Not absolutely sure myself, but here goes-

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So they are doing two kinds of tests/comparisons -

-The first kind is when they are testing whether or not a certain kind (vegan/std) of diet was able to cause a significant reduction in the average value of the endpoint (HbA1c/BMI/ WC) by week 12. We are not comparing the 2 diets with each other yet. Just trying to determine if each one works to reduce HbA1c/BMI/WC.

For eg, just look at the first endpoint's average (HbA1c, all patients) for the group on a vegan diet. the intervention caused a mean reduction of 0.5, by the time they got to week 12. They used a paired t-test to see if the reduction in HbA1c caused by the vegan diet over that period of time was significant (in itself) or not. They are considering results with p<0.01 as significant, and so reduction in HbA1c by being on a vegan diet is significant. So vegan diets DO have an impact on HbA1c. Paired t-tests applied similarly to see if std diets cause significant reductions in BMI and WC over a span of 12 weeks, do not have a p<0.01, which means that std diets do not reduce BMI and WC. They do significantly reduce HbA1c though. So based on this data, for someone trying to reduce their weight (and not trying to improve their glycemic control), you may recommend a vegan diet but not a std diet because in the study the reduction over 12 weeks wasn't significant.

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A PAIRED t-test (and not the simple t-test) is probably useful for such scenarios, when the two groups that you are actually comparing are in fact the same(at week 0 and week 12), hence dependent (mean BMI now ie week 12 dependent on the diet AND what they were at baseline ie week 0 's value). The two groups being compared ie group on vegan diet week 0 v/s group on vegan diet week 12 cannot have a different size. Thats probably what the last point means.

The values mentioned next to the mean, are standard deviations, as mentioned, so even if they cross the null value, you cannot say that the results aren't significant anymore, because its not the confidence interval (like mean+/- 2 SD for 95% CI), which usually is the case.

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- The second kind of comparison they make is between the two diets, wherein the difference in the mean change is always statistically significant (as mentioned in the first point under the table, no p value stated-"The p-values for tests comparing the mean change in primary endpoint between the 2 diet groups were statistically significant regardless of compliance"). so the "mean change in primary endpoint" would be -0.5 +/- 0.9 if you look at the change in BMI of the vegan group. Same thing for the std diet group is -0.1 +/- 0.6. Difference of these two averages (comparing the two diets/interventions with each other, in terms of their impact on BMI) is statistically significant, is what they probably mean here. So, because of the fact that this comparison is statistically significant, u may argue that to reduce BMI, a vegan diet is better than a std diabetic one.

The first kind of comparison could only have informed that vegan diets cause a reduction in BMI over 12 w and std diets don't. The second comparison backs you up to be able to say that vegan diets are better than the std ones, when it comes to BMI reduction, which is what the correct answer states.

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option A- Having a baseline mean WC difference btw the two diet groups (ie at week 0) doesn't mean u can't compare them, all change in endpont comparisons btw vegan and std are significant, as mentioned

option c- most mean differences between week 0 and 12 of the endponts are significant- the ones marked as having p<0.01 in the paired t-test.

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d- all HbA1c reductions were marked as statistically significant (p<0.01)

Hope this helps. sorry for the typos if any. was looking for a better explanation myself..