Left-handedness tends to be more common among men than women, while autoimmune thyroid disease tends to happen more in women. Thus if you try to find out the frequency of any degree of left-handedness among thyroid patients the answer you get depends on whether you ask men or women with thyroid trouble about hand preference.
In an informal research survey, Doctors Lawrence Wood and David Cooper asked 74 men with Graves' or Hashimoto's disease about this and found that 12 were pure left handers, 40 ambidextrous, and only 22 pure right handers. Thus, 70 percent of these men had some degree of left-handedness. In contrast, among 24 individuals with other types of thyroid problems such, as benign and cancerous nodules, only two were left-handed and four ambidextrous for a total of 25%; 75% being right-handed.
So if you or someone in your family are completely or partially left-handed, this may be a clue that there is also a tendency to autoimmune problems including Graves' and Hashimoto's diseases on that side of the family.