This question's explanation and your answers so far.
N社はスポーツ用品の小売販売業者で，実店舗販売の他，インターネットのショッピングサイトを利用した通信販売も行っている。ショッピングサイトのサーバの運用は外部に委託しており，毎月，委託先からアクセスログの分析結果が報告されるので，この報告に基づき，サイトの運営や改善に当たっている。 ショッピングサイトのトップページから商品購入手続完了に至る経路は，図1のとおりであり，図1中の矢印はリンクの経路を示す。ここで，A～Fは矢印の元のページから先のページへのアクセス率である。例えば，トップページにアクセスした利用者のA%が商品紹介のページにアクセスし，商品紹介のページにアクセスした利用者のC%が購入手続のページにアクセスしていることを示している。また，トップページへの外部からのアクセス件数に対する購入手続完了の件数の割合をコンバージョン率といい，先月のコンバージョン率は5%であった。 図1の経路図から，このサイトのコンバージョン率を求める式として，適切なものはどれか。ここで，式中のa～fは，図1に示したA%～F%のアクセス率を小数の値に変換した数値である。
(a+b)×(c+d+e)×f is wrong because it first adds up the access rates stage by stage and only then multiplies them. Addition may be used only when combining the proportions of separate paths that arrive at the same point. a and b are branches that split from the top page to two different pages, product information and campaign information, and c, d and e are likewise branches with different starting points, so adding them first breaks the correspondence between the paths. In fact, if you expand this formula, terms such as a×d×f and a×e×f appear, but no D% or E% arrow leaves the product information page, so no such path exists in Figure 1. The order in which multiplication and addition are applied is reversed, and the formula ends up counting paths that do not exist at all.
(a+c+f)×(b+d+c+f)×(b+e+f) is wrong because it turns a series relationship, which ought to be multiplied, into addition. a, c and f form a single connected series path, top page → product information → purchase procedure → purchase completion, so they should be written as a×c×f; adding them does not produce a meaningful value. In addition, c, f and b appear repeatedly in more than one set of parentheses, so the same arrow is counted several times over. The structure of multiplying three sets of parentheses also does not correspond to the three paths in Figure 1, which should instead be added together. This formula completely mixes up when to use a product and when to use a sum, and its value cannot be interpreted as a proportion either.
正解 The correct answer is ウ, a×c×f+b×d×c×f+b×e×f. The conversion rate is an indicator showing what proportion of the accesses that come to the top page from outside finally reach completion of the purchase procedure. You only need to remember two calculation rules for a path diagram. First, the proportion of users who follow one path all the way to the end equals the access rates of the arrows along that path multiplied together in order (a series connection means multiplication). For example, of the users on the top page, the fraction a moves to product information, and of those, the fraction c moves to the purchase procedure, so on the basis of the top page it becomes a×c. Second, when there are several paths that reach the goal, add up the values obtained for each path (a parallel connection means addition). In Figure 1 there are the following three paths from the top page to purchase completion. (1) top page →(A%)→ product information →(C%)→ purchase procedure →(F%)→ purchase completion, that is a×c×f. (2) top page →(B%)→ campaign information →(D%)→ product information →(C%)→ purchase procedure →(F%)→ purchase completion, that is b×d×c×f. (3) top page →(B%)→ campaign information →(E%)→ purchase procedure →(F%)→ purchase completion, that is b×e×f. The crux of this question is that beyond the campaign information page the route splits into two branches, the D% branch going back to product information and the E% branch going directly to the purchase procedure, so the paths starting with b must be counted as two. Adding these three together gives a×c×f+b×d×c×f+b×e×f, which is the conversion rate, so ウ is correct.
f÷(a+b) is wrong because it uses division, which never appears in path diagram calculations. Since a through f are all decimals between 0 and 1, dividing f by (a+b) can give a value greater than 1, which is impossible for a proportion. It also does not use c, d or e at all, ignoring the fact that some users drop out without going any further after the product information or campaign information page. f is no more than the proportion of users who complete the procedure among those who have reached the purchase procedure page; to turn it into a proportion based on the top page, the access rates of every stage leading up to that page must be multiplied in.