Current Slide

• Z-score: 

\[ z=\frac{x-\mu}{\sigma } \]

• X: raw score to be standardized, μ: mean of the population, σ: standard deviation
• the distance between the raw score and the population mean in units of the standard deviation
• negative when the raw score is below the mean, “+” when above
• An alternative way: Calculate the mean absolute deviation, where

\[ m_{f}= \frac{1}{n}(x_{1f}+x_{2f}+...+x_{nf}) \]

• standardized measure (z-score):

\[ z_{if}=\frac{(x_{if}-m_{f})}{S_{f}} \]

• Using mean absolute deviation is more robust than using standard deviation