Many students and professionals use statistical terms so routinely that their meanings become assumed rather than understood, which can be confusing. This article identifies several terms that, in my experience, need clarification for new researchers.
Qualitative vs. Quantitative Research
Using qualitative data or non-numeric attributes of a subject does not classify a study as qualitative, just as using numeric data does not necessarily make research quantitative. The distinction between qualitative and quantitative research lies in their objectives, methodologies, and analytical approaches.
Qualitative research typically involves methods such as in-depth interviews, focus groups, participant observation, and thematic analysis. It addresses open-ended questions like “why” and “how” by exploring participants’ experiences and perspectives. Its primary objective is to generate insights and formulate theories.
On the other hand, quantitative research is primarily concerned with testing theories. It employs structured methods, such as surveys or experiments designed to collect data that can be analyzed using statistical techniques. This approach addresses close-ended questions like “what,” “how much,” or “how many,” focusing on measurement, hypothesis testing, and generalization of findings.
It is also important to note that quantitative research may incorporate qualitative data, and qualitative studies can include quantitative elements. The two approaches are not always mutually exclusive and are also combined in mixed-methods research to make use of their strengths and address the weaknesses. For instance, this integration can help reduce potential bias in qualitative research while adding contextual depth to the more structured, data-driven nature of quantitative methods.
Parametric vs. Non-parametric Tests
A parametric test is conducted based on specific assumptions about the population. It is used for continuous variables and normally distributed data. Examples of parametric tests are the t-test, the z-test, Analysis of Variance (ANOVA), and Regression Analysis. A non-parametric test does not require any assumption about the data. Examples of non-parametric tests are the Wilcoxon Rank Test, Mann-Whitney U Test, and the Kruskal-Wallis Test.
A parametric test is generally more powerful than a non-parametric test. As a result, researchers may still choose to use it even when the data is not perfectly normally distributed, particularly when the sample size is large, the data are continuous, and variances are approximately equal. In such cases, it is common practice to compare the results of a parametric test (e.g., t-test or ANOVA) with those of a non-parametric counterpart (e.g., Mann–Whitney U test or Kruskal–Wallis test) to assess the robustness and reliability of the findings.
Level of Significance vs. Confidence level
The Level of Significance refers to the probability that we reject the null hypothesis when it is true, also known as the Type 1 error or false positive. The Confidence Level is the proportion of times that the confidence interval contains the true population parameter if we repeat the study many times. They complement each other in statistical analysis. For example, you set the level of significance at 0.05, which means you’re 95% confident in your estimate, and there’s a 5% chance you’re making a Type I error if you reject the null hypothesis.
Source: thedatascientist.com
Distribution vs. Frequency Distribution
A distribution describes how the values of a random variable are spread in a range; it is the structure of the data, while a frequency distribution is the representation of the structure but focuses on how often a value or values appear in a dataset. Most common type of distribution is the normal distribution which follows a bell shape. A distribution is used to know the underlying behavior of the data in inferential statistics for prediction and tests while frequency distribution is used in descriptive statistics for data visualization.
Standard Deviation vs. Standard Error vs. Residuals
Standard Deviation refers to how far individual data points are from the mean (used in descriptive statistics). Residuals refer to how far your predicted values are from the actual data (used in regression analysis). The standard error refers to how much a statistic like the sample mean would vary if different samples were taken (used in inferential statistics). They are all measures of variability but in different contexts.
Likelihood vs. Probability
Probability is the measure of the chance that a future event will occur, given a set of assumptions. Its value ranges from 0 (impossibility) to 1 (certainty). On the other hand, likelihood measures the plausibility of various assumptions given the observed data. Classic example is the coin flipping. In predicting flips, probability would say “if the coin is fair, each flip has a 50% chance of heads.” After many flips, if the results seem unusual (say 90 heads out of 100 flips), likelihood comes into play. We then doubt the “fair coin” assumption. Likelihood asks: “Given these flip results, which coin biases (fair or not) would make this outcome most probable?
It’s easy to mix up terms in Statistics, especially when they sound or look similar in our everyday language. But knowing the difference between things can make a difference in how we understand or interpret data, because in Statistics, precision is not just helpful, it is essential!
References
Streefkerk, R. (2019, April 12). Qualitative vs. quantitative research: Differences, examples & methods (Revised June 2023). Scribbr. https://www.scribbr.com/methodology/qualitative-quantitative-research/
National University. (2023, April 27). What is qualitative vs. quantitative study? https://www.nu.edu/blog/qualitative-vs-quantitative-study/
BYJU’S. (n.d.). Difference between parametric and nonparametric tests. Retrieved May 22, 2025, from https://byjus.com/maths/difference-between-parametric-and-nonparametric/
Albert Einstein College of Medicine. (n.d.). Parametric vs. non-parametric statistical tests. Retrieved May 22, 2025, from https://einsteinmed.edu/uploadedfiles/centers/ictr/new/parametric-vs-non-parametric-statistical-tests.pdf
Kampakis, S. (2023, December 9). Comparing significance level, confidence level, and confidence interval. The Data Scientist. https://thedatascientist.com/comparing-significance-level-confidence-level-and-confidence-interval/1_fnuggz5wfbbhrxw6zwyklg/5wfbbhrxw6zwyklg/
