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First, let's look at the results of our sampling efforts. When we sample, the units that we sample -- usually people -- supply us with one or more responses. In this sense, a response is a specific measurement value that a sampling unit supplies.
In the figure, the person is responding to a survey instrument and gives a response of '4'. When we look across the responses that we get for our entire sample, we use a statistic. There are a wide variety of statistics we can use -- mean, median, mode, and so on. In this example, we see that the mean or average for the sample is 3.
But the reason we sample is so that we might get an estimate for the population we sampled from. If we could, we would much prefer to measure the entire population. If you measure the entire population and calculate a value like a mean or average, we don't refer to this as a statistic, we call it a parameter of the population.
The Sampling Distribution So how do we get from our sample statistic to an estimate of the population parameter? A crucial midway concept you need to understand is the sampling distribution. In order to understand it, you have to be able and willing to do a thought experiment.
Imagine that instead of just taking a single sample like we do in a typical study, you took three independent samples of the same population.
And furthermore, imagine that for each of your three samples, you collected a single response and computed a single statistic, say, the mean of the response. Even though all three samples came from the same population, you wouldn't expect to get the exact same statistic from each.
They would differ slightly just due to the random "luck of the draw" or to the natural fluctuations or vagaries of drawing a sample.
But you would expect that all three samples would yield a similar statistical estimate because they were drawn from the same population. Now, for the leap of imagination! Imagine that you did an infinite number of samples from the same population and computed the average for each one.
If you plotted them on a histogram or bar graph you should find that most of them converge on the same central value and that you get fewer and fewer samples that have averages farther away up or down from that central value.
In other words, the bar graph would be well described by the bell curve shape that is an indication of a "normal" distribution in statistics.
The distribution of an infinite number of samples of the same size as the sample in your study is known as the sampling distribution. We don't ever actually construct a sampling distribution. You're not paying attention!Welcome to the American Perspectives Volume I eText Website for Houston Community College.
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This started with a tweet. I’m embarrassed how often that happens. Frustrated by a sense of global mispriorities, I blurted out some snarky and mildly regrettable tweets on the lack of attention to climate change in the tech industry (Twitter being a sublime medium for the snarky and regrettable).
Climate change is the problem of our time, it’s everyone’s problem, and most of our problem. You have to copy paste the work to your desktop to transfer it.
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