Dear Jyoti Sharma, yes, your conclusion about the p-value and the rejection of the null hypothesis are correct. However, you looked at percentages in your data. A Mann-Whitney-U-Test is usually used for a non-normal distribution of continuous data. However, a percentage implies that your outcome measure is already related to a hypothetical 100%. I am not sure whether we can still use the same statistical methods with percentages. Maybe another RG member can help us out here?

I don't think the way you have framed the hypotheses is correct. Your null hypothesis is literally in it's name: it is a hypothesis of null effects. So it should be:

H0: There is no difference between A and B with respect to recovery percentages.

H1: There is a difference.

Also Andreas is unfortunately incorrect and this is a common misconception about p values. Even Fisher, the guy who developed the original workings of null hypothesis testing, noted that we can neither accept the null or alternative hypothesis, but we can tentatively reject the null. These are not equivalent statements so it is important to be careful about the wording. For a Bayesian view this would be a bit different, but since you highlight p values this would be important to understand.

As always, the usual caveats go with a low p-value. It would be very important to include things like effect sizes, confidence intervals, etc. to quantify what the actual effect is since p-values say nothing about the actual magnitude of the effect, only that the probability of a null effect being very low.

References:

- Fisher, R. A. (1935). The design of experiments (9. ed). Hafner Press.

- Wasserstein, R. L., & Lazar, N. A. (2016). The ASA statement on p-values: Context, process, and purpose. The American Statistician, 70(2), 129–133. https://doi.org/10.1080/00031305.2016.1154108

Thank you Andreas for your response

Thank you @shawn for your responce and clar