![]() ![]() That is what we'll do is convert every score in the distribution into a standardized score, making the overall distribution standardized.Ī standard score is a transformed score that provides information about its location in a distribution. For example, we can transform these data into z-scores. In other words, we need to convert the two distributions into a form that we can make a comparison. Standardized distributions are used to make dissimilar distributions comparable. So to be able to make a comparison, one approach would be to transform both distributions into a standardized distribution.Ī standardized distribution is composed of transformed scores that result in predetermined values for m and s, regardless of their values for the raw score distribution. The comparison that we just did is what z-scores are all about. so the ACT score is better than the SAT score So an 8 is 1.33 SD above the mean (8 / 6) How might we go about it?1) look at the distribution graphs, locate the scores and compare - still hard to tell2) think about cumulative percentiles and percentile ranks - this will work3) try and take the deviations and standard deviations into accountĮ.g., ACT mean = 18, SD = 6, deviation = 26 - 18 = 8 It is hard to do a direct comparison here because the two distributions have different properties: different means, and different variabilities. Which do you want to send them (that is, which score is better, 26 or 620?). The college that you apply to only needs one score. You get a 26 on the ACT and a 620 on the SAT. But, if we want to compare two scores from two distributions, then the situation gets much harder.Ĭonsider the following situation. If we are only concerned about a single distribution, then this seems to be pretty easy to do. So a natural choice for describing the location of a data point would be the deviation score (x - m) or (x - ). Our goal is to be able to find our raw scores within the distribution, and to be able to describe where it falls.Ī good point of reference is the mean (since it is usually easy to find). While this isn't evey detail about a distribution, it does give us a pretty good picture of what the distribution looks like.įor most bell-shaped curves (e.g., symmetric and unimodal), the mean should be at the mid-point and the standard deviation should be somewhere half-way between the mean and the most extreme values. New York: West Publishing.Ĭhapter 5: Z-Scores: Location of scores and standardized distributionsĭescriptive statistics, like the mean and standard deviation, describe distributions by summarizing the center (central tendency) and spread (variability). Statistics for the Behavioral Sciences:Ī First Course for Students of Psychology and Education, 4th Edition. Psychology 240: Statistics 1 Lectures: Chapter 5 Psychology 240 Lectures ![]()
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