Here is a quote from an NPR article:

The report found that for every 15 boys who own a phone, only 10 girls do. And the difference is 18 vs. 10 for smartphone ownership. That’s according to a report released this month by the nonprofit organization Girl Effect.

Say what?? Why do we report data in this way? Is it not enough that people have trouble interpreting data? To me, this presentation of the data appears to be attempting to obfuscate what is going on.

#### Report ``percentage more’’

If we try to unpack the statement ``for every 15 boys who own a phone, only 10 girls do’’, we find that the ratio is 15/10 = 3/2= 1.5, i.e. there are 50% more boys with phones than girls. Reporting this percentage more seems a convenient and consistent way to report this type of data. For example, rather than 18 vs. 10 for those with smartphones, we could report 80% more.

#### Report estimated percentage

An additional issue is that these statistics don’t tell us what percentage of girls and boys have phones. The following pairs of percentages all produce 50% more boys with phones than girls:

• 100% boys vs 66% girls
• 60% boys vs 40% girls
• 3% boys vs 2% girls
• 0.00003% boys vs 0.00002% girls

It is not clear that we should care equally about these differences and therefore it would be good to know what the estimated percentages are.

#### Bias in surveys

The article mentions that the data were collected via surveys and in-person interviews, but also that there is a stigma against girls having phones in some locales. Thus, it is entirely possible that the reported percentage of girls who have phones is biased low. Thus, it isn’t even clear that the reported ratio (15 vs 10) is at all accurate.

24 October 2018