series: “Section 1: Introduction - do the Design of Experiments”

Before going further in this example, let’s talk a little bit about sampling and sample properties. Consider the following: For a science fair, a student, determined the average height of his or her classmates. The response variable, The thing that this tool than this measuring is the height. As the classmates have different heights, We can characterize the data by the average or mean: the sum of all observations divided by the total number of observations, and by the variance: the difference between each individual observation and the mean, to the square. The variance measures the spread of the population around the mean. In this case, this student used the whole population of the classroom to determine the mean height and the height variability.

Let’s now consider a modified example: for scientific study a research group aims to determine the average height of grade eight students in Canada. However, there are almost three hundred and fifty thousand students in grade eight. Is it really necessary to measure the height of all students? No, it isn’t. As the number of students is very large, they will estimate the average height by using a random sample. A certain number of students will be randomly chosen to represent the population and then they can estimate the average height and the variance of the population by using the average and the variance of the sample. The sample mean is a point estimator of the population mean, and the sample variance is a point estimator of the population variance. In a random sample, each individual observation can be described by the mean, plus a random error. And experimental result shows that the individual observations in a random sample usually follow a normal distribution around the mean.