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TutorTinnieZ-scores

Z-Scores

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TutorTinnieZ-scores

  1. 1. Also known as standard scores It is used to identify and describe the exact location of each score in a distribution A score by itself does not necessarily provide much information about its position within a distribution It tells the exact location of the original X value The number tells the distance between the score and the mean
  2. 2. 𝑧 = π‘₯βˆ’ π‘₯ 𝑠𝐷 𝑠𝐷 = π‘₯βˆ’π‘…π‘  𝑧 π‘₯ = 𝑅𝑠 βˆ’ 𝑠𝑑 β‹… 𝑧 Standardized Score = 50 + 10(z)
  3. 3. Z-Scores will have exactly the same shape as the original distribution of scores Z-scores will always have a mean of zero The distribution of Z-scores will always have a standard deviation of 1 One advantage of standardizing distributions is that it makes it possible to compare different individuals even though they are from completely different distributions.
  4. 4. You are doing a research with homeless people. You want to be able to identify those who are depressed so they can be referred to treatment. You used the Beck Depression Inventory. With n = 50, π‘₯ = 15 and 𝜎 = 2. The following are the scores obtained: Participant Original Score Z-Score T- score/Sta ndardized Alicia 16.5 Christina 14 Chelsea 13 Sabrina 16 Kim 19
  5. 5. Alicia: 16.5βˆ’15 2 = +0.75 Christina: 14βˆ’15 2 = βˆ’0.50 Chelsea: 13βˆ’15 2 = βˆ’1.00 Sabrina: 16βˆ’15 2 = +0.50 Kim: 19βˆ’15 2 = +2.00
  6. 6. Alicia: 50 + 10 +0.75 = 57.50 Christina: 50 + 10 (-0.50) = 45.00 Chelsea: 50 + 10 (-1.00) = 40.00 Sabrina: 50 + 10 (+0.50) = 55.00 Kim: 50 + 10 (+2.00) = 70.00

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