Second Class Poll Ends: A Statistic is to a Sample what a Parameter is to a Population

I’m not surprised that most (84%) who participated in the second class poll got it right (see the inset chart below). Over the first few class periods, my focus was to link the following four concepts: statistic, sample, parameter and population. Any discussion in a statistics class begins with this conceptual framework.

Since we seldom have complete knowledge of the parameters of a population, such as the mean of the population (µ) and its standard deviation (σ), we must obtain a representative (aka, random) sample from that population. In doing so, we are then working with statistics that describe the sample, not the population. Statistics calculated from sample data will, in turn, serve two broad purposes:

1. Descriptive Analysis. There are four ways that statistics describe sample data. They allow the researcher to examine levels of skewedness (degree of symmetry) and kurtosis (level of peakedness) of a variable’s distribution. They also quantify the central tendency (mode, median and mean) and dispersion (range, standard deviation and variance) of sample data that comprise a variable’s distribution.  Refer to my "Weekly PowerPoints" for details on the role of descriptive statistics.

2. Inferential Analysis. An important second purpose of sample statistics is to generalize outcomes found in sample data to the population from which the sample was drawn. The two broad roles for inferential analyses were reviewed in a previous blog which examined the outcome of our first class poll: Estimating Population Parameters and Testing Hypotheses.

The upshot is that for every statistic that describes some characteristic of a sample there is a corresponding parameter that describes the same characteristic of a population. We analyze sample statistics so that we may generalize statistical outcomes from the sample to the population of interest.