Development

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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1) Salthouse, Berish, and Miles (2002) determined that certain tests of cognitive ability were correlated with each other and appeared to measure the same property. Those tests that measured similar properties had higher correlations or higher criterion validity with each other and those that measure dissimilar things had lower correlations or higher discriminant validity with each other. Knowing that we want the correlation to be as high as possible (closer to 1.00 than 0.00) for convergent validity, what test was most related or similar to block design? (Pick “Block design” for the X-axis. Cycle through the other tests on the Y-axis to see which one has the highest correlation (look at the r value) and has the tightest clustering of points on the graph to a straight line.)

Paper folding had the highest correlation (r = 0.757) with block design.

Picture vocabulary had the highest correlation (r = 0.319) with block design.

Spatial relations and paper folding had the highest correlations, both above 0.75, with block design.

Letter series and paper folding had the highest correlations, both above 0.73, with block design.

Correct.

Incorrect.

Question

2) Based on question 1 and what you know about correlations and validity, is there high or low convergent validity between block design, spatial relations, and paper folding? In other words, does it seem that these three tests are measuring similar abilities?

There is low convergent validity between these three tests, which means they are measuring similar abilities.

There is high convergent validity between these three tests, which means they are measuring similar abilities.

There is low convergent validity between these three tests, which means they are measuring different abilities.

There is high convergent validity between these three tests, which means they are measuring different abilities.

Correct.

Incorrect.

Question

3) In the previous two questions we evaluated convergent validity. Now let’s look at divergent validity. Knowing that we want the correlation to be as low as possible (closer to 0.00 than 1.00) for divergent validity, what test was least related to block design? (Pick “Block design” for the X-axis. Cycle through the other tests on the Y-axis to see which one has the lowest correlation (look at the r value) and has the loosest clustering of points on the graph so it does not resemble a straight line.)

Picture vocabulary and letter series had the lowest correlations, both below 0.73, with block design.

Spatial relations had the lowest correlation (r = 0.797) with block design.

Recall had the lowest correlation (r = 0.467) with block design.

Picture vocabulary had the lowest correlation (r = 0.319) with block design.

Correct.

Incorrect.

Question

4) Based on question 3, is there evidence of divergent validity between block design and picture vocabulary? What about spatial relations and paper folding with picture vocabulary? In other words, does it seem that these three tests are measuring different abilities than picture vocabulary? (Pick “Picture Vocabulary” for the X-axis. Cycle through “Block Design, “Spatial Relations”, and “Paper Folding” on the Y-axis. Note the size of the correlation (look at the r value) for each pair.)

Since all of the correlations are high, there is divergent validity, which means these tests are measuring different abilities than picture vocabulary.

Since all of the correlations are high, there is no divergent validity, which means these tests are measuring a similar ability as picture vocabulary.

Since all of the correlations are low, there is no divergent validity, which means these tests are measuring a similar ability as picture vocabulary.

Since all of the correlations are low, there is divergent validity, which means these tests are measuring a different ability than picture vocabulary.

Correct.

Incorrect.

Question

5) Look back at our conclusions for questions 2 and 4. What does looking at these correlations and validities tell us about these tests and their relationship to each other?

It seems that block design, spatial relations, and paper folding measure a similar property, while picture vocabulary measures a different property.

It seems that block design, spatial relations, paper folding, and picture vocabulary all measure a similar property.

It seems that block design and spatial relations measure a similar property, while picture vocabulary and paper folding measure a different property.

It seems that block design and picture vocabulary measure a similar property, while spatial relations and paper folding measure a different property.

Correct.

Incorrect.

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.

Question

6) A major interest to the researchers in this study was the relationship between age and the various abilities being measured. Recalling what you know about correlation, what was the relationship between age and recall? (Pick “Age” for the X-axis and “Recall” for the Y-axis and note the correlation (r value) for the relationship.)

There was a moderate positive relationship between age and recall (r = 0.548) showing that as age increased, scores decreased.

There was a moderate negative relationship between age and recall (r = -0.548) showing that as age increased, scores increased as well.

There was a moderate negative relationship between age and recall (r = -0.548) showing that as age increased, scores decreased.

There was a moderate positive relationship between age and recall (r = 0.548) showing that as age increased, scores increased as well.

Correct.

Incorrect.

Question

7) A major interest to the researchers in this study was the relationship between age and the various abilities being measured. Remembering that positive z scores are above the average, which is at 0, and negative z scores are below the average, what was the relationship between age and recall? (Pick “Age” for the X-axis and “Recall” for the Y-axis and note how the scores are distributed above and below 0 on the Y-axis.)

Older individuals were more likely to score above average, while younger individuals were more likely to score below average.

Since some individuals scored above average and some scored below average, the scores cancel themselves out.

All of the individuals studied scored about average.

Older individuals were more likely to score below average, while younger individuals were more likely to score above average.

Correct.

Incorrect.

Question

8) Evaluate the relationship between age and the average spatial, reasoning, and memory scores. What appears to be the relationship between these abilities and one’s age? (Pick “Age” for the X-axis and cycle through “Average spatial”, “Average reasoning”, and “Average memory” for the Y-axis and note the correlation (r value) for the relationships.)

All of these abilities are negatively correlated with age, meaning that as age increases, the scores in these areas decrease.

All of these abilities have no correlation with age, meaning that there is no relationship between age and performance in these areas.

All of these abilities are negatively correlated with age, meaning that as age increases, so do scores in these areas.

All of these abilities are positively correlated with age, meaning that as age increases, so do scores in these areas.

Correct.

Incorrect.

Question

9) Now, evaluate the relationship between age and the average vocabulary scores. What appears to be the relationship between abilities in this area and one’s age? (Pick “Age” for the X-axis and “Average vocabulary” for the Y-axis and note the correlation (r value) for the relationship.)

Average vocabulary scores are negatively correlated with age, meaning that as age increases, so do the scores in these areas.

Average vocabulary scores are positively correlated with age, meaning that as age increases, so do scores in this area.

Average vocabulary scores have no correlation with age, meaning that there is no relationship between age and performance in this area.

Average vocabulary scores are positively correlated with age, meaning that as age increases, scores in this area decrease.

Correct.

Incorrect.

Question

10) Based on the data analyzed in this applet, what can we conclude about the relationship between age and various types of abilities? Are we doomed to decline cognitively as we age?

The findings demonstrate that even there is a negative relationship between some cognitive areas and age, and these correlations were close to perfect, showing that it is inevitable to experience major decline in all cognitive areas as we age.

The findings demonstrate that even though there is a negative relationship between some cognitive areas and age, these correlations were not perfect and some areas even showed slight improvement with age.

The findings demonstrate that even though there is a positive relationship between most cognitive areas and age, a few showed decline with age.

The findings demonstrate that even though there is a negative relationship between all cognitive areas and age, these correlations were not perfect.

Correct.

Incorrect.

Chapter 11. Development

11.1 Development

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