You should use a parametric test when your data meets three conditions: it’s measured on a continuous scale, it’s approximately normally distributed, and the groups you’re comparing have roughly equal variance. When these assumptions hold, parametric tests give you more statistical power than their non-parametric alternatives, meaning you’re more likely to detect a real difference if one exists.
The Three Core Assumptions
Parametric tests work by making specific assumptions about the shape and spread of your data. Before choosing one, you need to check whether your data satisfies these requirements.
Continuous measurement scale. Your outcome variable needs to be measured on an interval or ratio scale. These are scales where the distance between values is meaningful and consistent. Height in centimeters, blood pressure in mmHg, test scores on a standardized exam, income in dollars. If your data is ranked (like a pain scale of 1 to 5) or categorical (like treatment groups), parametric tests aren’t designed for it.
Approximate normality. The data in each group should follow a roughly bell-shaped distribution. It doesn’t need to be perfect. Slight skewness or a few values in the tails won’t invalidate your results, especially with larger samples. But if your data is heavily skewed, has extreme outliers, or follows a fundamentally different shape, parametric tests lose reliability. You can check this visually with a histogram or Q-Q plot, or formally with a Shapiro-Wilk test.
Equal variance across groups. When comparing two or more groups, the spread of data within each group should be similar. This property is called homogeneity of variance. If one group’s values are tightly clustered while another group’s values are scattered widely, the test’s math breaks down. Levene’s test is the most common way to check this. If variances are unequal, one common workaround is transforming the data (using a log or square root transformation, for example) so the spread becomes more consistent.
There’s also a fourth assumption that often goes unstated because it applies to nearly all statistical tests: your observations need to be independent of each other. One person’s data point shouldn’t influence another’s. This is typically handled through study design rather than checked after the fact.
Why Sample Size Changes the Rules
The normality assumption becomes less important as your sample grows. This is because of the central limit theorem, which states that the average of a large enough sample will follow a normal distribution regardless of the shape of the original data. The commonly cited threshold is a sample size of 30 per group. Once you’re above that number, the sampling distribution of the mean approximates a normal curve closely enough that parametric tests remain valid even when the raw data isn’t perfectly bell-shaped.
This doesn’t mean you can ignore normality entirely with large samples. Extreme skewness or heavy-tailed distributions can still cause problems. The power of t-tests and F-tests deteriorates rapidly when distributions have long tails, even with reasonable sample sizes. But for mild to moderate departures from normality, a sample of 30 or more per group gives you a comfortable safety margin.
With small samples (under 15 or so per group), the normality assumption matters much more. A single outlier can pull the mean far from the center of the data, and there aren’t enough observations to stabilize the estimate. In these situations, you either need strong evidence that the data is normally distributed or should consider a non-parametric alternative.
Common Parametric Tests and When to Use Each
Different parametric tests handle different research designs. The choice depends on how many groups you’re comparing and whether measurements are independent or repeated.
- Independent samples t-test: Compares the means of two separate groups. Use this when you have two unrelated groups and want to know if they differ on a continuous outcome. Example: comparing average recovery time between a treatment group and a control group.
- Paired t-test: Compares means from the same group measured at two time points, or from matched pairs. Example: measuring patients’ blood pressure before and after a medication.
- One-way ANOVA: Extends the t-test to three or more independent groups defined by a single factor. Example: comparing test scores across students taught with three different methods.
- Repeated measures ANOVA: Compares means when the same subjects are measured under multiple conditions or at multiple time points.
- Two-way or three-way ANOVA: Tests the effects of two or three grouping variables simultaneously, including their interactions.
- Pearson correlation: Measures the strength and direction of a linear relationship between two continuous variables.
- Linear regression: Predicts a continuous outcome from one or more predictor variables.
The Power Advantage Over Non-Parametric Tests
When your data genuinely meets the assumptions, parametric tests are more powerful than their non-parametric equivalents. “Power” means the ability to detect a real effect. A non-parametric test applied to data that’s actually normal will be less likely to find a statistically significant result, even when a true difference exists. You’d need a larger sample to achieve the same sensitivity.
This is the core tradeoff. Parametric tests extract more information from your data by using the actual values, not just their ranks. A t-test works with means and standard deviations. Its non-parametric counterpart, the Wilcoxon rank sum test (also called the Mann-Whitney U test), converts all values to ranks and compares medians. That ranking process throws away information about how far apart the values are, which costs you statistical power.
The same relationship holds at every level: ANOVA is more powerful than its non-parametric equivalent, the Kruskal-Wallis test. Pearson correlation is more powerful than Spearman correlation. When assumptions are met, you’re leaving detection ability on the table by going non-parametric.
When to Switch to a Non-Parametric Test
If your data clearly violates the assumptions and you can’t fix it through transformation or increased sample size, non-parametric tests are the better choice. Several specific situations call for this switch.
Ordinal data is the most clear-cut case. If your outcome is a Likert scale, a ranking, or any variable where the gaps between values aren’t consistent, parametric tests don’t apply. The mean of a 1-to-5 satisfaction scale isn’t mathematically meaningful in the same way as the mean of a set of temperatures.
Heavy skewness with small samples is another trigger. If your data has a long tail in one direction and you have fewer than 30 observations per group, the mean becomes an unreliable summary of the data’s center. The median, which non-parametric tests typically use, is far more resistant to outliers. It takes just one extreme value to pull a mean in a misleading direction, while the median stays anchored at the middle of the distribution.
Severely unequal variances that can’t be corrected through transformation also warrant a non-parametric approach. If Levene’s test flags a significant difference in spread between groups, and no transformation stabilizes it, the parametric test’s p-value becomes untrustworthy.
A Practical Decision Process
Start by asking what type of variable your outcome is. If it’s not continuous (interval or ratio scale), stop here and use a non-parametric test. If it is continuous, check your sample size. With 30 or more per group, mild violations of normality are generally tolerable, and you can proceed with a parametric test as long as variances are reasonably equal.
With smaller samples, plot your data. Look at histograms for obvious skew and check for outliers. Run a Shapiro-Wilk test if you want a formal check on normality, and Levene’s test for equal variances. If both look reasonable, use the parametric test. If normality fails, try a log or square root transformation and recheck. If the data still doesn’t cooperate, switch to the non-parametric equivalent: Wilcoxon for a t-test, Kruskal-Wallis for ANOVA, Spearman for Pearson correlation.
When in doubt, you can run both versions. If they give you the same conclusion, you can report the parametric result with confidence. If they disagree, the non-parametric result is typically the safer one to trust, since it makes fewer assumptions about your data’s behavior.