$5 \cdot 80$ Two different drugs $A$ and $B$ have undergone clinical trials in two hospitals. The trial results show that in both hospitals, drug $A$ is more effective than drug $B$. However, it is strange that when the results are combined, drug $B$ appears to be more effective than drug $A$. Is this possible, or is there a calculation error?
［Solution］It may be possible.
Consider two cases.
(1) If drugs $A$ and $B$ are tested on $n$ people each in Hospital A, and the number of effective cases are $a$ and $b$ respectively, then $\frac{a}{n}>\frac{b}{n}$. Thus, $a>b$. Suppose drugs $A$ and $B$ are tested on $m$ people each in Hospital B, and the number of effective cases are $c$ and $d$ respectively, then $c>d$. Therefore, $a+c>b+d$, which implies $\frac{a+c}{m+n}>\frac{b+d}{m+n}$. That is, when the number of people tested in both hospitals is the same, the combined results still show that drug $A$ is more effective than drug $B$.
(2) When the number of people tested in at least one of the hospitals is different, the situation described in the problem can be realized. For example, if drugs $A$ and $B$ are tested on 10 people each in Hospital A, with effective cases being 3 and 2 respectively; and drugs $A$ and $B$ are tested on 90 and 990 people respectively in Hospital B, with effective cases being 45 and 488 respectively. It is easy to see that
$$
\frac{3}{10}>\frac{2}{10}, \frac{45}{90}>\frac{488}{990} \text {. }
$$

However, when combined, we have
$$
\frac{3+45}{10+90}=\frac{48}{100}<\frac{490}{1000}=\frac{2+488}{10+990} .
$$

That is, drug $B$ is more effective than drug $A$.