# Chapter 1. Development

## 1.1Development

Topic: Is there cognitive decline with age regardless of the cognitive stimulation?

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.

Introduction

Development happens over the entire life span, beginning from conception and continuing until death. As we age, things change, including our physical appearance, attitudes, interests, and emotions. Even though we tend to think of these changes as declines, there are some areas in which we continue to excel or increase in over time. The Development chapter covers how our semantic and episodic memory change over time, with the former increasing or staying the same and the latter decreasing as we age. Research conducted by Salthouse, Berish, and Miles (2002) is used for this applet and explores these cognitive areas in more detail to evaluate the relationship between age and cognitive functioning.

Richard Alan Hullinger, Indiana University, Bloomington
Melanie Maggard, University of the Rockies
Statistical Lesson. A topic related to correlation is validity. The text defines validity as the goodness with which a concrete event defines a property. It uses the example for concrete event as “frequency of smiling” to define the property of “happiness.” When we create a test to measure the property “statistical knowledge,” we want to make sure the test is valid in that it actually measures statistical concepts and skills, not attitudes, feelings, or other things. So, using the concept of correlation loosely, do the items in the test appear “on the face” to relate or correlate to what we are measuring? This is what we refer to as face validity.

There are two other types of validity that help us evaluate a test – convergent and discriminant validity.

• Convergent validity tells us how well a test measures a specific property compared to another test that measures the same property. We expect the relationship between two tests that are measuring the same or a similar property to have a high correlation.
• Discriminant validity tells us how well a test measures a property compared to another test that measures a different property. We expect the relationship between two tests that are measuring different things to have little or no correlation, meaning there is no relationship between what these tests measure.

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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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