Significance in Longitudinal Data I feel like this question has a very silly (simple) answer, so I apologize. I have a data set that only has 5 points
41.9
32.2
113.3
110.2
102.6

Clearly something significant happens between the 2nd and 3rd data points (but not between the 1st and 2nd, 3rd and 4th, etc.). What statistical test could I employ to show this in a more rigorous sense?
EDIT: Note, I was not clear with my question (sorry). The data is an ordered set. I would like to determine that the difference between 2-3 is statistically larger than 1-2, 3-4, and 4-5.
Thanks!
 A: Of the $5! = 120$ distinct sequences that can be formed of those five numbers, 


*

*$4\times 2!\times 3! = 48$ of them will have the small values $41.9$ and $32.2$ next to each other.  (There are four places for this pair to occur, $2!$ ways of ordering them, and $3!$ ways to order the other three numbers.)

*Yet another $2! \times 3! = 12$ sequences will alternate between a high value in $\{102.6, 110.2, 113.3\}$ and a low value in $\{32.2, 41.9\}$.

*Another $2! \times 3! = 12$ will bracket the three high values with a low value on either end.
I have enumerated $72$ so far, which is $60\%$ of all the possible sequences.  Thus, depending on what kinds of patterns might catch your notice (which is a matter for your psychologist to explore), the total number of such "clearly something significant" sequences could easily be more frequent than sequences that do not clearly have something significant!  From this we may draw two conclusions:


*

*Not a single one of these patterns is rare enough to be considered "statistically significant" at a conventional ($5\%$, or $6/120$) level.

*Any conclusion about "significance" derived after recognizing a "clear, significant" pattern when exploring dataset must be considered subjective.
(This is not to say such conclusions are without value. It only maintains that statistics, correctly applied, will not sanctify the conclusions of an open-ended exploratory analysis with any level of "significance," because it cannot.)

Such quantitative reasoning leads generally to the following statistico-psychological metatheorem:

In any collection of random patterns, the majority will be unusual.

Those of you familiar with Garrison Keillor may recognize an echo of the Lake Wobegon population: "... and all the children are above average."  However, I privately refer to this as the Shirley MacLaine principle, in honor of her well-known work as a "spiritual missionary," a seer of things and causes that do not exist.
A: It looks like the simplest way is to use Chow test. If your sequence was assumed to be iid with no covariates, then it's probably equivalent to a two-sample test (e.g. a t-test) for the equality of means with 2 and 3 observations per sample. However, based on the Chow article, I don't see how it adjusts for data snooping, i.e. for the fact that the split into the two groups is suggested by the data. 
