# How to phrase the results of a t-test?

At work, a team I'm on is researching the differences between majority-African American census tracts and all other census tracts in my county. Here is an example of one of the T-tests that I ran in Excel:

The mean of the median year-built for African American census tracts is 1976, as opposed to other census tract structures having a build date of around 1970. Obviously p < 0.05, so the difference in means is significant, but in my writeup, is it correct to say the following?

In [name] county, statistically, majority-African American census tracts have newer structures.

Or am I only able to use the phrasing below?

Statistically, majority-African American census tracts have a different age of structures from non-majority-African American tracts, and on average they are newer.

I have about 12 attributes that the t-tests found statistically different, but I just need to know how to represent my findings clearly without being disingenuous with my conclusions.

• How was the data collected? Is it a random sample? Jan 15, 2020 at 20:28
• @MichaelM 2017 ACS Census data. The data set contains all of the tracts in the county at hand. Jan 16, 2020 at 17:56

I don't see that the second statement adds anything crucial to the first statement--if the finding shown in your table is reliable.

There are, however, some important cautions to consider before you make any statements.

First, I find analysis of the "mean of the median year-built" to be a bit awkward, and potentially a bit misleading as it doesn't take into account any different numbers of structures among the census tracts.

Second, with the variances so similar it's not clear why you ran a test assuming unequal variances. Perhaps associated with that, it's not clear why with 182 observations (tracts?) your test reports only 77 degrees of freedom.

Third, as you are looking separately at 12 different attributes (probably even more, as what you say is that you found 12 to differ) you need to take into account the possibility of false-positive results arising from the multiple-comparisons problem. If you corrected for multiple comparisons it's not clear that the p = 0.043 value in your table would remain statistically significant.

• I agree with your point on the poor phrasing, I'll fix that. I used t-test assuming unequal variances for all of my tests because I wasn't sure what the variance would be until I actually ran the math in Excel. In this example they're pretty close, but in most they are quite different (e.g., variances of 430 and 59 on college graduation rates). We're certainly keeping the multiple-comparisons problem in mind, right now we're just describing differences between the two types of tracts, not necessarily root causes. Jan 16, 2020 at 18:08
• @BrendanBow you might consider non-parametric tests instead of t-tests, avoid normality/variance assumptions, and give a more straightforward report of test results. The Mann-Whitney test has reasonable power even when values are normally distributed. A positive M-W result could be presented as: "the median age of a structure in a (randomly selected) Maj-AA census tract is likely to be less than the median age of a structure in a (randomly selected) Non-Maj-AA tract."
– EdM
Jan 16, 2020 at 18:23
• I actually did also run Mann-Whitney tests on the same set of analyses, just to try and get a bigger picture of the data at hand. They agreed with all the t-tests I ran, except for a couple (which I explain in the text). Thanks for your help! Jan 16, 2020 at 18:41