The universe continually expanded but remained statistically unchanged as new matter is constantly created.
What is the statistically unchanged? Could you give me an example?
That would be referring to the average density of the universe. If space is expanding in a measurable manner (that is, if expansion is such that localised clusters of mass, such as an observer can detect the change), then the statement asserts that matter is being created in the "new space" at a rate sufficient to maintain the average density of matter in the universe. It's that average, or statistical mean density that is being referred to in the your example sentence.
 If all space were expanding at the same rate, including the space between particle probability waves and their wavelengths, then the observer would be expanding at the same rate as the universe, as would any measurement references, so the expansion would be unmeasurable.
I think the author may be using the phrase in a slightly unscientific/unorthodox way.
Usually, following an apparent change, something remains "statistically unchanged" if the change is not statistically significant. If you measure something, there will usually be some degree of change that indicates that the phenomenon you are measuring has "really" changed due to some factor/influence, and smaller changes in the measurement which are just down to "random" fluctuation or measurement errors and which you'd expect to get by pure chance on repeatd measures even if nothing has really changed the thing you're measuring. There are statistical tests to determine the probability of an observed change in a measurement actually reflecting a "real" change in the observed variable.
I can't exactly reconcile this with the example sentence you gave-- I think they could be misusing the term slightly-- but usually, "statistically unchanged" would imply "may have changed in terms of the raw measurement, but this change does not pass the relevant test(s) for statistical significance".