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Then, ¨ What is the T score for scores of 250, 125, and 133? ( Answers) ¨ What is the T score for a score of 175? ( Answer) n n To find the T score, compute the Z score and then multiply Z by 10Īnd add 50: n So, using the example above where the mean is 175 and the SD isĢ5, a score of 200 has a T score of 60. Scores n A T score is similar to a Z score, except that the mean is alwaysĥ0 and the SD is always 10. n The scores do not have to follow any particular Which can be useful for identifying groups of people who are similar. Percentiles allow categorizing scores into n The percentile of a score tells you what proportion of the populationĬentral tendency of percentiles is 50% and the range is 0% to Percentiles n Percentiles were discussed in You can also get the percentiles using Excel ( click here). –Z) to get the percentile for that Z score. So if a score is above the mean, you have toĪdd 0.50 to the value in Table A.1 (the percent of scores between the mean and Recall that, if the scores are normally distributed, 50% of the scores This is because a positive Z score indicates a score above the mean ¨ If your Z score is positive add 0.50 to the value in Table A.1. Subtract the value in Table A.1 (the percent of scores between the mean and –Z)įrom 0.50 to get the percentile for that Z score. So if a score is below the mean, you have to This is because a negative Z score indicates a score below the mean ¨ If your Z score is negative, subtract the value in Table A.1 fromĠ.50. ¨ Using Table A.1, find the value for your Z score.
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¨ Table A.1 in the textbook (Appendix A) provides the percent of scores between any given Z scoreĪ Z score using the Table's percentage values. Percentile a Z score of 1 is the 84th percentile. This means that a Z score of -1 corresponds to the 16th So, in a normal distribution about 68% of the population (a little more than Mean and +1 SD an additional 34% of the scores are between the mean and –1 n In a normal distribution,Īpproximately 34% of the scores are between the The Z score is also known because of the relation between the normalĭistribution and percentiles. Normal, the percentage of the population’s scores that are between the mean and n When the Z score is known and the distribution of scores is Scores are normalized to the SD of the original variable.
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¨ What is the Z score for scores of 250, 125, and 133 in thisĭistribution? ( Answers) ¨ What is the Z score for a score of 175? ( Answer) n The mean of a distribution of Z scores is always 0 with an SD of 1.0. n A Z score is calculated by subtracting the meanĭividing the difference by the SD: n So, for example, if the mean is 175 and the SD is 25, a score ofĢ00 has a Z score of 1.0. n A Z score converts a raw score into the number of standardĭeviations that the score lies from the mean of the distribution. ¨ The normal distribution is the distribution that manyĬommon and important variables follow. Specific relation to the normal distribution. Previous topic, the standard deviation (SD) has a n There are four standard scores discussed in the text: Z scores, Someone else's performance in a 1 mile run to evaluate who is the "better"Īthlete? n Standard scores have a known mean and variability.Ĭonverting raw, observed scores to standard scores aids in comparisons. ¨ For example, how would you compare someone's performance in the long jump to Have different means and variability is difficult. Standard Scores n Comparing variables that are not measured in the same units and Problems of scoring, sampling, and hypothesis testing. N To demonstrate the application of the normal distribution in Including the relations among percentiles, central tendency, and variability. Reading n Vincent & Weir, Statistics in Kinesiology 4th ed., ChapterĦ “The Normal Curve” and Chapter 7 "Fundamentals of Statistical Inference" Purpose n To demonstrate the properties of the normal distribution, Normal Distribution Section 5.1 n This Topic has 4 Sections. 005: Normal Distribution PEP 6305 Measurement in