I'm not Deerman, but I will answer this in a way that I hope explains why that is incorrect.
Sex-linked traits are due to genes located on the Z chromosome (in birds). Females have one Z and one W chromosome (corresponding to the reverse in mammals, where males have one X and one Y chromosome). Males have two Z chromosomes. Traits that are recessive will not show when a bird has one copy of the gene associated with it, and one copy of the normal version of the gene. Because Purple is due to a gene mutation on the Z chromosome that is recessive to the normal version, only males can be "split" to Purple (i.e. having one copy of the Purple version of the gene, and one copy of the Normal version of the gene, which requires the bird to have two Z chromosomes, which only males have). Females, because they have only one Z chromosome, are "either-or" -- they are either Purple or they are Normal.
When peafowl breed, each parent gives one of each of its paired chromosomes. In the case of Z and W in females, they give either one. If a female is Purple and mated to a Normal male, then there are only two possible outcomes with respect to their Z chromosomes:
1) The female can give her Z (with the Purple version of the gene on it) and the male can give either of his Zs (each with only the Normal version of the gene on it), resulting in a ZZ bird (male) which has one copy of the Purple gene (thus, the males would be "Normal split to Purple").
2) The female can give her W (which does not carry the gene for Purple) and the male can give either of his Zs (each with only the Normal version of the gene on it), resulting in a ZW bird (female) which does not have any copies of the Purple gene (thus, the females would be "Normal").
When you have the reverse (Purple male X Normal female), then these are your possibilities:
1) The female can give her Z (with the Normal version of the gene on it) and the male can give his Z (with the Purple version of the gene on it) resulting in a ZZ bird (male) with one copy of the Purple gene and one copy of the Normal gene (thus, the males would be "Normal split to Purple").
2) The female can give her W (which does not carry the gene for Purple) and the male can give either of his Zs (each with only the Normal version of the gene on it), resulting in a ZW bird (female) which has one copy of the Purple gene (thus, the females would be "Purple").
A third situation possible would be a male split to Purple X Normal female. In this case, because the male could give either a Z with the Normal gene OR the Purple gene, there are now four equally-likely possibilities:
1) The female can give her Z (with the Normal version of the gene on it) and the male can give his Z with the Purple version of the gene on it, resulting in a ZZ bird (male) with one copy of the Purple gene and one copy of the Normal gene (thus, these males would be "Normal split to Purple").
2) The female can give her Z (with the Normal version of the gene on it) and the male can give his Z with the Normal version of the gene on it, resulting in a ZZ bird (male) with no copies of the Purple gene and two copies of the Normal gene (thus, these males would be "Normal").
3) The female can give her W (with does not carry the gene for Purple) and the male can give his Z with the Purple version of the gene on it, resulting in a ZW bird (female) with one copy of the Purple gene (thus, these females would be "Purple").
4) The female can give her W (which does not carry the gene for Purple) and the male can give his Z with the Normal version of the gene on it, resulting in a ZW bird (female) with one copy of the Normal gene (thus, these females would be "Normal").
What we can summarize from the above is that:
1) Purple females must have a father that is either Purple or Normal split to Purple, because she gets her Z chromosome (which is where the Purple gene is located) from her father. She gets her W from her mother.
2) Purple males must have a Purple mother, and either a Purple father or a Normal split to Purple father, since they need two copies of the Purple gene (one on each of their two Z chromosomes), and they get one from each parent.
Additionally, you won't be able to tell apart males that are Normal or Normal split to Purple without test-breeding to a Purple female -- if you get any Purple offspring from such a pairing, the male MUST be split to Purple (and the Purple offspring will all be females).
The other two possibilities are Normal split to Purple male X Purple female, and Purple male X Purple female. I'll give away the easy answer -- Purple X Purple = Purple (both sexes), but I'll let you try to figure out the other one based on what I've shown you.
