statistics (II)

STATISTICS II

The second statistical trial will focus on 76 primary directions, which are supposed to be independent. These 76 directions come from the review of the biographies on this blog, from the first try of statistics ; that is to say that the beginning of the calculations is from the Chiromantic Coclitis nativity chart. We work in terms of a null hypothesis. The main criterion is that the primary directions according to Placidus or Regio-Campanus do not give a better result than the control group, consisting of declared fictitious methods (AR, AO, symbolic, Goldmayer).

The alternative hypothesis is that the directions according to Placidus or Regio-Campanus give a better result than the control directions.

We have used the Friedman test ; it is a non-parametric statistical test developed by Milton Friedman. Similar to the parametric repeated measures ANOVA, it is used to detect differences in treatments across multiple test attempts. The procedure involves ranking each row (or block) together, then considering the values of ranks by columns. Applicable to complete block designs, it is thus a special case of the Durbin test.
Classic examples of use are:
 n wine judges each rate k different wines. Are any of the k wines ranked consistently higher or lower than the others?
 n welders each use k welding torches, and the ensuing welds were rated on quality. Do any of the k torches produce consistently better or worse welds?
The Friedman test is used for one-way repeated measures analysis of variance by ranks. In its use of ranks it is similar to the Kruskal–Wallis one-way analysis of variance by ranks. 

Here, instead of 'wine' or 'torches', we used as 'judge' the arc of direction, and instead of 'wine', the method of direction. Here are the (preliminary) second results :

1)- data : 76 primary directions

For the seven techniques, I have identified the rays of primary direction. First, the Morinus software is used to save time; in a second step, the analysis is completely redone and then the synthesis allowing the statistical processing of the data. One row consist on the number of rays. All the rays all summarized in the natal chart file and the biographies. As before for the 1st trial, i recommend to output the data > 1 for Regio-Campa and Placidus sous-group.

 

Regio-Campa	Placidus	AO	Gold Regio	Gold Plac	Symb	AR
1	1	0	0	0	0	0
0	0	0	0	2	0	0
1	1	0	0	0	2	2
1	1	0	0	0	0	0
1	0	0	0	0	0	0
1	0	0	0	2	0	0
0	0	0	2	1	0	0
1	1	0	0	0	0	0
1	1	2	0	0	0	0
1	1	0	0	0	2	1
1	0	0	0	2	0	1
1	1	0	0	0	0	2
0	1	0	0	0	1	0
1	1	0	0	0	0	0
1	1	0	2	2	0	0
1	1	0	0	0	2	2
1	1	0	0	2	0	0
1	1	0	0	0	0	0
1	1	0	0	0	0	0
1	1	0	0	0	0	1
1	1	0	1	0	0	0
1	1	0	0	0	0	0
1	1	1	0	0	1	1
1	1	1	0	0	0	0
1	1	0	0	1	0	0
1	1	1	1	0	0	0
1	0	0	0	0	0	0
1	0	0	0	0	0	0
1	1	0	0	0	0	0
1	1	0	0	0	0	0
1	1	0	1	1	0	0
1	1	0	0	0	0	0
1	1	0	0	1	0	0
1	0	1	0	0	0	0
1	0	0	0	0	0	0
0	0	1	0	0	0	0
1	0	0	0	0	0	0
1	1	0	0	0	0	0
1	1	0	1	0	0	0
1	1	0	0	1	1	0
1	0	0	0	0	0	0
1	0	0	1	0	1	1
1	1	0	0	0	0	1
0	1	0	0	0	1	1
1	1	0	0	0	1	1
1	1	0	0	0	1	1
1	1	0	0	0	1	0
0	1	0	0	0	0	1
1	1	0	0	1	0	0
1	0	0	0	1	0	0
1	0	0	0	0	0	0
1	1	0	0	0	0	0
1	1	0	1	0	0	1
1	1	0	0	1	0	0
1	1	0	0	1	0	0
1	1	0	0	0	1	1
1	0	0	0	0	0	0
1	1	0	1	0	0	0
1	1	0	0	0	1	0
1	1	0	0	1	0	0
1	1	0	0	0	0	0
0	1	0	0	0	0	0
0	1	0	1	1	0	0
1	1	0	0	0	0	0
1	1	0	1	1	0	1
1	1	1	0	0	1	1
1	1	0	0	0	0	1
1	1	0	0	0	0	1
1	1	0	0	0	0	1
1	1	0	1	1	0	0
1	1	0	1	0	0	0
1	1	0	1	0	0	0
0	0	0	1	1	1	0
1	1	0	1	0	0	0
1	1	0	0	0	0	1
1	1	0	0	0	0	0

2)- Friedman test

Friedman's Test

N	532
N (=t)	76
k (=b)	7
SRj2	684521,5
T	106,042
p	0
critical value 5%
ties	512
corr. for ties	0,667
T'	159,081
p'	0

The Friedman test shows that the overall results are highly significant. There is no statistical difference between Placidus and Regio-Campanus ; but there is a statistical difference with all the other pseudo methods, notably AR, OA or symbolic.

recall : it is an overall estimation of the results of the standard methods used in the field of primary directions in astrology. If the 'value' is > 80.91, the result is statistically significant.

-------------------------------------------- 

 

Differences		threshold value
regio-campa-placidus =	27,00		80,91
regio-campa-AO =	203,00		80,91
regio-campa-Gold Regio =	171,00		80,91
regio-campa-Gold Plac =	159,00		80,91
regio-campa-Symb =	172,50		80,91
regio-campa-AR =	153,00		80,91
placidus-AO =	176,00		80,91
placidus-Gold-Regio =	144,00		80,91
placidus-Gold-Pla =	132,00		80,91
placidus-Symb =	145,50		80,91
placidus-AR  =	126,00		80,91
AO-Gold Regio =	32,00		80,91
AO-Gold Plac =	44,00		80,91
AO-Symb =	30,50		80,91
AO-AR =	50,00		80,91
Gold Regio-Gold Plac =	12,00		80,91
Gold Regio-Symb =	1,50		80,91
Gold Regio-AR =	18,00		80,91
Gold Plac-Symb =	13,50		80,91
Gold Plac-AR =	6,00		80,91
Symb-AR =	19,50		80,91

3)- Page test

The Page test is an alternative to the Friedman test in case it wishes to use an alternative hypothesis classifying the modalities instead of simply considering the case of a difference between at least two modalities. This test therefore makes it possible, when it makes sense, to extract more information from the data collected.

Page's Test
N (= t)	76
k (= b)	7
L	7806
m	8512
s	99,653
SL	7,085
p	0,00389
critical value for L [ 5 | 1 | 0.1 ] %	not available