Question
Asked 26 April 2024

What kind of research methodology, the Hypotheses are non-applicable?

q,

All Answers (2)

Haider Ali
Islamia University of Bahawalpur
Hypotheses are non-applicable in qualitative research methodology because it uses research questions to guide the inquiry and gather rich, descriptive data.
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Donald Ratcliff
No institutional affiliation
In qualitative research you often do not begin with hypotheses. Rather, hypotheses are more likely the result of your research.
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Similar questions and discussions

How can there be empirical evidence for space and time when they are universally recognized as abstract concepts?
Question
1 answer
  • Soumendra Nath ThakurSoumendra Nath Thakur
Scientifically, physical objects (such as a clock) can undergo changes due to applied forces or relativistic effects.
However, abstract concepts—such as numbers, addition, dimensions, space, and time—are not physically alterable, as they are conceptual rather than material. This is a well-established scientific fact.
Despite this, the notion of curvature in spacetime has led to the misconception that spacetime itself is physical rather than abstract.
Since neither space nor time possesses physical properties, they cannot be subjects of direct experimentation. Instead, they serve as conceptual dimensions—a framework within which physical objects exist and can be measured.
Measurements in physics are always performed on physical entities, not on dimensions themselves. For example, in a coordinate system, dimensions such as x, y, z, and t are graphical representations—they do not measure space or time itself but rather the physical objects within them. Similarly, space and time, as dimensions, do not physically change—only objects within these dimensions undergo measurable transformations. These transformations are always physical (e.g., changes in material properties or energy states), whereas space and time remain conceptual constructs.
Thus, the idea of spacetime curvature is fundamentally flawed because only physical entities—such as electromagnetic fields, gravitational fields, or massive objects—can bend or curve. Space and time, being dimensions, do not possess length, height, or depth themselves; rather, they define the extent of objects that have these properties.
In mathematics and geometry, space and time are represented abstractly, but this does not imply they are physically capable of curvature.
If curvature exists, it must be a property of physical objects, such as mass-bearing structures or massless fields like electromagnetism or gravity—not of spacetime itself.
Do you acknowledge the key points I have stated above?
Can you recommend additional books addressing the "a-test-of-medians" fallacy for the Mann-Whitney (Wilcoxon) and Kruskal-Wallis?
Question
5 answers
  • Adrian OlszewskiAdrian Olszewski
Hello,
I'm preparing for a webinar addressing several common statistical misconceptions in clinical trials that I observed many times. Now I'm collecting "good resources", clearing these misconceptions (+ doing my own simulations illustrating them).
One of the most common misconception I saw in various textbooks, presentations, discussions, etc. is that "both Mann-Whitney (-Wilcoxon) and Kruskal-Wallis compare medians", which is often stated:
a) without any additional conditions, which is wrong in general and easy to disprove just by example (or less easy, formally, as in the 1st book cited below)
b) as a "location-shift" problem, which doesn't translate to medians easily without additional conditions of IID samples or symmetry around the medians - which is a very strict condition and practically a "zombie" one. Zombie - means that this is rarely (if ever) checked in practice, as far as I could observe over years. Which sometimes makes researchers surprised to learn that:
1) stochastic equality (even at very high p-value) was claimed at very different means or medians
2) stochastic superiority (even at very low p-value) was claimed at exactly same means or medians. They simply forgot to check variances and shapes of the distributions. They also learned, that "happy juggling with tests", as I call it, in case of violated normality assumption may lead to testing different hypothesis, consistent or inconsistent with the original questions. In other words, it's not impossible to obtain a technically valid answer to a never asked question.
Funny, the original papers by Wilcoxon ("Individual Comparisons by Ranking Methods") and Mann-Whitney ("On a Test of Whether one of Two Random Variables is Stochastically Larger than the Other") don't refer to medians.
So far I found two excellent books, explaining this very issue, and a couple of articles, software manuals, and forum discussions:
Books:
1. Brunner, E., Bathke, A. C., & Konietschke, F. (2018). Rank and Pseudo-Rank Procedures for Independent Observations in Factorial Designs: Using R and SAS. Springer International Publishing.
  • ISBN: 978-3-030-02912-8 (Print), 978-3-030-02914-2 (eBook)
  • DOI: 10.1007/978-3-030-02914-2
This book shows step by step why do the MW(W), Fligner-Poicello and Brunner-Munzel are not consistent for detecting different medians or means.
2. Nussbaum, E. Michael. (2024). Categorical and Nonparametric Data Analysis: Choosing the Best Statistical Technique (2nd ed.). Routledge.
  • ISBN: 978-0-367-69815-7 (Paperback)
3. Thomas D. Cook, David L. DeMets. (2007). Introduction to Statistical Methods for Clinical Trials.Chapman and Hall/CRC
  • ISBN: 9781-5-848-80271
Links:
2. The Wilcoxon–Mann–Whitney Procedure Fails as a Test of Medians
3. What hypotheses do “nonparametric” two-group tests actually test?
- The Mann-Whitney test doesn't really compare medians
- Example 2014.6: Comparing medians and the Wilcoxon rank-sum test
- Mann-Whitney test is not just a test of medians: differences in spread can be important
- FAQ: Why is the Mann-Whitney significant when the medians are equal?
- Wilcoxon signed-rank test null hypothesis statement
- Yoon-Jae Whang, Econometric Analysis of Stochastic Dominance. Concepts, Methods, Tools, and Applications, ISBN: 9781108602204. [page 64: Test of stochastic dominance: Basic results]
Could you, please, recommend any other titles (books, papers) that cover this very topic in any way, less or more formal?

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