Is "This box is biger than that one" correct?

Why

Rohan has correctly added "-er" to a short adjective, which is exactly the right method for a word like "big". What's missing is a small spelling rule that applies to short words shaped a particular way: one vowel sandwiched between two consonants at the end of the word, like "big" (b-i-g) or "hot" (h-o-t). For these, the final consonant is doubled before adding "-er" or "-est" — big becomes bigger, hot becomes hotter, thin becomes thinner — to keep the vowel sound short instead of accidentally making it sound long and open. Without doubling the "g", "biger" would actually look like it should rhyme with "tiger", which isn't the sound the word needs at all. Test: compare a word that ISN'T shaped this way, like "fast" (already ending in two consonants) — it simply becomes "faster", no doubling needed, because the doubling rule only kicks in for that specific single-vowel-plus-single-consonant ending. His sister is right: "bigger" needs the doubled "g" to keep its short vowel sound, and "biger" is a spelling gap, not a valid alternative.