Stand up to your Defense Panel with Small Non Random Samples
Power and Efficiency at high price
Older science (and social science) students remember being told during their one applied statistics course, like “Statistics for Communication” or “Research Statistics” that parametric tests, such as t-tests and analysis of variance are powerful and more efficient in discriminating between true and false hypotheses than non parametric tests.
In general, this is true. But the power and efficiency of parametric tests impose a priori stringent conditions: for examples, the level of measurement must be in interval or ratio scales; samples must be randomly selected, and they must be large enough [(or as statisticians love to call them, “asymptotic”); how large can be precisely calculated, provided you have an idea of “tolerable variance”. Some statisticians give 100 approximately, some 50, Walpole allows 30, BUT!!]; they must come from approximately normal populations. How do you know if the population is normal? Well, you must have made certain that they aren’t skewed, and also mesokurtic [if youre not a math or stats major, and you`re just doing research for an undergraduate thesis, I fully sympathize with you].
Randomization tests to the rescue
So your samples are “ridiculously” small, say two groups at n=4 each? And your sampling wasn’t “totally” random (c`mon now, they weren’t random at all, were they? Because they were pre-defined groups you were very interested in, such as special kids (your own?), or children with disabilities in special learning modules (I applaud your altruism). However, they were measured very carefully, through commercially available questionnaire protocols, so that anybody would agree that your measurements were pre-validated and highly reliable. In spite of that, your defense panel, your adviser to boot, or God forbid, your research funder all have shown contempt for your experimental design, and loudly snorted at your “ridiculously” SMALL samples.
WHAT DO YOU DO?
You go to someone who knows how to do Fisher’s randomization test, or exact permutation tests, exact probability tests, whatever else they call it in avant-garde schools nowadays. THAT`S ME.
Email me a brief description of your research problem. If you`re in the Metro Los Angeles area, we can set up a free consultation meeting, and its a toss up who pays for the coffee. Seriously, I will propose in simple terms how I can solve your statistical or methodological problem, detail what you can expect in terms of both mathematical results, and substantive explanations, AND!! IMPORTANTLY, the support I`ll give you during your defense.
Reach out for help. There is no dishonor in not knowing what randomization tests are, and how they can kick t tests and ANOVA in the ass, when it comes to small non random samples. Mail me at arthur_anthony@yahoo.com
Older science (and social science) students remember being told during their one applied statistics course, like “Statistics for Communication” or “Research Statistics” that parametric tests, such as t-tests and analysis of variance are powerful and more efficient in discriminating between true and false hypotheses than non parametric tests.
In general, this is true. But the power and efficiency of parametric tests impose a priori stringent conditions: for examples, the level of measurement must be in interval or ratio scales; samples must be randomly selected, and they must be large enough [(or as statisticians love to call them, “asymptotic”); how large can be precisely calculated, provided you have an idea of “tolerable variance”. Some statisticians give 100 approximately, some 50, Walpole allows 30, BUT!!]; they must come from approximately normal populations. How do you know if the population is normal? Well, you must have made certain that they aren’t skewed, and also mesokurtic [if youre not a math or stats major, and you`re just doing research for an undergraduate thesis, I fully sympathize with you].
Randomization tests to the rescue
So your samples are “ridiculously” small, say two groups at n=4 each? And your sampling wasn’t “totally” random (c`mon now, they weren’t random at all, were they? Because they were pre-defined groups you were very interested in, such as special kids (your own?), or children with disabilities in special learning modules (I applaud your altruism). However, they were measured very carefully, through commercially available questionnaire protocols, so that anybody would agree that your measurements were pre-validated and highly reliable. In spite of that, your defense panel, your adviser to boot, or God forbid, your research funder all have shown contempt for your experimental design, and loudly snorted at your “ridiculously” SMALL samples.
WHAT DO YOU DO?
You go to someone who knows how to do Fisher’s randomization test, or exact permutation tests, exact probability tests, whatever else they call it in avant-garde schools nowadays. THAT`S ME.
Email me a brief description of your research problem. If you`re in the Metro Los Angeles area, we can set up a free consultation meeting, and its a toss up who pays for the coffee. Seriously, I will propose in simple terms how I can solve your statistical or methodological problem, detail what you can expect in terms of both mathematical results, and substantive explanations, AND!! IMPORTANTLY, the support I`ll give you during your defense.
Reach out for help. There is no dishonor in not knowing what randomization tests are, and how they can kick t tests and ANOVA in the ass, when it comes to small non random samples. Mail me at arthur_anthony@yahoo.com
Comments
- Marian Cachuela,
MBA, University of Santo Tomas