Introduction Modelling Binary Data

Second EditionD. Collet

1991

Lidia Mayangsari7414627

Montgomery and Peck (1982) describe a study on the compressive strength of an alloy fastener used in the construction of an airplane.

Ten pressure loads, increasing in units of 200 psi from 2500 psi to 4300 psi were used with different numbers of fastener

being tested at each of these loads.

Example 1.5Aircraft Fastener

Observational Result

Binary Outcome Variable

Sigmoid Curve,

A graph of the probability of failure against increasing loads will have an elongated S-shape.

Smith (1932) bioassay which decribed a study of protective effect of Serum 32 on pneumococcus.

For all the mice that died during the seven day period

following inoculation, a blood smear taken for the heart and examined to check the pneumococcus.

Example 1.6 Anti Penumococcus Serum

Learning Point

The objective of example 1.5 and 1.6 is to estimate the value of a continuous variable (pressure load or dose of serum) that would be expected to a particular response probability.

The trend emerge will be recorded for experimental unit.

ESR is the rate at which red blood cells settle out suspension in blood plasma when measured under normal condition.

It increases if the level of certain proteins in the blood plasma rise.Collett and Jemain (1985) presented the data produced by Institute

of Medical Research Kuala Lumpur Malaysia to examine the relationship between fibrinogen and globulin for 32 individuals.

ESR limit for health: 20 mm/hr.

Example 1.7 Determination of the Erythrocyte Sedimentation Rate

Binary Outcome Variable

“To determine the strength of any relationship between the probability of an ESR reading

greater than 20 mm/hr and the level of two plasma proteins.”

The remaining examples give rise to somewhat larger data sets that include both categorical variable (factors) and continuous variable (variates). Such data sets are typical in many areas of scientific enquiry.

Survey by University of Chicago concerned with the relationship between education and sex of the respondents to attitudes towards the role of women in society.

Whether they agree or disagree with the statement: “Women should take care of running their homes and leave running country up to men.”

Example 1.8 Women’s Role in Society

2927 individuals: 3 did not give educational level and 53 were tentatively agree with the statement.

The remaining 1305 male and 1566 female respondents were given by Haberman (1978).

Example 1.8 Women’s Role in Society

Binary Outcome Variable Binary Outcome Variable

Learning Point

To analyse the relationship between the proportion of respondents in agreement with the statement and the number of years of

education would be determined and compared between two sexes.

Conclusion

The examples 1.5 until 1.7 concerns studies where interest focuses on relationship between a binary response variable and one or

more explanatory variables. The example 1.8 concerns studies where interest focuses on relationship between a categorical and continuous variable.

“Arigatou Gozaimasu”

“All the statistics in the world can't measure the warmth of a smile.― Chris Hart