Psionic Pstone Pstatistics: Results and Conclusions - Part 2

Psionic Pstone Pstatistics: Results part 2 ind Conclusions By Arglebargle Rumpleslitz Ritzleyhopper Dinklehoffer

Preface: Note that you should have and have read a copy oj the first book in this series, to understanding oj these conclusions.

5 disciplines never appeared (Do they ever appear on stones?? Need bigger sample size than 100 to be sureness! - note that they did ne appear on the discarded 50 stones from sampling error either) that have been manifested/exhibited/displayed previously by psions: Cannibalize, Psionic Residue, Psionic Vampirism, Psychic Drain, Receptacle.

4 disciplines appeared that are never manifested by psions normally: Convocation, Control Light, Chemical Simulation ind Control Wind. Incidentally, Control Wind is extremely important discipline especially if you eat the Burning Poopenschliemer Bean Surprise while spending timing on dwergen rothe cattle rustling roundups near Marazdin! Jaa! Is true!

(total instances oj disciplines = 359) / (number oj different disciplines = 78) = (expected number oj times a discipline should appear on average) which is tiny bit over 4.6, (actually equal to 4.6025641025641 but rounding off to 4.6 because too hard to use abacus meit too many decimal placeys). Note: Need bigger abacus!

Taking our data, number oj instances oj 78 disciplines on 100 stones. Null hypothesis, if our results are a random sampling oj pstones, is that there is an equal probability for any oj the 78 disciplines to appear in any "slot" 1-6 on a stone. Alternate, is not equal or truly random, thus weighted somehow. Expected, in perfect theoretical (ie, fantasy) world where there is random number oj 1-6 disciplines on each stone, is that in 359 instances oj 78 disciplines, each discipline would be represented 4.6 times (359/78). This is the expected value, the mean or average.

We log each numerical value, whether 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 or 10, for how many times each different discipline appeared. We take (Observed - Expected) difference (say, if there were 4 disciplines on a stone, (Obs-Exp) = 4 - 4.6 = -0.6 Square that (multiply by itself), is = 0.36 - this gives a positive number when observations were lower than 5. Then, divide 0.36 by Expected again, 0.36 / 4.6 = ~ 0.08. This calculation is done for all 78 disciplines, and then all results totaled; this total is then compared to the above chart at the appropriate DF (chart was truncated for space). This is the Psquaring Pstatistic calculation.

Total oj all these = 116.40. This is the value oj the statistic. If looking at our listing oj paired values in parens, at DF of 77, that b-value is found between p-values oj 0.005 and 0.002. Can reasonably estimate at 0.003. Use the p-value we found ind decide whether to support or reject the null hypothesis. In general, small p-values (1% to 5%) would cause you to reject the null hypothesis. This even smaller p-value (0.3%) means that the null hypothesis should be rejected.

Conclusions:

Now, for how this all applying, jaa?

We thus reject the null hypothesis that disciplines on power stones are equally distributed (equal chances to appear on a stone), and say that the results obtained indicate that disciplines on power stones are ne equally distributed. Oddness observed, is ne just typical Forian-messing-with-the-chaosity. Why, ind how much, is cause for further discussion ind testings, but most probableness, some disciplines appear more frequently than others on stones. Other conclusion: ARGLE NEEDING FINDING A BIGGER AND BETTER ABACUS!

Problems meit the study: There are three problems Argle seeing meit these methods ind conclusions: a) Difficulty to get proper number oj stones for gudie sample size (1000): Can ne be helped. Making do meit 100 stones since Argle ne wanting spend 10 more years gathering pstones for data collectings. Pstatistics still applies, just is less certain oj results. More advanced pstatistics such as Analysis oj Variance (ANOVA, or a big boomie! Whee!) or Multivariate Analysis oj Variance, may need to be applied instead oj psquaring pstatistic used herely. b) Since once a discipline appears on a stone, this alters the chances that all the following slots on that stone will contain that discipline, to zero. This, oj coarseness, plays havoc meit the mathemagics oj pstatistical calculations - needing much better ind bigger abacuses (abacusi?) ind would change the expected value oj 4.6, to one that is lower. By how much? Unknown. But even if by factor oj 10, that would cause p-value to be 0.03, or 3%, which is still well meitin tolerances (1%-5%) for rejecting the null hypothesis. c) Since there were 5 disciplines that never appeared, is unsure if is proper to leave them out oj calculations for means ind p-value. If doing so, this would further deflate expected values in calculations, ind cause a higher value for the statistic, thus causing us not to reject the null hypothesis. Argle inviting other researchers to repeat pstudy ind gather own conclusions - especially if finding some pstones having the missing disciplines (Cannibalize, Psionic Residue, Psionic Vampirism, Psychic Drain, Receptacle). Argle going back to researching fuzzy math, chaos theory ind Andrinor's True Magic oj Whole Zatas.

The Poopenschliemer

Daavensplaats given to: Tower oj Iron Will, Ysgard; Tower oj the Mind, Luminous Order, Mikona; Various unnamed-herely psions, for: addressing oj stones, usings oj libraries, ind relatings oj experiences using stones Various unnamed-herely merchants who sold Argle lots oj psionic pstones.

Arglebargle Rumpleslitz Ritzleyhopper Dinklehoffer, Red Order oj Flamings, Mikona