Two Crossover Factors

รูปแบบต่างๆ ของ Balanced repeated measures (Kleinbaum, 1998)

2. A Balanced Repeated Measures Design With Two Crossover Factors

Table 4 Data layout for balanced repeated measures design with two crossover factors.

ANOVA model treating both Factor A and Factor B as fixed factors

Y_ijk = m + S_i + a_j + b_k + d_jk + S_ij + S_ik + E_ijk (2)

Where

i = 1,…,s (s = number of subject)

j = 1,…,a (a = Number of level of Factor A)

k = 1,…,b (b = Number of level of Factor B)

m = Overall mean

a_j = Fixed effect of level j of Factor A (and åa_j =0)

b_k = Fixed effect of level k of Factor B (and åb_k =0)

d_jk = Fixed interaction effect of level j Factor A with level k of Factor B

(and åd_jk =0 for each k, åd_jk =0 for each j)

S_i = Random effect of subject i

S_ij = Random effect of level j of Factor A within subject i

S_ik = Random effect of level k of Factor B within subject i

E_ijk = Random error for level j of Factor A and level k Factor B within subject i

And we assumed that

{ S_i },{ S_ij },{ S_ik } and { E_ijk } are mutually independent.

S_i is distributed as N(0,s_S²)

S_ij is distributed as N(0,s_SA²)

S_ik is distributed as N(0,s_SB²)

E_ijk is distributed as N(0,s²)

Figure 2 Partitioning the total sums of squares for balanced repeated measures design with two crossover factors.

คลิกขยายภาพ

Table 5 ANOVA table for balanced repeated measure design with Two crossover factor.

(ตัวอย่างการวิเคราะห์ สามารถศึกษาตัวอย่างการวิเคราะห์ด้วย SPSS ได้ที่ Using SPSS: Two-way Repeated-Measures ANOVA และคำอธิบายโดยละเอียดที่ (Research Methods 2): Two Way Repeated Measures ANOVA )