Home sales fell 41% year over year in February, but press didn't understand numbers, said they went up.

Not to mention that this is new home sales we're talking about, a product that has had a huge hit in supply. It would be more interesting to see sales year over year based on percentage of supply sold.

Basically any way you slice it you can argue the other person is full of shit. That doesn't mean anyone actually is.

To be clear - he isn't arguing that month over month data is not important. Specifically the problem is that because the confidence interval is -13.6% to 23% we don't actually know if the the true data is positive or negative at this point. The way confidence intervals are reported a 90% confidence interval means if you conducted 100 trials 90 of the times you would expect the number reported to be within your confidence interval (-13.6%, 23%). Why this number is meaningless though doesn't have anything to do with it being a month over month number, it has to do with the fact that we can't actually tell if February is higher or lower than January. Since the interval includes 0 and negative numbers, it's very possible and in fact highly probably that housing starts didn't grow at all in February but actually shrank compared to January.

The reason the year over year numbers are more useful is because they give us a "statistically meaningful" result. Because the year over year confidence interval is -49% to -33.2%, we can very confidently say the numbers are significantly lower this year than they were last year. Again, that's not because it's a year over year number, but because the confidence interval is no where near zero. 90 out of 100 times we would expect the data to be between -49% and -33.2%. In fact we can go even further. If this is a true 90% interval, we can calculate that 1 standard deviation is 4.79% and a 3 standard deviation range would be (-55.46%, -26.74%) this means that we would expect our observation to fall within this confidence interval 99.7% of the time. Notice that we can with a high degree of confidence state that that year over year numbers experienced a significant drop. For kicks and giggles let's look at the month over month number. 1 standard deviation is 11.09% and 3 standard deviations is plus or minus 33.27%. Meaning that our 99.7% confidence interval is -28.57% to 37.97% So our true value lies somewhere from housing shrinking from 28.57% to growing 37.97%! So we can't say with any statistical certainty that housing numbers decreased by 1/4th or increased by 1/3rd! That standard deviation is absolutely monstrous. So the problem isn't that month over month is unimportant and year over year is more important. It's that based on the numbers we just don't know what the actual month over month number is - we don't with any measure of statistical certainty know if it's actually up or down. Whereas with the year over year number we know with virtual statistical certainty that it is substantially down.

* one quick note - typically 95% confidence intervals are used because they reduce certain types of errors in your conclusions. I expanded the range to a 3 standard deviation range primarily for illustration purposes. I hope it helped rather than confused. Statistics is packed full of jargon and technicalities, and it's easy to project incorrect conclusions if you aren't very precise with your language.

edit, I just noticed it's a 90% confidence interval and not a 95% confidence interval. My original numbers above were based on a more typical 95% confidence interval which would represent 2 standard deviations. 90% Confidence intervals are 1.65 standard deviations from the mean. I've adjusted my 3 standard deviation ranges accordingly.

The term 'Seasonally Adjusted' means they even these seasonal tendencies out- thus giving meaning to month-over-month % changes. So it is not the same as your Pumpkin Sales example.

> Though he argues this data does not yield a statistically significant indication of either direction

Then it is noise and irrelevant.

This doesn't address my criticism in the slightest, and I'm extremely well aware of all of this. My comment did not concern what statistics the press should report in presenting financial data, only the lie of the original headline which suggested that the press incorrectly thought homes sales went up when they actually went down. For the scope that the press intended, the stats they reported were accurate.

To reiterate (and not to clarify, because my original comment is clear): When the press reports rises and declines, if they do not explicitly say year over year, they are talking month over month. Indeed, this VERY article contains an example of it, with the press reporting that home sales were up 4.7%. The original title of this submission, before it was edited to include "year over year", specifically played upon this implied and incorrect comparison to provoke a response.

Indeed, I'm not the only one who found the headline misleading; my comment had been voted up to at least 5 shortly after I posted, and before the headline was altered and your tangential comment sent people on a wild goose chase.