Ugrás a tartalomhoz

## SOCIAL STATISTICS

Renáta Németh, Dávid Simon

ELTE

Other associational indices for nominal variables

## Other associational indices for nominal variables

Some other indices to show the connection between two nominal variables:

• odds ratio

• Rogoff ratio

Notation:

Let’s take two nominal variables with two values each.

Gender: male/female

Height: taller than 180 cm / shorter than 180 cm

 tall short sum of row female f11 f12 f1+ male f21 f22 f2+ sum of column f+1 f+2 f++

thus:

f11 no. of tall women

f+1 no. of tall respondents

f++ total no. of cases

Rogoff ratio:

8.5. egyenlet - where the second part of the formula is the number of cases in cell f11 with the given marginal distributions if the two variables are independent. That is, how great is the difference compared to the independence.

Characteristics:

• symmetric

• its minimum and maximum values depend on the marginal disribution (variationally not independent)

• it’s always 1 if (and only if) the variables are independent

• the table can be easily reconstructed knowing only the marginals

Gender: male/female

Height: taller than 180 cm / shorter than 180 cm

 talll short sum of row female f11 f12 f1+ male f21 f22 f2+ sum of column f+1 f+2 f++

thus:

f11 no. of tall women

f+1 no. of tall respondents

f++ total no. of cases

the odds ratio (α):

8.6. egyenlet - Interpretation: The ratio of two frequencies (or probabilities) are called odds. Think of bookies: what are the odds that the horse called Nick Carter is going to win? If it’s 3:1, it means it’s going to win once in every four cases. The odds ratio shows how much greater the odds of one event is than that of another.

Characteristics:

• symmetrical

• minimum value: 0

• maximum value: + • its value if and only if independent: 1

• if we take its logarithm, the same absolute values mean ’the same strength’ connection

• if we know the marginals, the table can be reconstructed but it’s complicated

• (variationally independent: it’s value doesn’t depend on the marginal distribution)

### Revision Questions

Which associational index shows the ’direction’ of the connection as well?

Why can’t lambda be negative?