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?

What are the advantages and disadvantages of the individual indices?

Which associational indices require us to specify a dependent and an independent variable?

For further thought

Why is it ’bad’ if the original table can’t be reconstructed knowing the associational index and the marginals?

Why doesn’t the value of the odds ratio depend on the individual distribution of the variables (i.e. the marginals?)

Why does the Rogoff ratio depend on the marginals?

When is lambda = 0 ?