Researchers for the company decided to examine mathematical ability and constructed a pencil and paper test by choosing, at random, questions from mathematics text books used in local schools. The eventual test consisted of 100 questions. Next the researchers approached 2 of the local schools from where the books were originally taken and chose at random ten eight-year old children from each of the schools.

A meeting was then scheduled between the researchers and the respective form teachers from each of the schools. At this meeting the teachers were informed about the nature of the research and that children from School A would be administered vitamins and that children from School B would be administered placebos. Of course, the children taking part were not told about whether they were in the placebo or vitamin group. Testing took place twice: once prior to the administration of pills and then again after three weeks of taking pills. Children at both schools were tested in a group during a school dinner time and the same maths test was administered on both occasions.

Means and standard deviations for the two groups at each time of testing are given in Table 1. Each question was given a single mark; hence the maximum possible mark on the test was 100.

**Table 1: Mean scores on arithmetic test for the two groups pre- and
post-treatment (standard deviations in parentheses)**

Pre-treatment | Post-treatment | |
---|---|---|

Vitamin Group | 53(28) | 79 (10) |

Placebo Group | 85 (9) | 96 (3) |

The data were analysed with a two-way split-plot analysis of variance in which Drug Group (Vitamins versus Placebo) acted as a between-subjects factor and Time of Test acted as a within-subjects factor. The analysis revealed statistically significant main effects of both factors and a significant interaction.

The researchers were extremely pleased with these results and concluded that the significant interaction had shown that the group of children who had received the vitamins had shown great improvement over the testing sessions - indeed far more improvement than that shown by the Placebo group.

Given that the first experiment used a standard dose of vitamins, the company now wished to demonstrate that the more vitamins taken the more the gain in ability. To this end they consulted their direct sales records and identified 60 families with children of primary school age. Researchers visited these families and tested the children using the same arithmetic test as before. They then correlated how much the family spent on vitamin products with the children's score on the arithmetic test.

The mean spending on vitamin products in the financial year 1990 /1 for these families, as computed from the company sales records, was £135 (standard deviation £84). The mean score on the arithmetic test was 31 (standard deviation 63). The Pearson product-moment correlation (r) was .62.

They therefore concluded that a vitamin-enriched diet clearly had beneficial effects. Tests had shown that, in particular, mathematical ability improved significantly following a regular intake of their vitamin product compared to when no such products were taken. In addition, the more such products taken the greater was the improvement.

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