Week 1

Univariate Frequency Distribution
o
Make a table with f
i
, rf
i
= f
i
/N, E
i
= N/k
o
To describe location, use Mode
o
To describe dispersion, use rf at Mode

χ2 Tests : Goodness of Fit
o
χ
2
=Σ (O
i
E
i
)
2
/ E
i
df = k1

χ2 Tests: Tests of Independence
o
Same χ2 as above, but
df = (r1)(c1)
o
E
ij
= R
i
* C
j
/ N

Explanation
o
State the precise relationship between the two factors, namely, that X are
more likely to do Y
o
Describe the overall distribution of each variable (w/ the mode and its
relative frequency)
Week 2

Necessary Sample Size
o
Perform a χ
2
with O
i
and E
i
values in prob. Form and multiplied by N

Probability
o
Addition Rule
p(A or B) = p(A) + p(B) – p(A and B)
o
Multiplication Rule for Indep. Events
p(A and B) = p(B)*p(A)
o
Bayes’ Rule
p(AB) = p(A and B) / p(B)
Note: p(A and B) = p(AB) * p(B)

Reminders
o
Make a Table
o
Take into account
“gets exactly 1 question right out of 4” = 4 ways to
do this
Week 3

rf and rcfhistograms for grouped data
o
SetUp
Make a table with rf
i
, rcf
i,
real interval, midpoints xbar
Real interval is initial interval +/ .5 on either end.
X
u
= Upper Limit Value
Rcf
u
= Upper limit rcf
P = Desired proportion
Rf
c
= Relative frequency of interval
W
c
= Width of Interval
o
X
p
= X
u
– [(rcf
u
– p) / rf
c
] * W
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 Fall '07
 Thomas,E
 Normal Distribution, Xu, xbar Real interval, sampling distribution xbar, XBar o CI

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