Choosing a statistical test

Understanding the type of data is important in selecting the appropriate statistical analysis method and interpreting the results correctly.

There are three main types of data: nominal, ordinal, and continuous.

Nominal data: Nominal data is a categorical data type that represents data in categories or names. It cannot be ranked or ordered in any way. Examples of nominal data include gender, race, religion, and marital status. Nominal data can be analyzed using frequency counts, percentages, or chi-square tests.
Ordinal data: Ordinal data is a categorical data type that represents data in an ordered way. The data can be ranked or ordered based on some criteria or preference, but the differences between the values are not necessarily equal. Examples of ordinal data include education levels, socioeconomic status, and survey responses such as Likert scales. Ordinal data can be analyzed using frequency distributions, median, and non-parametric tests such as Wilcoxon rank-sum test.
Continuous data: Continuous data is a numerical data type that represents data on a continuous scale. Continuous data can take any value on a continuous range of values, and the differences between values are equal. Examples of continuous data include height, weight, age, and blood pressure. Continuous data can be analyzed using descriptive statistics such as mean and standard deviation, and parametric tests such as t-tests, ANOVA, and regression analysis.

Parametric and nonparametric are two types of statistical methods used to analyze data.

Parametric statistical methods assume that the data come from a specific distribution, usually the normal distribution, and that the data meet certain assumptions, such as homogeneity of variance and independence. Parametric tests are typically more powerful than nonparametric tests, meaning they are better able to detect a difference or relationship when one exists. Examples of parametric tests include t-tests, ANOVA, and linear regression.
Nonparametric statistical methods, on the other hand, do not make assumptions about the distribution of the data. Nonparametric tests are often used when the data do not meet the assumptions of parametric tests, such as when the data are not normally distributed, the variances are not equal, or the data are ordinal or nominal. Examples of nonparametric tests include the Wilcoxon rank-sum test, the Kruskal-Wallis test, and the Spearman correlation.

The choice between parametric and nonparametric methods depends on the type of data being analyzed and the underlying assumptions of the test. If the data meet the assumptions of parametric tests, it is generally better to use a parametric test, since it is more powerful and can provide more accurate results. If the assumptions of parametric tests are not met, or if the data are not normally distributed, a nonparametric test may be more appropriate.

Paired and unpaired are terms used to describe the relationship between two sets of data that are being compared.

In the case of paired data, each observation in one set is directly linked or matched to an observation in the other set, meaning that each pair of observations in the two sets is related in some way. Paired data arises when the same individual or unit is measured twice, such as in a before-and-after study, a crossover study, or a matched case-control study. For example, if we want to compare the effectiveness of a new drug to a placebo, we might measure the outcome of interest (e.g., blood pressure) in each patient before and after receiving each treatment, resulting in paired data.
In the case of unpaired data, the two sets of data being compared are not related or matched in any way, and each observation in one set is independent of the observations in the other set. Unpaired data arises when two separate groups are being compared, such as in a randomized controlled trial or an observational study. For example, if we want to compare the mean blood pressure of patients who received the new drug versus those who received the placebo, we might randomly assign patients to each group and measure their blood pressure, resulting in unpaired data.

In statistical analysis, the appropriate method for comparing paired or unpaired data will depend on the study design and the research question being asked.

Check our web app, Statistical Test Selector, which will walk you through the algorithm of choosing the appropriate statistical test for your data.

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