Parametric vs Nonparametric Tests in Nursing Research

Introduction

Your supervisor has looked at your output and said, “Your data aren’t normal.” Now you’re wondering whether your whole analysis needs to change. Take a breath. This is one of the most common comments on nursing dissertations, and it rarely means your analysis is ruined.

Here’s the short answer. Non-normal data don’t automatically mean you need a nonparametric test. The right test depends on your research question, your outcome variable, how many groups you have, whether your observations are independent or related, and the assumptions of the specific test you’re considering.

This guide explains the difference between parametric and nonparametric tests, shows which tests pair with which, and walks you through a decision process you can use for any nursing research question.

What are parametric tests?

Parametric tests estimate or compare population parameters, such as means, mean differences, correlations and regression coefficients. You’ll usually use them with continuous outcomes, like blood pressure, length of stay or a total score on a validated questionnaire.

Common examples are the independent-samples t test, the paired-samples t test, one-way ANOVA, repeated-measures ANOVA, Pearson’s correlation and linear regression.

A widespread myth is that parametric tests need all your raw data to be normally distributed. They don’t. Each test has its own assumptions:

• Independent t test: the outcome should be roughly normal within each group, not across the whole sample.
• Paired t test: the differences between the paired scores should be roughly normal.
• ANOVA and regression: the residuals (the errors left after fitting the model) matter, not the raw outcome.
• Pearson’s correlation: the relationship should be linear, with no single point pulling the line around.

When these assumptions hold well enough, parametric tests are powerful. They also give you numbers that are easy to interpret clinically, such as “the intervention group’s pain scores were 0.6 points lower on average”.

What are nonparametric tests?

Nonparametric tests make fewer assumptions about how your data are distributed. Most of the common ones work by ranking your scores from lowest to highest and analysing the ranks instead of the raw values.

The ones you’re most likely to meet are the Mann-Whitney U test, the Wilcoxon signed-rank test, the Kruskal-Wallis test, the Friedman test and Spearman’s correlation.

They’re especially useful when your outcome is ordinal (ordered categories, like a single Likert item) or when a continuous outcome badly breaks the assumptions of the parametric test.

Two points that often trip students up:

• They don’t simply test medians. Mann-Whitney U and Kruskal-Wallis compare rank distributions. You can only describe the result as a difference in medians if the groups’ distributions have a similar shape.
• They aren’t automatically safer. When parametric assumptions hold, a parametric test usually has more power to detect a real effect. When those assumptions are badly violated, the nonparametric test can be the better choice.

Parametric vs nonparametric tests: key differences

The real difference isn’t “normal vs not normal”. It’s what each test compares and what it assumes.

Parametric tests and their common nonparametric alternatives

Several common parametric tests have widely used nonparametric alternatives for similar study designs.

These pairs suit similar designs, but they aren’t interchangeable versions of the same test. An independent t test asks whether two group means differ. Mann-Whitney U asks whether scores in one group tend to rank higher than in the other. When you switch tests, your research question changes slightly too, so your results and discussion chapters need to describe the findings accordingly.

How to choose the right test

Work through these six questions in order. Most students start with step 5, which is why they get stuck.

1. What is your research question? Are you comparing groups, measuring change in the same people, or looking at a relationship? “Do patients who receive music therapy report less pain than those who receive usual care?” compares two groups. “Is nurse workload associated with burnout?” looks at a relationship.
2. What type of outcome do you have? Continuous (blood pressure, a total scale score), ordinal (a single Likert item), or categorical (yes/no, ward type). Categorical outcomes need different tests altogether, which are covered further down.
3. How many groups are you comparing? Two, or three or more.
4. Are your observations independent or related? Different people in each group are independent. The same people measured twice, or deliberately matched pairs, are related.
5. Do the assumptions of the test you’re considering hold? Check only the assumptions that apply to that test, such as normal residuals, equal variances or a linear relationship. Don’t ask “Is my whole dataset normal?”
6. Choose the test and justify it. Your choice should follow from steps 1 to 5, and your methods chapter should say so.

Once you’ve answered these questions, this table gives you a starting point:

What if your data are not normally distributed?

Don’t switch tests straight away. Work through these checks first.

Check the right thing. For an independent t test, look at each group separately. For a paired t test, look at the difference scores. For ANOVA and regression, look at the residuals. A histogram of your whole raw dataset may be checking the wrong thing.

Judge how big the problem is. Plot histograms and Q-Q plots. Mild skew is very different from a strongly skewed distribution with extreme values. Many parametric tests cope well with mild departures, especially when groups are a similar size.

Consider your sample size. You’ll often see n ≥ 30 per group quoted as a rough guide to when parametric tests become robust to non-normality. It isn’t a rule that makes normality irrelevant. With heavy skew or outliers, 30 may not be enough, while with mild skew, fewer may be fine.

