We often hear talk about how `experts' draw inferences from data taken in a sample.
If we could do a study on all children who gained places in grammar schools this year we would not be drawing on a normally distributed sample of children. We would be looking at bright and able children who had the ability to do well on tests. This would be a biased sample of all the children spread across England.
Another example of a biased sample would be if views on grammar schools were sought from all families who owned three cars. This would not be a representative sample of every one in the whole country.
To obtain a sample that avoids bias, use is made of random samples. This would involve writing every name of the parents of every Year Six child on a slip of paper. We would then need to put all the slips into a great big drum, and then draw out a number of names. If only three names were drawn then this could not be considered a truly unbiased sample. As the data can only from Year 6 parents, we would need to treat the Year 6 data as not being truly representative of the all the children in England.
When our children sit an Eleven Plus test they are working from a sample of questions held in a data base.