Read Chapter 5

Please respond to all questions.

1) What are the easiest and hardest concepts in the chapter? Explain your answer.

2) Why are Z scores important and how are they used?

Helpful Video: https://www.khanacademy.org/math/ap-statistics/density-curves-normal-distribution-ap/measuring-position/v/z-score-introduction

Chapter 5. z-Scores: Location of Scores and Standardized Distributions

Figure 5.1.

An example of a perceptual speed task. The participant is asked to search through the display as quickly as possible and circle each pair of digits that add up to 10.

64	23	19	31	19	46	31	91	83	82	82	46	19	87
11	42	94	87	64	44	19	55	82	46	57	98	39	46
78	73	72	66	63	71	67	42	62	73	45	22	62	99
73	91	52	37	55	97	91	51	44	23	46	64	97	62
97	31	21	49	93	91	89	46	73	82	55	98	12	56
73	82	37	55	89	83	73	27	83	82	73	46	97	62
57	96	46	55	46	19	13	67	73	26	58	64	32	73
23	94	66	55	91	73	67	73	82	55	64	62	46	39
87	11	99	73	56	73	63	73	91	82	63	33	16	88
19	42	62	91	12	82	32	92	73	46	68	19	11	64
93	91	32	82	63	91	46	46	36	55	19	92	62	71

Suppose that you took Ackerman and Beier's test and your combined time and errors produced a score of 92. How did you do? Are you faster than average, fairly normal in perceptual speed, or does your score indicate a serious deficit in cognitive skill? The answer is that you have no idea how your score of 92 compares with scores for others who took the same test. Now suppose that you are also told that the distribution of perceptual speed scores has a mean of =86.75 and a standard deviation of =10.50 . With this additional information, you should realize that your score (X=92) is somewhat higher than average but not an exceptionally high score.

In this chapter we introduce a statistical procedure for converting individual scores into z-scores, so that each z-score is a meaningful value that identifies exactly where the original score is located in the distribution. As you will see, z-scores use the mean as a reference point to determine whether the score is above or below average. A z-score also uses the standard deviation as a yardstick for describing how much an individual score differs from average. For example, a z-score will tell you if your score is above the mean by a distance equal to two standard deviations, or below the mean by one-half of a standard deviation. A good understanding of the mean and the standard deviation will be a valuable background for learning about z-scores.

5.1. Introduction to z-ScoresLearning Objective

1. Describe the two general purposes for transforming X values into z-scores.

In the previous two chapters, we introduced the concepts of the mean and standard deviation as methods for describing an entire distribution of scores. Now we shift attention to the individual scores within a distribution. In this chapter, we introduce a statistical technique that uses the mean and the standard deviation to transform each score (X value) into a z-scoreor a standard score. The purpose of z-scores, or standard scores, is to identify and describe the exact location of each score in a distribution.

The following example demonstrates why z-scores are useful and introduces the general concept of transforming X values into z-scores.

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