I am a diocesan priest in the parish of Cyrill and Method in the Archdiocese of Vienna, and a teacher at the In the article "Religious Differences Between Married and Celibate Clergy: Does Celibacy Make a Difference?" in Sociology of Religion (1998) (full text available to members of subscribing libraries or universities), Don Swenson attempts to make an empirical argument against some of the reasons advanced by the Church for clerical celibacy. While the experiment itself is poorly constructed to the point of being ludicrous, the idea is an interesting one, and I am of the opinion that this sort of empirical study could be profitably employed more within the Church (as it often is within large organizations).
Basically the idea of the study was to take a sample of married clergy and a sample of celibate clergy, measure devotion to Christ (religiosity) and the ability to devote oneself to parishioners, and see whether there is a significant statistical difference between the married and celibate clergy. Devotion to Christ was measured through responses made to questions about "thanking, talking to, loving, taking time with, worshiping, feeling close to and listening to God, reflecting on the Bible, acting on what I believe God is saying, achieving insights in prayer, sensing a divine presence, and experiencing peace" and the time spent in prayer. The ability to devote oneself to parishioners was measured by the amount of time spent in ministry.
The responses to the survey indicated that "there was no significant difference regarding MEDITATION [measuring religiosity and devotion to Christ] and PASTORAL COMMITMENT", while the priests spent more time in prayer and prayed more frequently than the married, evangelical clergy. The author argues that the "experiential religiosity" which the study aimed to measure is a better measure of devotion to Christ, and thus there was no significant difference between the two groups in terms of that devotion.
While the stated conclusion, "The results of this study are substantially consistent with the hypothesis that there are no significant differences in dimensions of religiosity and parochial commitments between celibate priests and married clergy" (emphasis added) is formally true, it is also true that the results of the study do not significantly support that hypothesis. The practical conclusion of the paper, "The implications of this study are that there is some empirical basis to argue for a change in the present law of clerical celibacy. In regards to one's devotional life and time for ministry, celibacy does not appear to matter" is therefore unwarranted. (Update: It was also pointed out in a comment that the study indicates that unmarried clergy spend more time in prayer and pray more frequently, and that this is itself in fact a reason for clergy to remain celibate, a point that the study ignored, as though prayer was of no value — or at least, that the question of prayer was basically irrelevant for the life of clergy.)
The study, in fact, has several glaring problems of which the author is apparently heedless. The two groups of clergy differed in multiple significant ways other than being celibate or married: (1) the one group was evangelical, the other Catholic (this was apparently the actual principle of division, since one group seems to have included all evangelical pastors, whether married or celibate). (2) One group (the evangelical) was taken as a sample from all over Canada, the other from only two dioceses. (3) The average age of the evangelical ministers was 44, while that of the priests was 60, a difference that the author points out, then proceeds to ignore. Lesser, though still significant problems, are that the response rate of priests was significantly lower than that of evangelical ministers, and that the total number of responses from priests was 80.
Was the author of the study clueless about what is necessary in order to establish a general statistical relationship? Or was he blinded by a bias with which he approached the study? It is not possible to say. But one thing is clear. If this kind of evidence is to be used to propose a change in the Latin or in the Oriental discipline, it should be collected much more soundly.
I am fairly confident that St. Paul would say that the fact that the celibate priests were able to pray more is in itself a sufficient reason for celibacy.
One might also note that denying that praying more for people is more beneficial for the people prayed for, in the end implies denying the efficacy of prayer completely.
Of course the study doesn't even really show that they were able to pray more, just that they did, which could also be because of the obligation to the Liturgy of the Hours. (Nothing is said indicating that the questions were asked in such a way as to exclude this). It may still be true, though, and probably is, that in fact married Catholic priests averagely spend less time in prayer than celibate priests.
It's not clear to me how your second argument would work. If one supposed the efficacy of our prayer to be measured only by the degree of charity with which one prays (and thereby the degree to which he is united to the prayer of Christ) and by the greatness or number of things for which one prays, so that the efficacy of prayer for an individual would correspond to the fervor of charity divided by the number of individuals for which someone prays (and the greatness of the impediment on the part of those individuals), would this imply a complete denial of the efficacy of prayer? Or would it only follow that this prayer at this moment cannot be assigned a given efficacy in abstraction from the rest of the prayers a person makes during their entire life?
By way of comparison, if someone denied that the greatness or duration of a work done did not make any difference, even an accidental or secondary or difference, to the reward merited for doing that work, and affirmed that the greatness of the merit of a work depended only on the charity with which it was performed, would that imply completely denying the meritoriousness of human action?
Regarding the first point, you correctly pointed out that the study doesn't prove anything because of the lack of controls. My only argument was simply that given their manner of argument, it would be just as reasonable to take the study as an argument in favor of celibacy, instead of taking it as they did.
Regarding the second point, it was not intended as a demonstrative argument but a claim about what that position amounted to in practice. For example, suppose I am praying a rosary for you. After the first Hail Mary, I realize I have already prayed for you, and praying more is not more effective than praying less, so there is no reason for me to continue.