Guttman (1945) derived six reliability formulas, each denoted by formula_78. Louis Guttman proved that all of these formulas were always less than or equal to reliability, and based on these characteristics, he referred to these formulas as 'lower bounds of reliability'. Guttman's formula_79 is formula_80, and formula_81 is formula_82. He proved that formula_83 is always greater than or equal to formula_81 (i.e., more accurate). At that time, all calculations were done with paper and pencil, and since the formula of formula_81 was simpler to calculate, he mentioned that formula_81 was useful under certain conditions.