statistics - first trial

STATISTICS I

The first statistical trial will focus on 59 primary directions, which are supposed to be independent. These 59 directions come from the review of the biographies on this blog, from the beginning of statistics 'statistic begin here' (ie 20 subjects) ; that is to say that the beginning of the calculations made is made from the Saxe-Coburg natal 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-Camapnus 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) results :

1)- primary data : 59 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.

directions
Regio-Campa	Placidus	AO	Gold Regio	Gold Plac	Symb	AR
2	3	2	0	0	0	0
0	2	0	0	0	0	0
2	1	0	0	0	0	0
2	1	0	0	0	0	2
2	1	0	0	0	0	0
5	1	0	0	0	0	0
2	2	2	1	1	0	0
3	0	0	0	0	0	0
3	0	2	0	0	0	0
1	1	3	0	0	0	0
2	2	2	1	1	0	0
2	2	1	0	0	0	0
4	3	0	1	6	2	4
2	7	0	1	2	1	3
3	1	0	0	2	0	0
4	3	2	0	1	0	0
2	3	1	1	3	0	0
1	2	2	0	2	0	0
2	4	0	0	0	0	0
0	0	0	0	0	3	1
2	7	5	0	0	4	1
1	3	0	0	1	0	0
2	1	0	0	0	0	0
2	4	0	0	0	0	0
1	2	0	0	0	0	0
2	3	0	0	0	0	0
1	0	1	2	1	0	0
2	2	2	1	1	0	0
0	2	0	0	0	0	0
3	5	0	0	0	0	0
0	2	0	0	0	3	1
1	4	0	0	0	2	2
4	2	0	3	1	0	0
3	0	0	0	0	0	0
3	0	0	0	0	0	0
2	0	0	1	0	0	0
0	2	0	0	1	0	0
2	1	0	1	1	0	1
2	2	0	0	0	1	1
3	2	1	0	0	0	1
1	1	0	0	0	0	0
2	0	0	0	0	0	0
1	1	0	0	0	0	0
1	1	0	0	0	0	0
1	1	1	0	1	0	0
2	0	0	0	0	0	0
1	1	0	0	0	0	0
1	1	0	0	0	0	0
2	2	0	1	1	0	0
4	3	0	1	0	0	0
2	4	0	1	1	0	0
2	1	0	0	0	0	0
2	5	0	0	1	0	0
0	2	0	0	0	0	0
1	1	0	0	0	0	2
2	2	0	0	0	0	0
0	2	0	0	0	0	0
2	2	0	0	2	2	1
1	2	0	0	0	0	0

2)- Friedman test

Friedman's Test
N	413
N (=t)	60
k (=b)	7
SRj2	423082,5
T	71,009
p	0
critical value 5%
ties	324
corr. for ties	0,715
T'	99,371
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

differences		values
regio-campa-placidus =	1,50	threshold value=	71.29
regio-campa-AO =	143,50	threshold value =	71.29
regio-campa-Gold Regio =	159,50	threshold value=	71.29
regio-campa-Gold Plac =	133,50	threshold value=	71.29
regio-campa-Symb =	167,00	threshold value=	71.29
regio-campa-AR =	154,50	threshold value=	71.29
placidus-AO =	142,00	threshold value=	71.29
placidus-Gold-Regio =	158,00	threshold value=	71.29
placidus-Gold-Pla =	132,00	threshold value=	71.29
placidus-Symb=	165,50	threshold value=	71.29
placidus-AR =	153,00	threshold value=	71.29
AO-Gold Regio =	16,00	threshold value=	71.29
AO-Gold Plac =	10,00	threshold value=	71.29
AO-Symb =	23,50	threshold value=	71.29
AO-AR =	11,00	threshold value=	71.29
Gold Regio-Gold Plac =	26,00	threshold value=	71.29
Gold Regio-Symb =	7,50	threshold value=	71.29
Gold Regio-AR =	5,00	threshold value=	71.29
Gold Plac-Symb =	33,50	threshold value=	71.29
Gold Plac-AR =	21,00	threshold value=	71.29
Symb-AR =	12,50	threshold value=	71.29

 
At present, therefore, we can say only one thing: the results are not random. But this does not mean that the difference observed is the sign of an astrological fact; it is therefore necessary to look for biases that might otherwise explain these results.

In combination with the Friedman test, we also calculated the Page's test. This test differs from the Friedman test or its variants for incomplete blocks because of the alternative hypothesis which assumes an order here.

3)- other tests

Page's Test
N (= t)	60
k (= b)	7
L	5823,5
m	6720
s	88,544
SL	10,125
p	0,00073
critical value for L [ 5 | 1 | 0.1 ] %	not available

2)- review of data  
It seems convenient to output the values of Regio-Campa and Placidus which are > 1 for standardization. So the data become :

Regio-Campa	Placidus	AO	Gold Regio	Gold Plac	Symb	AR
1	1	2	0	0	0	0
0	1	0	0	0	0	0
1	1	0	0	0	0	0
1	1	0	0	0	0	2
1	1	0	0	0	0	0
1	1	0	0	0	0	0
1	1	2	1	1	0	0
1	0	0	0	0	0	0
1	0	2	0	0	0	0
1	1	3	0	0	0	0
1	1	2	1	1	0	0
1	1	1	0	0	0	0
1	1	0	1	6	2	4
1	1	0	1	2	1	3
1	1	0	0	2	0	0
1	1	2	0	1	0	0
1	1	1	1	3	0	0
1	1	2	0	2	0	0
1	1	0	0	0	0	0
0	0	0	0	0	3	1
1	1	5	0	0	4	1
1	1	0	0	1	0	0
1	1	0	0	0	0	0
1	1	0	0	0	0	0
1	1	0	0	0	0	0
1	1	0	0	0	0	0
1	0	1	2	1	0	0
1	1	2	1	1	0	0
0	1	0	0	0	0	0
1	1	0	0	0	0	0
0	1	0	0	0	3	1
1	1	0	0	0	2	2
1	1	0	3	1	0	0
1	0	0	0	0	0	0
1	0	0	0	0	0	0
0	0
1	0	0	1	0	0	0
0	1	0	0	1	0	0
1	1	0	1	1	0	1
1	1	0	0	0	1	1
1	1	1	0	0	0	1
1	1	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	1	0	1	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	1	0	0	0
1	1	0	1	1	0	0
1	1	0	0	0	0	0
1	1	0	0	1	0	0
0	1	0	0	0	0	0
1	1	0	0	0	0	2
1	1	2	0	0	0	0
1	1	0	0	0	1	0
1	1	0	1	0	0	0
1	1	0	0	0	0	0
1	1	0	0	1	0	0

Friedman's Test
N	422
N (=t)	61
k (=b)	7
SRj2	426772
T	35,199
p	0
critical value 5%
ties	387
corr. for ties	0,689
T'	51,122
p'	0
Page's Test
N (= t)	61
k (= b)	7
L	6060,5
m	6832
s	89,279
SL	8,641
p	0,00164
critical value for L [ 5 | 1 | 0.1 ] %	not available
Kendall's coefficient of concordance
k	61
N	7
df	6
s	22130,7143
W	0,212
F	0,309
T for ties	532
W*	0,309
p	0
critical value of W [5 | 1] %

The test are concordant with the precedent but give, naturally, fewer statistical values.