Parametric vs Nonparametric Tests

Updated for the 2026-2027 CFA® Level I curriculum.

Choosing between a parametric and nonparametric test starts with the research question and the type of data available. Parametric tests use the numerical values in the sample and rely on specific assumptions about the population. Nonparametric tests make fewer assumptions about the population’s distribution and often work with ranks, signs, or category frequencies.

For CFA Level I, you should be able to recognize which family fits a given scenario and explain the reason for that choice.

Key Takeaways About Parametric vs Nonparametric Tests

• Parametric tests specify assumptions about the population distribution.

• Nonparametric tests require fewer assumptions about the distribution’s form.

• Parametric methods generally use the actual numerical magnitudes of observations.

• Nonparametric methods commonly use ranks, signs, or category frequencies.

• Interval and ratio data can support parametric testing when the relevant assumptions hold.

• Ordinal and nominal data generally require nonparametric methods.

• Parametric tests often have greater power when their assumptions are satisfied.

• Rank-based nonparametric tests are usually less affected by extreme observations.

• Pearson correlation testing is parametric, while Spearman rank correlation testing is nonparametric.

• A chi-square test of independence is also a nonparametric procedure.

What You Need to Know for CFA Level I

For CFA Level I, focus on your ability to:

• Explain what makes a statistical test parametric or nonparametric.

• Match the test family with the measurement scale of the data.

• Recognize when distributional assumptions appear reasonable.

• Explain the trade-off between statistical power and fewer assumptions.

• Distinguish Pearson correlation from Spearman rank correlation.

• Recognize the chi-square test of independence as nonparametric.

• Select the more appropriate method from an exam-style scenario.

• Justify the choice using the characteristics of the data.

What Is a Parametric Test?

A parametric test makes assumptions about the form of the population distribution and uses the sample to draw conclusions about one or more population parameters.

Common parameters include:

• The population mean

• The population variance

• The difference between two population means

• The population correlation coefficient

Parametric methods normally use the actual magnitudes of the observations. For example, returns of 12% and 2% are treated as ten percentage points apart. This allows the test to use more information than a method based only on ranks.

The assumptions depend on the procedure. They may include:

• A particular population distribution, often normality

• Independent observations

• Equal population variances across groups

• A linear relationship between variables

• Interval- or ratio-scale data

For CFA Level I, examples of parametric procedures include tests involving population means, variances, and the Pearson population correlation coefficient.

What Is a Nonparametric Test?

A nonparametric test makes fewer assumptions about the form of the population distribution. These methods are often described as distribution-free because they do not require the population to follow a specific distribution such as the normal distribution.

They still rely on assumptions that suit the procedure, including independent observations and an appropriate data structure.

Nonparametric methods often transform the observations into:

• Ranks

• Positive or negative signs

• Category counts

• Relative ordering

This makes them useful when the numerical distance between observations has limited meaning. Credit ratings, preference rankings, and risk categories are examples of ordinal data where the order matters but the gaps between categories cannot be treated as equal.

Nonparametric methods can also be useful when:

• A distribution is strongly skewed.

• A small number of extreme observations would influence a parametric result.

• The relationship between two variables is monotonic but not linear.

• The sample does not support the distributional assumptions required by the parametric method.

Level I examples include the Spearman rank correlation test and the chi-square test of independence using contingency-table data.

Parametric vs Nonparametric Tests: Main Differences

When Should You Use a Parametric Test?

A parametric test is generally appropriate when the measurement scale, research question, and sample characteristics support the method’s assumptions.

Consider a parametric method when:

• The observations are measured on an interval or ratio scale.

• The numerical distance between observations has meaning.

• The research question concerns a parameter such as a mean or correlation coefficient.

• The required distributional assumptions appear reasonable.

• The relationship is approximately linear when testing correlation.

• No influential observations dominate the result.

• The observations meet the procedure’s independence requirements.

Parametric tests preserve the full numerical information in the sample. When the assumptions hold, this usually gives them greater power to detect an effect.

A large sample can make the sampling distribution of some statistics approximately normal. Sample size alone does not resolve ordinal measurement, dependent observations, severe outliers, or a relationship that is fundamentally nonlinear.

When Should You Use a Nonparametric Test?

A nonparametric method is generally more suitable when the data or relationship cannot reasonably support a parametric procedure.

Consider a nonparametric test when:

• The observations are ranks or ordinal categories.

• The data consist of nominal category counts.

• The population distribution is strongly non-normal.

• The sample is too limited to rely on a suitable large-sample approximation.

• Influential outliers would distort a parametric statistic.

• Two variables have a monotonic but nonlinear relationship.

• The assumptions required by the parametric test cannot be supported.

The chosen test should still match the research question. A rank-based correlation test and a contingency-table independence test are both nonparametric, but they analyze different forms of data and answer different questions.

Pearson vs Spearman Correlation Tests

Pearson and Spearman correlation tests provide a clear example of the difference between parametric and nonparametric methods.

