Example
Local independence can be explained by an example of Lazarsfeld and Henry (1968). Suppose that a sample of 1000 people asked whether they read journals A and B. Their responses were as follows:
|
Read A |
Did not read A |
Total |
|
|
Read B |
260 |
140 |
400 |
|
Did not read B |
240 |
360 |
600 |
|
Total |
500 |
500 |
1000 |
One can easily see that the two variables (reading A and reading B) are strongly related, and thus dependent on each other. Readers of A tend to read B more often (52%) than non-readers of A (28%). If reading A and B were independent, then the formula P(A&B) = P(A)×P(B) would hold. But 260/1000 isn't 400/1000 × 500/1000. Thus, reading A and B are statistically dependent on each other.
If the analysis is extended to also look at the education level of these people, the following tables are found.
|
High education |
Read A |
Did not read A |
Total |
Low education |
Read A |
Did not read A |
Total |
|
|
Read B |
240 |
60 |
300 |
Read B |
20 |
80 |
100 |
|
|
Did not read B |
160 |
40 |
200 |
Did not read B |
80 |
320 |
400 |
|
|
Total |
400 |
100 |
500 |
Total |
100 |
400 |
500 |
Again, if reading A and B were independent, then P(A&B) = P(A)×P(B) would hold separately for each education level. And, in fact, 240/500 = 300/500×400/500 and 20/500 = 100/500×100/500. Thus if a separation is made between people with high and low education backgrounds, there is no dependence between readership of the two journals. That is, reading A and B are independent once educational level is taken into consideration. The educational level 'explains' the difference in reading of A and B. If educational level is never actually observed or known, it may still appear as a latent variable in the model.
Read more about this topic: Local Independence
Famous quotes containing the word example:
“Our intellect is not the most subtle, the most powerful, the most appropriate, instrument for revealing the truth. It is life that, little by little, example by example, permits us to see that what is most important to our heart, or to our mind, is learned not by reasoning but through other agencies. Then it is that the intellect, observing their superiority, abdicates its control to them upon reasoned grounds and agrees to become their collaborator and lackey.”
—Marcel Proust (1871–1922)