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# 10-11 and 10-13 notes SWRK 344

WKU

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This 3 page Class Notes was uploaded by Kirsten Swikert on Tuesday October 18, 2016. The Class Notes belongs to SWRK 344 at Western Kentucky University taught by Dr. Getch in Fall 2016. Since its upload, it has received 6 views. For similar materials see Social Work Statistics and Data Analysis in Social Work at Western Kentucky University.

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Date Created: 10/18/16

Z Scores • Is a common standard using the standard normal distribution • Z scores allow us to compare different samples even if the samples have different means • All raw scores have a Z score that corresponds • Because Z scores take into account the standard deviation in their calculation, they can be compared to another Z score from another sample • You can convert Z scores to percentiles and see where the score lies in comparison to other scores • All raw scores have a corresponding Z score and a corresponding percentile p.78 mistake in book: sentence 4, answer is .06 Converting Raw Scores to Z Scores • Raw score – mean / standard deviation • Now you can understand why the standard deviation is so important o It allows us to convert raw scores from different populations and compare them o It allows us to then look at the scores percentile rank o We can compare scores from different samples and know what scores are higher and where these scores “rank” in comparison to one another • 82-83.7= -1.7/9.49= -.18 • 94-83.7= 10.3/9.49= 1.08 • 76-83.7= -7.7/9.49= -.81 Converting to Percentiles • Knowing whether the z score is positive or negative matters • Positive z scores o Find the corresponding percentage under the standard normal curve o Add this number to .50 to get the percentile rank o Always above 50% • Negative z scores o Find the corresponding percentage under the standard normal curve o Subtract this from .50 to get the percentile rank o Always below 50% Important Reminders • Only use when samples approximate the normal curve • Skewed distributions do not have similar areas under the curve • Z scores and percentile ranks are often used for standardized tests Areas under the normal curve • Z scores and the corresponding percentage can be found in a table • At the 50 percentile the z score is at 0 • At -1 standard deviation the z score is -1 and the corresponding area on the table is .3413 or 34.13% Finding the Area Under the Curve • If your raw score is 88 and your mean is 80, your z score would be 88-80 divided by the standard deviation • Ex: standard deviation is 10 o 88-80/10 o 8/10= .8 o Z score is .8 o Under the standard normal curve z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.0000 0.0040 0.0080 0.0120 0.0160 0.0199 0.0239 0.0279 0.0319 0.0359 0.1 0.0398 0.0438 0.0478 0.0517 0.0557 0.0596 0.0636 0.0675 0.0714 0.0753 0.2 0.0793 0.0832 0.0871 0.0910 0.0948 0.0987 0.1026 0.1064 0.1103 0.1141 0.3 0.1179 0.1217 0.1255 0.1293 0.1331 0.1368 0.1406 0.1443 0.1480 0.1517 0.4 0.1554 0.1591 0.1628 0.1664 0.1700 0.1736 0.1772 0.1808 0.1844 0.1879 0.5 0.1915 0.1950 0.1985 0.2019 0.2054 0.2088 0.2123 0.2157 0.2190 0.2224 0.6 0.2257 0.2291 0.2324 0.2357 0.2389 0.2422 0.2454 0.2486 0.2517 0.2549 0.7 0.2580 0.2611 0.2642 0.2673 0.2704 0.2734 0.2764 0.2794 0.2823 0.2852 0.8 0.2881 0.2910 0.2939 0.2967 0.2995 0.3023 0.3051 0.3078 0.3106 0.3133 0.9 0.3159 0.3186 0.3212 0.3238 0.3264 0.3289 0.3315 0.3340 0.3365 0.3389 • Because the z score is positive, it will be to the right of the 50 percentile o To find exactly where it is, you will add .50 and .2881 o .5+.2881=.7881 th o The corresponding percentile is 78.81 or the 79 percentile Getting Raw Scores from Percentiles • You are reversing the process and finding X (the raw score) o Take the z score and multiply it by the standard deviation, then add the mean o Ex: z score is -1.53, standard deviation is 15, mean is 60 § -1.53*15=-22.95+60=37.05 § Raw score is 37 or 37.05 Why do we Need to Know This? • You can interpret the results of standardized testing • We can compare the results of two different treatment group samples • It is useful in program evaluations when comparing results of one program to the results of another program by taking the different means, variation, and standard deviations into account

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