Pearson Correlation

The Pearson correlation coefficient measures the strength and direction of a linear relationship between two quantitative variables.

Testing whether the population Pearson correlation coefficient equals zero is a parametric procedure. The test uses the actual values of the observations and commonly relies on assumptions that include bivariate normality for exact inference.

Pearson correlation is generally appropriate when:

• Both variables are quantitative.

• The relationship is approximately linear.

• The distributional assumptions are reasonable.

• Influential outliers are absent.

Spearman Rank Correlation

The Spearman rank correlation coefficient measures the strength and direction of a monotonic relationship between two variables.

A monotonic relationship moves consistently upward or downward, although the rate of change may vary. The relationship can therefore curve while preserving the same general direction.

Spearman correlation is nonparametric because it works with the ranks of the observations rather than their original magnitudes.

It is generally appropriate when:

• One or both variables are ordinal.

• The relationship is monotonic but not linear.

• Extreme observations would strongly affect Pearson correlation.

• The distributional assumptions required for Pearson correlation are unsupported.

Pearson vs Spearman at a Glance

The coefficients answer related but distinct questions. A strong Spearman correlation can exist when the relationship is steadily increasing but curved, even if the Pearson correlation understates that association.

How Do Assumptions Affect Statistical Power?

Statistical power is the probability of rejecting a false null hypothesis. A more powerful test has a better chance of detecting an effect that truly exists.

Parametric tests often have greater power because they retain the numerical distances between observations. A return of 12% carries more information than simply labeling it the highest-ranked return.

This advantage applies when the assumptions behind the parametric test are reasonable. If those assumptions fail, the reported p-value and significance level may no longer behave as intended.

Nonparametric tests reduce their reliance on distributional form by using ranks, signs, or counts. That transformation may discard some information, but it can produce more dependable inferences when the parametric model is unsuitable.

The practical sequence is:

1. Identify the type of data.

2. Check the assumptions required by the parametric method.

3. Determine whether those assumptions are reasonable.

4. Compare the available valid methods.

5. Consider power after confirming that the test is appropriate.

Worked Example: Choosing the Test Family

An analyst wants to examine whether two characteristics are associated across 40 equity funds.

Case 1: Quantitative Return and Risk Data

The analyst records each fund’s annualized three-year return and annualized standard deviation.

Both variables are quantitative and measured on a ratio scale. A scatterplot shows an approximately linear relationship, and no extreme observations appear to dominate the result. The relevant distributional assumptions also appear reasonable.

A parametric approach is appropriate. The analyst can calculate the Pearson correlation coefficient and test whether the population correlation equals zero.

The original numerical values provide useful information about the strength of the linear relationship, so retaining those magnitudes supports the analysis.

Case 2: Ordinal Governance Scores

The analyst then compares each fund company’s governance rating, reported on an ordered five-point scale, with manager tenure measured in years.

A plot shows that tenure generally increases as the governance rating improves, although the relationship flattens at the upper end. Two firms also have unusually long-tenured managers.

A nonparametric approach is more suitable. The governance ratings are ordinal, the relationship is monotonic rather than clearly linear, and the extreme tenure values could strongly influence Pearson correlation.

Spearman rank correlation allows the analyst to test whether higher governance ratings tend to accompany longer manager tenure without treating the gaps between ratings as equal numerical distances.

The sample size is the same in both cases. The measurement scale, relationship shape, outliers, and assumptions lead to the different test choices.

Common Exam Traps

• Treating nonparametric tests as assumption-free. Each procedure still has requirements, including assumptions about independence and data structure.

• Selecting a method from sample size alone. The measurement scale, relationship, and distributional assumptions also matter.

• Using Pearson correlation for ordinal data. Pearson relies on meaningful numerical distances between observations.

• Treating Pearson and Spearman as interchangeable. Pearson measures linear association using values, while Spearman measures monotonic association using ranks.

• Assuming all nonparametric tests use ranks. Chi-square testing uses category frequencies rather than ranks.

• Choosing a parametric test only because it has more power. The power advantage applies when the parametric test is valid for the data.

• Assuming a large sample resolves every problem. More observations do not create equal distances between ordinal categories or turn a curved relationship into a linear one.

• Naming the test without explaining the choice. Connect the selection to the measurement scale, distribution, outliers, and form of the relationship.

Practice Question

An analyst examines whether higher corporate governance ratings are associated with longer CEO tenure across 25 companies.

Governance ratings are reported on an ordinal scale from 1 to 5. A plot shows that CEO tenure generally rises with the governance rating but begins to flatten at higher ratings. Two companies also have unusually long CEO tenures.

Which test approach is most appropriate?

1. A parametric Pearson correlation test because 25 observations are sufficient to assume normality

2. A nonparametric Spearman rank correlation test because the governance data are ordinal, the relationship is monotonic, and influential observations are present

3. A parametric Pearson correlation test because parametric procedures generally have greater statistical power

FAQs About Parametric vs Nonparametric Tests