STANDARDIZATION

• Standardization


  The process of converting individual scores from different normal distributions to a shared normal distribution with a known mean, standard deviation, and percentiles

  
• Need for standardization


  • Different variables are measured on different scales, so we need a way to put them on the same standardized scale
• Standardizing variables


  Use the mean and standard deviation to convert raw scores into z-scores

  
• 1. score


  The number of standard deviations a particular score is from the mean

  
• 1. distribution


  • Always has a mean of 0 and a standard deviation of 1, no matter the original distribution

  
• Transforming raw scores into z-scores

  z = (raw score - mean) / standard deviation
• Transforming z-scores into raw scores


  raw score = (z * standard deviation) + mean
• Percentile rank


  Indicates the percentage of scores that fall below a particular score
• Transforming z-scores into percentiles


  Use the normal curve to convert z-scores to percentiles
• Approximately 68% of scores fall within 1 standard deviation of the mean, 96% within 2 standard deviations, and nearly all within 3 standard deviations
• Using the z-table


  Convert raw score to z-score

  2. Look up z-score on z-table to find percentage of scores between mean and that z-score

  3. Multiply result by 100 to get percentile
• Compute the following z-scores to percentile ranks

  • z = -2.03

  2. z = 0.00

  3. z = 3.00

  4. z = -1.17

  5. z = -0.55

  6. z = -1.78

  7. z = 1.50