Formula Sheet for Final Exam
POS 3713  Spring 2007 (Dr. Hensel)
ChiSquare
X
2
(obtained)
=
!
(f
o
"
f
e
)
2
f
e
(where f
o
= observed cell frequencies, f
e
= frequencies expected if the variables were indep.)
f
e
= (Row marginal * Column marginal) / N
df = (r  1)(c  1)
(where r = # of rows in table, c = # of columns)
Phi
Phi =
X
2
N
(where X
2
is calculated as above, and N is the # of cases in the table)
Cramer’s V
V =
X
2
N *min(r
!
1,c
!
1)
(where X
2
is calculated as above, N = # cases, r = # rows in table, c = #columns in table)
Lambda
!
=
E
1
!
E
2
E
1
(where E1 = errors without knowing X = based on [Nrow marginal] for each row;
E2 = errors knowing X = based on [column marginal – largest cell] for each column)
Gamma
Gamma =
N
s
!
N
d
N
s
+
N
d
(where Ns = # same order pairs in data set [cell a*cell d in following example],
Nd = # inverse order pairs [cell b*cell c])
Low
High
Low
Cell a
Cell b
High
Cell c
Cell d
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ANOVA
SST =
"
(X
i
2
) – [N * (Xbar
2
)]
SSB =
"
[N
k
* (Xbar
k
 Xbar)
2
]
SSW = SST  SSB
dfb = k1, dfw = Nk
(where
!
(X
i
2
) = sum of all squared scores in the data set, k=# categories, N=sample size,
Xbar=sample mean)
F(obtained)
=
MSB
=
[SSB/(k1)]
MSW
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 Fall '11
 PaulHensel
 Statistics, Normal Distribution, Regression Analysis, Chisquare distribution, var iance

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