Let's take one 'characteristic' as an example: Diastolic BP.
If you have the original data so you can check that the data
are nearly normal, then a two-sample t test would be appropriate.
As it is, you have only the median and the range, and no other
information about the individual
If data are nearly normal, then the sample means $\bar X_c \approx 78 $ and $\bar X_p \approx 105$
should be close to the medians (78 and 105). For normal samples of size $n = 10$ one can
guess the standard deviation from the range (max - min): multiply the
range by 0.32 to estimate the SD. So $S_c \approx 0.32(85-70) = 4.8$
and $S_p \approx 0.32(110-95) = 4.8.$
Then a pooled two-sample t test has a P-value is less than 0.0005
(according to the Minitab 17 printout below), which agrees with
the P-value recorded in your table.
Two-Sample T-Test and CI
Sample N Mean StDev SE Mean
1 10 78.00 4.80 1.5
2 10 105.00 4.80 1.5
Difference = μ (1) - μ (2)
Estimate for difference: -27.00
95% CI for difference: (-31.51, -22.49)
T-Test of difference = 0 (vs ≠):
T-Value = -12.58 P-Value = 0.000 DF = 18
Both use Pooled StDev = 4.8000
By contrast the data for Gestational Age (about which you ask specifically) do not seem normal for the
control group. The main
clue is that the median 39 is nowhere near the midpoint of 34.4 and 39.6.
One would have to see the actual data to be sure. For non-normal
data, I would recommend the nonparametric Mann-Whitney test (equivalent to the Wilcoxon rank sum)
test to compare the medians.
If the question is what kind of test to use based just on median, min and
max. I don't know that any of the two-sample tests in your list would be
appropriate. But I suppose the question is whether the original data might be
tested to verify the reported P-values; then you would need to look at
the original data to see whether they seem to be normal.
None of the paired tests seem appropriate here because there
is no pairing between subjects in the two groups. It is also hard
to imagine how Friedman, linear regression,
or correlation procedures would apply to the two-sample situation
of your table. (One-way ANOVA and Kruskal-Wallis procedures generally
apply to comparing $g \ge 2$ groups, but they can be used for $g = 2$
I have given you some clues to get you started, but I would recommend you look at the discussion in your text of each of
the tests on the list. What are the assumptions, and do those assumptions
seem to apply for each of the characteristics listed.
I think the purpose of this question is to get you to review all
of these tests and think about they types of designs and data for
which each is appropriate.