Basic Analysis and Graphing - SAS

182 Performing Oneway Analysis Chapter 5
Statistical Details for the Oneway Platform
The Levene F is the model F statistic from an ANOVA on z ij
= y ij
– y i. where y i. is the mean response for
the ith level.
Bartlett’s test is calculated as follows:
T
v i
v ---s 2
log
v i – v i
s2
log( i
)
i
i
= ----------------------------------------------------------------- where and
1
---
1 v i
= n i
– 1 v = v i
–
v --
i
v
i
1 ------------------- i
+
3( k – 1)
and n i is the count on the ith level and s i
2 is the response sample variance on the ith level. The Bartlett
statistic has a χ 2 -distribution. Dividing the Chi-square test statistic by the degrees of freedom results in the
reported F value.
Welch’s Test F Ratio
The Welch’s Test F Ratio is computed as follows:
F
w i
( y i – y .. ) 2
----------------------------------
i
k – 1
= -----------------------------------------------------------------------
n
w where , , ,
i
1 – ---- 2
i
w
w
i
= --- u =
2 w i
ỹ i
y i.
.. = ----------
2( k – 2)
1 -------------------
u
s
u
+ ----------------------
i i
i
k 2
– 1 i
n i
– 1
and n i is the count on the ith level, y i.
variance for the ith level.
is the mean response for the ith level, and s i 2 is the response sample
Welch’s Test DF Den
The Welch approximation for the denominator degrees of freedom is as follows:
1
df = -------------------------------------------------
w 2 i
1 – ----
-------------
3 u
k 2 -----------------
n
– 1 i
– 1
i
where w i , n i , and u are defined as in the F ratio formula.