While conducting research for a new agent-based model I came across a 2013 paper titled, "Testing the efficacy of homemade masks: would they protect in an influenza pandemic?" It details how well different materials fared when faced, no pun intended, with the task of stopping a virus.
In Table 1 (yellow highlights are mine) various materials are tested against the virus simulate MS2. This is an egress test (protection from the wearer) and not an ingress test (protection of the wearer). Notice how tight the standard deviation (SD) is around the surgical mask as compared to the 100% cotton T-shirt. Mask manufacturing standards matter. At two standard deviations, covering about 95 of the normal distribution, the cotton mask efficiency could be as low as 17% or as a high as 84%. Based on their research, the paper authors state:
We would not recommend the use of homemade face masks as a method of reducing transmission of infection from aerosols.
Of course, this is not the entire picture as a virus can be suspended in a droplet that is much bigger than an aerosol. In the end you will have to judge what to use and when.
Source: Davies, A., Thompson, K. A., Giri, K., Kafatos, G., Walker, J., & Bennett, A. (2013). Testing the efficacy of homemade masks: would they protect in an influenza pandemic?. Disaster medicine and public health preparedness, 7(4), 413-418.