CONTINGENCY (CROSS- TABULATION) TABLES - Middle East Technical University

[Pages:68]CONTINGENCY (CROSSTABULATION) TABLES

? Presents counts of two or more variables

A1

B1

a

B2

c

Total a+c

A2

Total

b

a+b

d

c+d

b+d n = a+b+c+d

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Joint, Marginal, and Conditional Probability

? We study methods to determine probabilities of events that result from combining other events in various ways.

? There are several types of combinations and relationships between events:

? Intersection of events ? Union of events ? Dependent and independent events ? Complement event

2

Joint, Marginal, and Conditional Probability

? Joint probability is the probability that two events will occur simultaneously.

? Marginal probability is the probability of the occurrence of the single event.

The joint prob. of A2 and B1

B1 B2 Total

A1 a/n c/n (a+c)/n

A2 b/n d/n (b+d)/n

Total (a+b)/n (c+d)/n

1

The marginal probability of A1.

3

Intersection

? Example 1

? A potential investor examined the relationship between the performance of mutual funds and the school the fund manager earned his/her MBA.

? The following table describes the joint probabilities.

Top 20 MBA program

Mutual fund outperform the market

.11

Mutual fund doesn't outperform the market

.29

Not top 20 MBA program

.06

.54

4

Intersection

? Example 1 ? continued

? The joint probability of

P(A1 and B1)

[mutual fund outperform...] and [...from a top 20 ...] = .11

? The joint probability of [mutual fund outperform...] and [...not from a top 20 ...] = .06

Mutual fund outperforms the market

(B1)

Top 20 MBA program

.11

(A1)

Not top 20 MBA program

.06

(A2)

Mutual fund doesn't outperform the market

(B2)

.29

.54

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Intersection

? Example 1 ? continued

? The joint probability of

[mutual fund outperform...] and [...from a top 20 ...] = .11

? The joint probability of

P(A1 and B1)

[mutual fund outperform...] and [...not from a top 20 ...] = .06

P(A2 and B1)

Mutual fund

Mutual fund

outperforms the

doesn't

market

outperform the

(B1)

market (B2)

Top 20 MBA program

.11

.29

(A1)

Not top 20 MBA program

.06

(A2)

.54

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Marginal Probability

? These probabilities are computed by adding across rows and down columns

Top 20 MBA program (A1)

Not top 20 MBA program (A2)

Marginal Probability P(Bj)

Mutual fund outperforms the market (B1)

Mutual fund doesn't outperform the market (B2)

Margina l Prob.

P(Ai)

P(A1 and B1)+ P(A1 and B2) = P(A1) P(A2 and B1)+ P(A2 and B2) = P(A2)

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Marginal Probability

? These probabilities are computed by adding across rows and down columns

Top 20 MBA program (A1)

Not top 20 MBA program (A2)

Marginal Probability P(Bj)

Mutual fund Mutual fund

Margina

outperforms doesn't

l Prob.

the market outperform the

(B1)

market (B2)

P(Ai)

.11 +

.29

= .40

.06 +

.54

= .60

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