{"id":2569,"date":"2019-08-27T17:37:00","date_gmt":"2019-08-27T17:37:00","guid":{"rendered":"https:\/\/analystprep.com\/cfa-level-1-exam\/?p=2569"},"modified":"2026-03-30T08:28:36","modified_gmt":"2026-03-30T08:28:36","slug":"parametric-tests-nonparametric-tests","status":"publish","type":"post","link":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/parametric-tests-nonparametric-tests\/","title":{"rendered":"Parametric vs. Non-Parametric Tests"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"VideoObject\",\n  \"name\": \"Hypothesis Testing (2025 Level I CFA\u00ae Exam \u2013 Quantitative Methods \u2013 Module 6)\",\n  \"description\": \"Master Hypothesis Testing for the 2025 CFA\u00ae Level I Quantitative Methods curriculum. This comprehensive lesson covers the full hypothesis testing framework, including null and alternative hypotheses, one-tailed vs. two-tailed tests, test statistics, Type I and Type II errors, significance levels, power of a test, decision rules, confidence intervals, p-values, and multiple testing considerations. You will also learn how to select and interpret appropriate test statistics for means, mean differences, variances, correlations, and tests of independence, as well as when to use parametric versus nonparametric tests. Learning Outcome Statements (LOS): Define a hypothesis and describe the steps of hypothesis testing. Compare one-tailed and two-tailed tests. Explain test statistics, significance levels, p-values, and decision rules. Identify appropriate hypothesis tests for means, variances, correlations, and independence and interpret results at a given significance level.\",\n  \"uploadDate\": \"2021-11-18\",\n  \"thumbnailUrl\": \"https:\/\/img.youtube.com\/vi\/twTTWMuEGx8\/hqdefault.jpg\",\n  \"contentUrl\": \"https:\/\/www.youtube.com\/watch?v=twTTWMuEGx8\",\n  \"embedUrl\": \"https:\/\/www.youtube.com\/embed\/twTTWMuEGx8\",\n  \"duration\": \"PT58M47S\"\n}\n<\/script>\n\n\n\n<iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/twTTWMuEGx8?si=Uc82IrCSO00Ybupp\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Parametric Tests<\/strong><\/h2>\n\n\n\n<p>Parametric tests are statistical tests in which we make assumptions regarding population distribution. Such tests involve the estimation of the key parameters of a distribution. For example, we may wish to estimate the mean or compare population proportions.<\/p>\n\n\n\n<div style=\"text-align: center; margin: 24px 0;\">\n  <div style=\"max-width: 680px; margin: 0 auto;\">\n    <a href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener noreferrer\"\n       style=\"display: inline-flex; align-items: center; justify-content: center;\n       width: 100%; padding: 12px 20px;\n       border: 2px solid #1a73e8; border-radius: 999px;\n       color: #1a73e8; text-decoration: none;\n       font-size: 15px; font-weight: 600;\n       line-height: 1.2; white-space: nowrap;\">\n      Compare parametric and nonparametric tests through our free trial.\n    <\/a>\n  <\/div>\n<\/div>\n\n\n<p><!--more--><\/p>\n<h3><strong>Breaking Down Parametric Tests<\/strong><\/h3>\n<p>When carrying out statistical tests, assuming the parameter follows a specific distribution, the distribution chosen directly affects the formulation of the test statistic. For instance, if we assume that a parameter follows a normal distribution, we have to compute the z-statistic.<\/p>\n<p>When conducting parametric testing, it may be necessary to approximate the normal distribution for non-normal distributions. This approximation is possible because of the central limit theorem, which asserts that as the sample size increases, most non-normal distributions \u201ctend to normalize.\u201d<\/p>\n<p>Parametric tests are generally considered to be stronger compared to non-parametric ones.<\/p>\n<h2><strong>Non-Parametric Tests<\/strong><\/h2>\n<p>Non-parametric tests \u2013 also called distribution-free tests by some researchers \u2013 are tests that do not make any assumption regarding the distribution of the parameter under study. Researchers use non-parametric testing when there are concerns about some quantities other than the parameter of the distribution.<\/p>\n<h2><strong>Situations Where Non-Parametric Tests are Appropriate<\/strong><\/h2>\n<h3 data-tadv-p=\"keep\"><strong>When the Median is More Desirable Compared to the Mean<\/strong><\/h3>\n<p>You can conduct a parametric test using non-normal data courtesy of the central limit theorem. There are situations, however, where the mean may not provide a fair measure of the central tendency, i.e., when there are large outliers.<\/p>\n<h4><strong>Example: Large Outliers<\/strong><\/h4>\n<p>Consider a situation where we want to establish the center of a rather skewed distribution such as that of the income of the residents of a given city. While majority of the residents could be categorized as the middle class, the presence of just a few billionaires in a sample can greatly increase the mean income. Such a mean, therefore, may not provide a very reliable or realistic measure of income.<\/p>\n<p>Instead, it may be more appropriate to use the median. Compared to the mean, the median can give a better representation of the center of the income distribution. This is due to the fact that 50% of the residents will be above median and the remaining 50%, below it.<\/p>\n<p>In a summary, \u201coutliers\u201d affect the mean when dealing with skewed data. The median, on the other hand, sticks closer to the center of the distribution.<\/p>\n<h3><strong>When the Sample Size is Very Small<\/strong><\/h3>\n<p>The absence of outright normal distribution of data might leave an analyst with insufficient information or too small a sample size to justify normal approximation. In the end, the analyst might not even successfully carry out distribution tests such as the goodness-of-fit test. In such a scenario, a non-parametric test may be appropriate.<\/p>\n<h3><strong>Analysis of Ordinal Data<\/strong><\/h3>\n<p>Although non-parametric tests are usually easier to conduct than parametric ones, they do not have as much statistical power. Nonetheless, they provide an efficient tool for analyzing ordinal, ranked, or very skewed data.<\/p>\n\n\n<div style=\"text-align: center; margin: 40px 0;\">\n  <a style=\"display: inline-flex; align-items: center; justify-content: center; padding: 12px 20px; border-radius: 999px; background-color: #1a73e8; color: #ffffff; text-decoration: none; font-weight: 600;\" href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener noreferrer\">\n    Start Free Trial \u2192\n  <\/a>\n  <p style=\"font-size: 15px; margin-top: 12px; color: #555;\">\n    Practice hypothesis testing and test selection with CFA Level I questions.\n  <\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Parametric Tests Parametric tests are statistical tests in which we make assumptions regarding population distribution. Such tests involve the estimation of the key parameters of a distribution. For example, we may wish to estimate the mean or compare population proportions&#8230;.<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[2],"tags":[],"class_list":["post-2569","post","type-post","status-publish","format-standard","hentry","category-quantitative-methods","blog-post","no-post-thumbnail","animate"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.9 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Parametric vs Nonparametric Tests | CFA Level 1<\/title>\n<meta name=\"description\" content=\"Understand the key differences between parametric and nonparametric tests, including their assumptions and applications in statistics.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link 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