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Select the best statistical test(s) to use to compare the gestational age at delivery between the two patient groups in the table below. More than one correct answer may apply.

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Which of these tests are appropriate to use:

T-test

Mann-Whitney test

ANOVA

Repeated measures ANOVA

Friedman

Kruskal-Wallis

Posthoc test (e.g. Dunns or Bonferoni)

Paired T-Test

Wilcoxon matched pairs text

Wilcoxon signed rank test

Linear Regression

Pearson correlation

Spearman correlation

Two-way ANOVA

D'Agostino-Pearson test

Fisher's Exact Test

Chi2 test

Could you also explain why it's correct as I'm struggling with this statistics module in my medical MSc.

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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 observations.

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 $g = 2$ groups.)

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.

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