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How to calculate the certainty students fudge data to make chi-square "work right?"

 
 
Acensor
 
Reply Sat 9 May, 2020 12:41 pm
Back in ancient days as an undergraduate biology major, in the lab portion of the genetics course each of us students sprouted statistically significant numbers of seedlings with genetics expected to manifest color (or some other trait that had three distinct forms (let’s say red, white, pink) at a 1:2:1 ratio.

https://www.mun.ca/biology/scarr/Dihybrid_Cross.html

Now here's the thing:
Every single student in the labs reported snd wrote up reports showing their data , subjected ti chi-square test, statistically confirmed the 1:2:1 hypotheses (or at least didn't reject it) .....probably at P-sub-0 of .05 IIRR.

Well, it occurred to me then, and now, that in a large enough group of students conducting that experiment and analysis that a noticeable percentage should be reporting that their data was _not_ consistent with ...was _not_appearing to confirm the Mendelian dihybrid genetics for the studied trait. That some random sample of seeds planted surely should have ratios way off the 1:2:1.
And if , as was the case, no students in a population of, say, 200 were not turning in reports saying they found no support for the 1:2:1 expected, that would mean there was an extremely high probability that any student whose chi-square failed to show what they "knew it 'should' " then recalculated with falsified data. 😏
My gut guess is that all the students' reporting the defacto expected chi-squrare results without forging their data the probability that some students is over 99%.😏

I believe I mentioned this to the professor, and he probably took it somewhat seriously.

But here are my question(s) finally:
I Was, and am, unable to take this meta-data (not one of the 200 students reported there sprouted plant appeared to be inconsistent with 1:2:1 inheritance) and calculate a formal statistical number as to how low the probability of this was without forged data. (That is.. since by many criteria we knew in fact the traits in students' seed sample _are_classical Mendelian dihybrid inherited.)

Q: would you agree that in the scenario I described logic and statistics very strongly suggest all the students' reporting "success" is a sold case some faked their data?

Q: Can you come up with any calculations or equations of either the improbability of all of them reporting expected outcomes without fudging data, and/or conversely the numeric level of confidence that one or more students fudged data? 🤔
.....Either generically or plugging in some hypothetical case numbers (such as “all 100 students lab reports indicated their data in chi-square was close enough to 1:2:1 to a 95% of better confidence level.)

This out of reach to me calculation has tantalized me for decades.
I have lovedto be able to go to the professor and say I have size statistical analysis that there’s a 99.9% certainty that students are routinely fudging data in thes labs.
I'd have loved to be able to go to the professor and show statistical analysis that there’s a 99.9% certainty that students fudge data in these labs...and I bet we can re-designed it so that can’t happen."😏


URL: https://able2know.org/post/ask/statistics/
 
engineer
 
  3  
Reply Sat 9 May, 2020 06:13 pm
@Acensor,
I don't really get your experiment, but the way to do this would be to set up a random number generator with the appropriate ratios, run 10,000 tests, and run the statistics on all of them. See what percentage of random sets run with the known 1:2:1 ratio reject the hypothesis.
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KarterNino
 
  -1  
Reply Fri 9 Oct, 2020 06:05 am
@Acensor,
Thank you for such a wonderful experience. This immediately reminded me of my student days when my classmates and I also needed to do interesting research.
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