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As part of a class session on research design, I discuss the topic of choosing a sample size. I use this learning activity immediately prior to a lecture component on statistical power and the relationship between sample size and confidence intervals. My pupose in creating this extended metaphor is to build my student's intuition about the advantages and disadvantages of large sample sizes. As shown in the screen shot from my PowerPoint presentation, I describe four different digital cameras with image resolution ranging from 3 megapixels to 24.6 megapixels. I describe how photos taken with the highest-resolution camera have fantastic image clarity, whereas photos taken with the lowest-resolution camera have relatively poor image clarity. To drive this point home, I produce two mounted 14" x 19" photos, and I pass them around the class. One photo is a 24.6 megapixel image of customers in front of a store. The other photo is a 3 megapixel version of the same image. As might be expected, the 3 megapixel version suffers from severe digital distortion and pixelation when enlarged that size. I point out that for maximum image clarity, there is no substitute for a high-resolution camera. (With the images that are shown to the right, I have tried to represent what the students see, but the printed photos are more striking.) I then point out that it's possible to enlarge the photos to "zoom in" and closely examine a part of the image that we're particularly interested in. I pass around another pair of large mounted photos. One photo is an enlargement of two customers in the 24.6 megapixel image, and the other photo is the same enlargement from the 3 megapixel image. I point out that if we want to "zoom in" on a particular part of the scene, the 24.6 megapixel image starts to suffer, but the 3 megapixel image is practically useless. I then direct students' attention back to the PowerPoint screen to discuss the prices of the cameras. Obviously, higher-resolution cameras are much more expensive. I ask students to imagine they are taking a photo archive of something important, such as a friend's wedding. I ask students to imagine they have a $2,500 budget for digital cameras to take this photo, but there is a catch: digital cameras can take only one picture, and after taking the one photo, the camera is useless. I ask, "Would you purchase one high-resolution camera? Or maybe four of the 12.2 megapixel cameras? After all, with four cameras you could take four pictures of the wedding. Maybe you could take the four pictures from different angles? Or maybe you could take four pictures at different times of the day? How about the 3 megapixel camera? You could buy 100 of those with your budget. Would you rather have 100 of those?" I do not let this discussion go on too long because it inevitably gets too specific into photographs and stretches the metaphor too thin. For this part of the discussion, I simply want students to recognize that low-resolution photos can be useful for certain things. I finish this extended metaphor by mapping it onto my topic of interest and then summarizing the take-aways: "We've been talking about digital photos, and they are metaphorically similar to sample sizes in survey design. High-resolution photos are a lot like surveys with large sample sizes. They give clarity into what we're seeing, and they let us 'zoom in' and look at specific sub-samples with decent clarity. However, they're very expensive. Low-resolution photos are a lot like surveys with small sample sizes. They give us a pretty good idea of the overall scene, but they do a poor job of letting us 'zoom in' to look at sub-samples. On the other hand, these small-sample studies don't cost nearly as much, which makes them useful for certain tasks." I then move to a lecture component on sample sizes, confidence intervals, and statistical power. I conclude the lecture component with a reprise of the learning points in this metaphor. |
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