1 Consider the assumptions made in using one- way analysis of variance, listed in the options. For each of the scenarios described below, select the assumption that is most obviously untrue.

Options:

(a) Each sample is representative of its population.

(b) Within each sample observations are independent of each other.

(c) Observations in one sample are independent of observations in the others.

(d) Observations in each population follow a Normal distribution.

(e) The population variances are equal.

Scenarios:

(i) Dental health education sessions were held

(a) at a school year- group meeting

(b) in a whole- school meeting (c)

at a local community centre. The ages of those attending

(excluding teachers for the schools) were obtained. For the year- group meeting the mean was 12 and the standard deviation was 0.25, for the whole- school group the mean was 15 and the standard deviation was 1.5, and for the community centre group the mean was 40 and the standard deviation was 10. The three groups are to be compared on age.
(ii) Information is required about the use of toothpaste and fl oss by children living in Britain. The samples are drawn from children admitted to British dental hospitals.
(iii) Adults from England, Scotland, and Wales were compared on the number of cigarettes smoked per day. The three samples included non- smokers.
(iv) The fi ve samples consist of measurements of salivary fl ow rate taken on the same individuals and obtained on fi ve consecutive days.
(v) Samples were taken that included all of the children living in selected households.