In accordance with the non-analytic stance taken in the introduction, we aspired no further dissection of variables related to so-called 'psi-processes' or 'psi-mechanisms'. Our hypothesis simply stated that the Eigensender technique would facilitate anomalous cognition. Existential evidence for psi would appear from the total number of hits, which amounted to 14 out of 32 sessions, resulting in an effect size of 43.75% (for raw data, click here).

Table 1. Hit-rate with p = 0.25
conditionN sessionsN hits (p = 0.25)ESz (corr.)p (one-sided)
ES 16 6 37.75
ES+ 16 8 50
total 32 14 43.75 2.45 .012

Manipulating the variable ES / ES+ with hit-rate ES: 6/16 = 37.75% and hit rate ES+: 8/16 =50%, clearly did not yield a significant difference.

This traditional one-in-four hit-rate effect size is a rather crude measure; it may filter out possible indications of psi in those trials where the target was not actually selected by J, as is for instance the case when possible psi-mediated target mentation is surpassed by decoy related material (as a result of either coincidental resemblances or the type of Ganzfeld displacement effects discussed in Wezelman et al., 1994). Therefore, putting quality before quantity, we planned to do a preferential ranking analysis to corroborate the existential evidence, applying the sum-of-ranks method described by Solfvin et al. (1978). This statistic is approximately normal for all values of N greater than 20; it follows from the formula:
    z = (M - Um 0,5) / SDm ,
    in which M is the observed sum-of-ranks,
    Um = N * (R + 1) / 2 the expected sum-of-ranks,
    and SDm = (N * (R * R - 1) / 12.
The observed total sum-of-ranks was converted from the ratings, with a hit ranked as 4. Table 2. sums up the result of this statistic:

Table 2. Probability of observed sum-of-ranks according to Solvin et al., 1978
sessions (N )ranks (R )sum-of-ranks (M )zp
32 4 100 3.083 .0012

Apart from these planned statistics concerning the question of evidence, we did a post hoc analysis testing for J's 'confidence' in scoring, another aspect of psi that is filtered out using the one-in-four ratio method. Using the fine-grained ratings (1 - 100) that perhaps would supply an even more precise measure than rankings, this test consisted of two ANOVA's. The first looked into the variance due to factor 'hit/miss' with dependent variable: the highest of the four ratings, normalised by divisor 'sum of second, third, and fourth rating'. The second ANOVA tested for effects of the 'hit/miss' factor on the dependent variable 'highest rating minus second highest rating'. Table 3 shows the results:

Table 3. ANOVA with factor: 'hit/miss' and dependent variables: 1) 'highest of four ratings, normalised by sum of second, third, and fourth rating', and 2) 'highest rating minus second highest rating'.
factordependent variableF p
hit/miss highest of four ratings divided by sum of ratings 2 - 4 2.160 .1521
hit/miss highest rating minus second highest rating 4.709 .0381

As can be seen in table 3, the first ANOVA yielded nothing, indicating that on average the picture in case of a 'hit', i.e. the target, is not rated higher than the highest rated picture in case of a 'miss'. Surprisingly though, this 'lack of confidence' is not confirmed by the result of the second ANOVA: the average 'highest rating minus second highest rating' in case of a 'hit' is significantly higher than 'highest rating minus second highest rating' in case of a 'miss', which could be read as an incidence of J's 'confidence' in rating. Combining the results would implicate that the second highest rated picture is rated considerably lower in case of a 'hit', as appears from table 4.

Table 4. Average highest rating, average second highest rating, and average highest rating minus second highest rating' according to hit/miss.
hit/missav. highest rat. (1hr)av. second highest rat. (2hr)1hr - 2hr
hit 77.857 53.928 23.929
miss 75.722 64.611 11.111