三、数字与比例不等价

数字与比例不等价是指根据一个比例所得出的结论是没有参考意义的。例如某地居民使用电视观看节目的比例上升了5%，但实际情况是总人口数大幅减少，才导致比例的上升，在这种情况下，5%的增长具有实际意义吗？答案显然是否定的。这就是数字与比例不等价的情况。鉴于此可能性，在没有给出基数的时候，不应简单地用百分比来说明问题。

具体结合例题如下（Day 3）：

The following appeared in a memorandum issued by a large city’s council on the arts：

“In a recent citywide poll，15 percent more residents said that they watch television programs about the visual arts than was the case in a poll conducted five years ago.During these past five years，the number of people visiting our city’s art museums has increased by a similar percentage.Since the corporate funding that supports public television，where most of the visual arts programs appear，is now being threatened with severe cuts，we can expect that attendance at our city’s art museums will also start to decrease.Thus some of the city’s funds for supporting the arts should be reallocated to public television.”

这是一个与调查研究相关的内容。文中提到“15 percent more residents said that they watch television programs about the visual arts than was the case in a poll conducted five years ago.”，这个百分比的数据一定能说明观看视觉艺术类电视节目的人数增长了吗？大家想想看百分比的增长在什么时候才等于实质性的增长？只有基数一样或更大时，百分比的增长才是实质性的增长。