I don't know what the heck the doctor tested. Have a look at the following info from this link.
Test Abbreviation Typical Ranges
Serum thyroxine T4 4.6-12 ug/dl
Free thyroxine fraction FT4F 0.03-0.005%
Free Thyroxine FT4 0.7-1.9 ng/dl
Thyroid hormone binding ratio THBR 0.9-1.1
Free Thyroxine index FT4I 4-11
Serum Triiodothyronine T3 80-180 ng/dl
Free Triiodothyronine l FT3 230-619 pg/d
Free T3 Index FT3I 80-180
Radioactive iodine uptake RAIU 10-30%
Serum thyrotropin TSH 0.5-6 uU/ml
Thyroxine-binding globulin TBG 12-20 ug/dl T4 +1.8 ugm
TRH stimulation test Peak TSH 9-30 uIU/ml at 20-30 min
Serum thyroglobulin l Tg 0-30 ng/m
Thyroid microsomal antibody titer TMAb Varies with method
Thyroglobulin antibody titer TgAb Varies with method
If it is really Free T3 Index, then the measurement units are different, plus that test seems to be outdated and not nearly as useful as a Free T3 test. Further, I have never seen that test done for any of the many members of this Forum over the last 8 years. When I read the following, I couldn't even figure out a reason to do that test.
In a large number of normal men (n = 111) and women (n = 110) the free triiodothyronine (T3), index, calculated from serum total T3 and T3-uptake, was highly correlated with free T3, measured by equilibrium dialysis. The correlation was almost as high as that of the free thyroxine (T4) index with free T4. The correlations of the total T3, free T3, and free T3 index with, respectively, the total T4, free T4, and free T4 index were much lower, though still statistically significant. The free T3 index is clinically useful because serum total T3 may sometimes be misleading. Hyperthyroid patients with apparent T4-toxicosis and normal total T3 may have an elevated free T3 index and thus physiologically elevated levels of both thyroid hormones. Calculation of the free T3 index might also make possible the diagnosis of T3-toxicosis in a patient with a normal free T4 index and normal total T3. Total T3 may be elevated without an elevated total T4 in women taking oral contraceptives; thus the free T3 index may prevent a misdiagnosis of T3-toxicosis. The free T3 index seems no better than total T3 in the diagnosis of primary hypothyroidism, but it can confirm the diagnosis of T3-hypothyroidism."
If the whole purpose of the FT3 Index test was to get an assessment of Free T3, as mentioned above, it seems to be a very round-a-bout way to do so. What possible reason not to just test Free T3?
Can you get a copy of the lab report?