I've been studying the effects of moon planting for long enough to know for sure that it's fact, not unprovable theory or mystical weirdness.
I’d be very interested to know what controls you have included in your study.
For the first few years I did a side-by-side comparison, sowing and planting various crops according to my usual regime and sowing/planting by moon calendar times using the same seeds/methods. Both would be planted in the same beds, although the times when each were fed, watered and harvested differed for obvious reasons.
Seeds sown by the moon had better percentage germination and subsequent growth. Crop yield was almost invariably better - for example, a crop of Linzer Delikatess potatoes exhibited huge yields, some roots having more than 60 potatoes, compared to the more usual 30 or so from the rows planted at my regular time at/around the beginning of April. Each crop received the same amount and type of fertiliser and was planted in the same bed.
Plants sown by the moon calendar were often visibly healthier and suffered less from disease and pests, too.
Once I was convinced of the efficacy of the method all my production was switched to the same calendar.