Investigate outliers. An extreme value could be a data-entry error, a measurement problem or a genuine patient. Fix errors, but never delete a real observation just because it makes your data look less normal.

Check whether the real issue is unequal variances. If your groups have very different spreads, Welch’s t test or Welch’s ANOVA can handle that while still comparing means.

If, after all that, your outcome is ordinal or the assumptions are badly broken, a nonparametric test is the right choice. That’s a perfectly defensible decision, as long as you explain why.

Do you always need a normality test?

Not on its own. The Shapiro-Wilk test is very sensitive to sample size. In large samples it flags tiny, harmless departures from normality, and in small samples it can miss real problems (Field, 2024). Use it alongside histograms and Q-Q plots, and don’t treat its p-value as a simple normal/not-normal switch. For a detailed explanation of the test, see our guide to the Shapiro-Wilk test and normality testing.

What about homogeneity of variance?

Homogeneity of variance means your groups have roughly the same spread of scores. It’s a separate assumption from normality, and it applies to tests that compare independent groups, such as the t test and one-way ANOVA. If the variances differ, you don’t need to abandon parametric testing: Welch’s t test and Welch’s ANOVA are designed for exactly this situation. To learn how to check the assumption, see our guide to Levene’s test for homogeneity of variance.

What about categorical data?

If your outcome is categorical, such as whether a patient developed a pressure ulcer (yes/no), the parametric vs nonparametric question doesn’t really apply. To test whether two categorical variables are associated, for example ward type and pressure ulcer incidence, you’d normally use a chi-square test of independence.

Nursing research textbooks usually class chi-square as nonparametric (Flanagan & Beck, 2024). But it isn’t a nonparametric alternative to a t test or ANOVA, because it answers a different question about counts in categories. If some of your expected cell counts are small, Fisher’s exact test is usually the better option. See our guide to the chi-square test in nursing research.

The Likert-scale question

This is one of the most debated issues in nursing research, so it helps to know where the agreement and disagreement lie.

A single Likert item, such as one question scored from “strongly disagree” to “strongly agree”, is ordinal. The answers are in order, but you can’t assume the gap between “agree” and “strongly agree” equals the gap between “neutral” and “agree”. For that reason, single items are often analysed with nonparametric tests, though practice varies between disciplines.

A total or average score across several Likert items, such as a validated 20-item burnout scale, is different. These scores are often treated as continuous and analysed with parametric tests, especially when the scale has good reliability and the scores are reasonably spread out.

There’s no single rule everyone accepts. Make your decision based on your scale, your data and your department’s conventions, then state it clearly in your methods chapter. If you’re unsure, ask your supervisor which approach they expect.

Worked nursing examples

All figures below are invented for illustration.

Example 1: Post-operative pain and music therapy

A researcher compares pain scores on a 0–10 numerical rating scale between 42 patients who received music therapy and 42 who received usual care. The groups contain different patients, so the observations are independent.

The music-therapy group’s mean score is 4.1 (SD = 1.5), and the usual-care group’s is 4.7 (SD = 1.6). Both distributions are mildly skewed (skewness 0.8 and 0.6) and there are no extreme values. Some researchers treat a 0–10 rating scale as ordinal, so the researcher explains in the methods chapter why it is treated as continuous here.

With equal group sizes, mild skew and no outliers, the independent t test is robust enough. Decision: independent-samples t test, even though the data are not perfectly normal.

Example 2: Patient satisfaction across three wards

A researcher compares satisfaction scores (0–100) for 96 patients across Ward A (n = 32), Ward B (n = 31) and Ward C (n = 33).

In every ward, most patients score near the top of the scale, with a long tail of very low scores from a few dissatisfied patients. The Q-Q plots show this is a large departure from normality, not a mild one, and the extreme scores are genuine responses.

With a badly skewed outcome and influential extreme values, ANOVA’s assumptions don’t hold. Decision: Kruskal-Wallis test, followed by post hoc comparisons to find which wards differ. The full result is in the reporting section below.

Example 3: Nurse burnout before and after an intervention

Fifty nurses complete a validated burnout scale before and six weeks after a wellbeing programme. The same nurses provide both scores, so the observations are related.

The researcher checks the difference scores (after minus before), not the raw scores. They’re roughly symmetric, with no outliers. Decision: paired-samples t test.

Mean burnout fell from 62.4 (SD = 9.1) to 56.8 (SD = 8.7), t(49) = 5.35, p < .001, mean difference = 5.6, 95% CI [3.50, 7.70], dz = 0.76. If the difference scores had been badly skewed, the Wilcoxon signed-rank test would be the alternative, but it also assumes the differences are roughly symmetric.

