The word psychometric is playable in Words With Friends™, no blanks required. Because it is longer than 7 letters, you would have to play off an existing word or do it in several moves.
Words With Friends™ Letter Score: 28
Highest Scoring Words With Friends™ Play In The Letters psychometric
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Seven Letter Word Alert: (84 words)
chemics, chemist, chicory, chipset, choicer, choices, chomper, chromes, chromic, chymics, chymist, ciphers, cithers, coheirs, cometic, copiers, copyist, cotypes, crochet, cryptic, cyphers, ectopic, erotics, hermits, heroics, heroism, history, homiest, hosiery, hospice, imports, imposer, isohyet, isotype, metrics, miscopy, mistype, moister, mopiest, morphic, mortise, mothers, mycotic, myotics, ostrich, permits, pitcher, pitches, poetics, porches, pothers, potiche, primost, promise, psychic, pyrites, repitch, rhotics, rhymist, richest, ropiest, rosehip, sceptic, scrimpy, scyther, scythic, shrimpy, smother, society, spermic, spheric, spicery, stomper, stripey, strophe, thermic, thermos, thymier, toprims, torches, triceps, trisomy, trophic, tropics