Understanding whether our perceptions of the world are influenced by the way in which statistics are presented is a critical issue for public policy discussions because policy debates are often based on our perceptions of the world through our interpretations of data, as in the case of issues pertaining to income inequality. In this study, we investigate the sensitivity of perceived inequality to different stratification measures. We randomly presented 15,000 Japanese adult respondents with either the stratification index proposed by Xiang Zhou or a series of household income percentiles, both of which were derived from the same data distribution spanning two periods in Japan. Our findings indicate that respondents perceived a more significant increase in inequality when they were presented with the income percentiles than when they were presented with Zhou’s stratification index. Therefore, to ensure consistency in public policy making, we must observe not only the same fact but also the same measurement of that fact. Different measurements of one fact may lead to different perceived worlds in our minds.