University of York
Department of Health Sciences
Applied Biostatistics
Exercise: Comparing the means of small samples
Question 1.
It was postulated that the increasing rate of hip fractures among elderly women may be
related to women now having longer femoral necks than in previous generations. 52 x-ray
pictures of hips of elderly women taken in the 1950s were compared to 52 similar pictures
taken in the 1990s. All the x-rays had been taken for routine diagnostic purposes with the
same equipment in the same rheumatology unit (Reid et al. 1994). The following table
appeared :
Mean (standard deviation) dimensions of proximal femur in 52 elderly
white women in New Zealand in 1950s compared with those of 52 in
1990s
Dimension (mm) 1950s 1990s P value
Length of hip axis 124.0 (8.6) 130.5 (8.6) 0.0002
Length of femoral neck 79.4 (7.6) 84.9 (6.3) 0.0001
Width of femoral neck 38.1 (4.1) 38.6 (3.6) 0.49
a) What method could be used to calculate P in this study?
b) What conditions, if any, do the data have to fulfil for the method to be valid?
c) Are they likely to be fulfilled here?
d) From these P values, can we conclude that the length of femoral neck in elderly women
has increased over time?
e) Can we conclude that the width of femoral neck in elderly women has not increased over
time?
Question 2.
Shortly after the grounding of the Braer oil tanker off the Shetland Isles, a study was
conducted to ascertain whether the respiratory tracts of children were being affected by the
crude oil vapour and droplet spray. Peak expiratory flow rate (PEFR) of 44 children ages 5-
12 years was measured twice: three days after the shipwreck and 9 to 12 days after when the
strong smell of oil had abated. Statistical analysis of the paired PEFRs (by Student’s t test for
difference of means for paired samples) showed no significant difference between the two
sets of values (P=0.502) (Crum 1993).
a) What is meant by no significant difference?
b) What is meant by a paired t test?
c) What assumptions are involved and are they likely to be justified here?
d) What can we conclude about the effect of spillage on the respiratory function of
children?
