is a parametric test. It measures the linear relationship between two continuous variables. It assumes that your data follows a normal distribution and that the relationship is a straight line.
When to use it for Likert data: Generally, you should only use Pearson if you have composite scores. For example, if you averaged 10 different Likert questions to create a single "Total Satisfaction" score, that score often behaves like a continuous variable.
2. Spearman’s Correlation (ρ)
Spearman is a non-parametric test. Instead of looking at raw values, it looks at the rank of the data. It measures "monotonic" relationships—meaning it just cares if as X goes up, Y also goes up (even if it's not in a straight line).
Why it’s usually better for Likert: A 5-point Likert scale is ordinal data. We know that "Strongly Agree" (5) is higher than "Agree" (4), but we cannot prove that the "distance" between 4 and 5 is the same as the distance between 1 and 2. Spearman respects this ordinal nature perfectly.
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The PSPP Mystery: What does the "a" mean?
In PSPP output, you might see a small letter "a" next to your correlation coefficient. This is a Significance Flag.
The Answer: Yes, the "a" means the result is Statistically Significant at the 0.05 level.
Essentially, PSPP is telling you that the p-value is less than 0.05 ($p < 0.05$). This means there is less than a 5% chance that the relationship you are seeing is just a random fluke. You can confidently reject the null hypothesis and state that a relationship exists in the population.
Final Verdict: Which one should you use?
- Use Spearman if you are comparing two individual Likert questions (e.g., "Is Question 1 correlated with Question 2?").
- Use Pearson only if you have aggregated several Likert items into a single mean score and your data is normally distributed.
When in doubt, report Spearman. It is the safer, more conservative choice for ordinal survey data.