Chapter 11. Development

Statistical Concepts Covered: In this applet, you’ll expand on your knowledge of correlation, and be introduced to the concept of z scores and standardization.

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Statistical Lesson. You’ve most likely heard of standardized testing from your experience in schooling. Standardization is a common method used in statistics so we can more effectively compare numbers, whether on the same measure or different ones. By using a standard scale, we are able to compare “apples” to “oranges” using the same scale. For example, let’s say you take a test in statistics and earn 85 out of 100 points and a test in psychology, where you earn 45 out of 60 points. It turns out that the average score for the stats test was 75 and the average score for the psychology test was 45. Which did you do better on in relation to the class? Because the two tests use different scales and have different averages, we can use standard scores to help us compare.

A common type of standardize score is a z score, which tells us how far from the average or mean our value lies. When we convert a value into a z score, it tells us how far that original value is from the average. A negative z score tells us that the value falls below the average, while a positive z score tells us that the value is above the average. A z score of 0 means that the value is right at the average. The large the z score, regardless of whether it is positive or negative, tells us how far away the value is from the average. So, a z score of 2.0 is farther from the average than 0.5, -1.2, or even -1.99; however, a z score of 0.5 is closer to the average than -1.2, -0.6, and 2.0.

We won’t cover how to calculate z scores in this applet, but let’s say we did and found that your z score for the statistics test was 0.67, and your z score for the psychology test was 0. Which did you do better on? Well, straight off we can see that the z score for the psychology test of 0 is right at the average so you performed on par with the class. However, your z score for the statistics test was above 0 since it was positive, which means you did better than the class average. Overall, you did better on your statistics class than the psychology test and we are able to compare these using the z scores. Keep these concepts in mind as you assess the data used for the following questions.

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