The research on the effects of animation is mixed but trends toward the negative.
One of the best summaries of the research on animation as an explanatory technique - not necessarily in statistical graphics though - is by Tversky.
This is a quote from that paper:
"if there are benefits to animation, they should be evident
especially for continuous rather than discrete changes, in particular, for manner of
change and for microsteps, the subtle and intricate timing relations among parts of a
Examples of more recent research on animation in bar charts, pie charts, and scatter plots can be found here. Their work builds on Tversky's principles for animation and describes 7 transitions suitable for 'data graphics'.
As with most problems in this area, the suitability of a design solution, e.g., animation, depends on the details of the problem.
helps doctors intepret scatter plots.
does not help analyze trends in multivariate data
does not help assess treatment risks
Here is my personal opinion. Motion design (aka animation) is a skill. The absence of the skill can lead to animations that detract from interpretation of statistical graphics whereas understanding of animation principles and attention to details will improve presentation of data. Take a look at this paper. It describes attempts to improve a well-known animated scientific visualization. The work they describe requires both an understanding of (1) animation principles, (2) the data being animated, and (3) the purpose of the presentation.