Does this mean that you're more likely than your other brothers to be gay, or you're more likely than than the 7% or whatever average people are gay? I think that makes a difference. And is there any significance to why this study only includes men? I'm not saying that the study is wrong, but it does bring up some questions. Statistics is a very very tricky field, so I also approach it with caution.
Whilst I am a researcher, this is not my field of study so I encourage you to read further and to examine the primary literature. Having said that, I'll try for a brief answer and point to some literature if you want to take it further.
Quoting the literature: "In men, sexual orientation correlates with an individual's number of older brothers, each additional older brother increasing the odds of homosexuality by approximately 33%" (Blanchard, 2001, p. 105). You will find very similar statements in a range of studies, including the one I cited above and some of those below, and I think this answers your first question.
You also asked about why only men - both have been studied, but it turns out that women don't matter (to the effect). Quoting Cantor
et al. (2002, p. 63, emphasis in original): "Epidemiological studies have repeatedly shown that older brothers increase the probability of homosexuality in later-born males (Blanchard, 1997, 2001; Jones & Blanchard, 1998 ). Older sisters, in contrast, do not affect the sexual orientation of later-born males, and neither older brothers nor older sisters affect the sexual orientation of later-born females. Because females are essentially invisible to this process, we have called it the
fraternal birth order effect."
I agree that one needs to be very careful with statistics, but the amount of research in this area, published in a variety of peer-reviewed journals, allows for a very high degree of confidence in the validity of the statistical methods used. Of course, problems can still arise with the interpretation of statistical results.
The study to which I referred (Cantor
et al., 2002) is not one that reports the fraternal birth order effect - rather, it is addressing the question of whether this effect contributes significantly to the size of the homosexual population. Their conclusion of about 1 in 7 has been confirmed by a study by Blanchard and Bogaert (2004, p. 151) who noted that their "results indicate that the proportion of homosexual men whose sexual orientation is attributable to fraternal birth order constitutes a minority, but not a negligible minority, of all homosexual men". If you want to have a closer look at the research that reports on the effect itself, some references are:
Blanchard, R. (1997). Birth order and sibling sex ratio in homosexual versus heterosexual males and females.
Annual Review of Sex Research, 8, 27 - 67.
Blanchard, R. (2001). Fraternal birth order and the maternal immune hypothesis of male homosexuality.
Hormones and Behaviour, 40, 105 - 114.
Jones, M. B. and Blanchard, R. (1998 ). Birth order and male homosexuality: An extension of Slater's Index.
Human Biology, 70, 775 - 787.
Blanchard, R. and Bogaert, A. F. (2004). Proportion of homosexual men who owe their sexual orientation to fraternal birth order: An estimate based on two national probability samples.
American Journal of Human Biology, 16, 151 - 157.
Some of this work has received large amounts of attention in the literature. For example, the earlier paper:
Blanchard, R. and Bogaert, A. F. (1996). Homosexuality in men and the number of older brothers.
American Journal of Psychiatry, 153, 27 - 31.
has been cited 75 times in other papers, according to a search on ISI.