How are factorial designs symbolized?
• Factorial designs are symbolized using shorthand notation. • Shorthand notation gives us three pieces of information: the number of variables, the number of levels of each treatment or I.V., and the total number of treatment conditions or groups. • For example, a study with 2 I.V.s with three levels each would be: 3×3. • Each number (3 in this case) tells us how many levels of each variable. Thus, we know each I.V. has three levels. • Each number also represents an I.V. Since there are two numbers (3 and 3) we know the study involved two variables. • By multiply the values (3×3=9), we know how many different treatment combinations were used. • A study with 3 I.V.s with three levels of each would be a 3x3x3 design with 27 treatment conditions; a study with 3 I.V.s with 2 levels of each would be a 2x2x2 design with 8 treatment conditions; a study with 2 I.V.s with 3 levels of one variable and 2 levels of the second would be a 3×2 design with 6 treatment conditions. • For example, imagi
