รูปแบบต่างๆ ของ Balanced repeated measures (Kleinbaum, 1998)

Analysis of Repeated Measures Data

1. A balanced repeated measures design with one crossover factor.

2. A balanced repeated measures design with two crossover factors.

3. A balanced repeated measures design with one nest factor.

4. A balanced repeated measures design with one crossover factor and one nest factor.

 

1. A Balanced Repeated Measures Design With One Crossover Factor

Table 2 Data layout for a balanced repeated measures design with one crossover factor

 

 

Treatment

Subject Number

1

2

…

t

1

Y11

Y12

 

Y1t

2

Y21

Y22

 

Y2t

3

Y31

Y32

 

Y3t

:

:

:

…

:

S

Ys1

Ys2

 

Yst

 

The ANOVA model for the crossover design in Table 2 is given as

Yij = m + Si + t j + Eij                              (1)

Where

          i    = 1,…,s          (s =number of subject)

          j    = 1,…,t           (j =number of treatment)

          Si = The random effect of subject i

          tj   = The fixed effect of treatment j

          Eij = The random error for treatment j within subject i

          And we assume that

          { Si } and { Eij } are mutually independent.

          Si is distributed as N(0,ss2)

          Eij is distributed as N(0,s2)  

Figure 1 Partitioning the sums of squares: Balanced repeated measures ANOVA with one crossover factor.


Table 3 ANOVA table for balanced repeated measure design with one crossover factor.

Source

d.f.

MS

F (Fixed or Random Treatments factor)

Between Subjects

s-1

MSS

MSS /MSTS

Within Subjects

s(t-1)

MSW

 

Treatments

t-1

MST

MST /MSTS

Treatments X Subjects

(i.e.Error)

(s-1)(t-1)

MSTS

 

Total (corrected)

st-1

 

 

 

 

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