Common mistakes nursing students make

• Switching to a nonparametric test as soon as Shapiro-Wilk is significant. Check the severity, sample size, outliers and robustness first.
• Treating Shapiro-Wilk p > .05 as proof of normality. A non-significant result only means the test didn’t find enough evidence against normality.
• Checking the wrong distribution. Normality applies to groups, difference scores or residuals, depending on the test, not usually to your whole raw dataset.
• Deleting outliers to make the data look better. Investigate them. Genuine patients stay in.
• Reporting Mann-Whitney U as a difference in medians. That’s only valid if the groups’ distributions have a similar shape.
• Using an independent test on paired data. If the same nurses or patients are measured twice, you need a paired test.
• Treating every Likert variable the same way. A single item and a multi-item scale may need different analyses.
• Not explaining the choice. Examiners want to see why you chose a test, not just which one.

How to report your choice in a nursing dissertation

In your methods chapter, one or two sentences justifying each test are usually enough:

Pain scores were treated as a continuous outcome. Because the two groups were independent and the distributions showed only mild skew with no influential outliers, an independent-samples t test was used to compare mean pain scores.

In your results chapter, report the full result, including the effect size, whether or not it’s significant. These examples use the invented data from the worked examples above.

Parametric result (Example 1):

Mean pain scores did not differ significantly between the music-therapy group (M = 4.1, SD = 1.5) and the usual-care group (M = 4.7, SD = 1.6), t(82) = −1.77, p = .080, mean difference = −0.60, 95% CI [−1.27, 0.07], d = 0.39.

This result isn’t significant, but it still matters. The 95% CI runs from a 1.27-point reduction to a 0.07-point increase. It includes no difference, but it also includes a reduction that could matter clinically, so a larger study would be needed to tell. Report non-significant results in full; don’t hide them.

Nonparametric result (Example 2):

Satisfaction scores differed significantly across the three wards, H(2) = 8.72, p = .013, η²H = .07. Median scores were 74 in Ward A (mean rank 46.4), 69 in Ward B (mean rank 39.1) and 82 in Ward C (mean rank 59.4). Dunn’s post hoc tests with Bonferroni correction showed that Ward C scored significantly higher than Ward B (adjusted p = .011). No other pairwise difference was significant.

For every test, report why you chose it, the assumption checks you ran, the test statistic, degrees of freedom where they apply, the p-value, an effect size, and a confidence interval where one is available.

Frequently asked questions

What is the difference between parametric and nonparametric tests?

Parametric tests compare parameters such as means and rely on assumptions specific to each test, such as normally distributed residuals. Nonparametric tests make fewer assumptions about the distribution and usually analyse ranks instead of raw scores. Neither is better in general. The right choice depends on your research question, outcome type, study design and whether the assumptions hold.

When should I use a nonparametric test?

Use a nonparametric test when your outcome is ordinal, such as a single Likert item, or when your continuous data badly break the assumptions of the parametric test. Don’t switch just because Shapiro-Wilk is significant. First consider how severe the departure is, your sample size, any outliers, and whether the parametric test is robust enough.

Is a nonparametric test better than a parametric test?

No. When the assumptions hold, parametric tests usually have more power and give you results, such as mean differences, that are easier to interpret clinically. Nonparametric tests are better suited to ordinal outcomes and to data that badly break parametric assumptions. Choose the test that fits your data and question, not the one that seems safer.

Can I use a parametric test if my data are not normally distributed?

Often, yes. Many parametric tests cope well with mild departures from normality, especially with similar group sizes and no extreme outliers. Check the distribution that actually matters for your test, such as each group, the difference scores or the residuals. If unequal variances are the problem, Welch’s tests can help.

Is chi-square parametric or nonparametric?

Chi-square is usually classed as nonparametric because it doesn’t assume a normally distributed outcome. But it isn’t an alternative to a t test or ANOVA. It tests whether two categorical variables are associated, such as ward type and pressure ulcer incidence. When expected cell counts are small, Fisher’s exact test is usually preferred.

Can I use parametric tests with Likert-scale data?

It depends on what you’re analysing. A single Likert item is ordinal and usually calls for a nonparametric test. Total or average scores from a multi-item scale are often treated as continuous and analysed with parametric tests. Base your decision on the scale, your data and your department’s conventions, and justify it in your methods chapter.

Conclusion

Choosing between parametric and nonparametric tests starts with your research question, not with a normality test. Identify your outcome type, count your groups, decide whether your observations are independent or related, and then check only the assumptions that apply to the test you’re considering. Mild non-normality is often fine for a parametric test. Ordinal outcomes and badly broken assumptions point towards a nonparametric one.

If you’re still unsure which test fits your data, our statisticians can review your research questions, dataset and analysis plan with you. Find out more about our SPSS data analysis help for nursing dissertations.

References

Field, A. (2024). Discovering statistics using IBM SPSS statistics (6th ed.). SAGE Publications.

Flanagan, J. M., & Beck, C. T. (2024). Polit & Beck’s nursing research: Generating and assessing evidence for nursing practice (12th ed.). Wolters Kluwer.