Introductory Biostatistics

n¼n 10 þn 01

p¼

y

yþ 1

This corresponds to the following likelihood function:

Lðx;yÞ¼

n 10 þn 01

n 10



y

yþ 1

n 10

1

yþ 1

n 01

leading to a simple point estimate for the odds ratioyy^¼n 10 =n 01.

4.7 NOTES ON COMPUTATIONS

All the computations for confidence intervals can be put together using a cal-
culator, even though some are quite tedious, especially the confidence intervals
for odds ratios and coe‰cients of correlation. Descriptive statistics such as
meanxand standard deviationscan be obtained with the help of Excel (see
Section 2.5). Standard normal andtcoe‰cients can also be obtained with the
help of Excel (see Section 3.5). If you try the first two usual steps: (1) click the
paste function icon, f*, and (2) clickStatistical, among the functions available
you will find CONFIDENCE, which is intended for use in forming confidence
intervals. But it is not worth the e¤ort; the process is only for 95% confidence
intervals for the mean using a large sample (with coe‰cient 1.96), and you still
need to enter the sample mean, standard deviation, and sample size.

EXERCISES

4.1 Consider a population consisting of four subjects,A,B,C, andD. The

values for a random variableXunder investigation are given in Table

E4.1. Form the sampling distribution for the sample mean of sizen¼ 2

and verify thatmx¼m. Then repeat the process with sample size of

n¼3.

TABLE E4.1

Subject Value

A 1

B 1

C 0

D 0

4.2 The body mass index (kg/m^2 ) is calculated by dividing a person’s weight

by the square of his or her height and is used as a measure of the extent

EXERCISES 173