Standard Scores
- A standard score is computed by taking into account how far a given score deviates from the mean.
- The deviation from the mean is expressed in terms of standard deviation units
- This is done by computing: standard score =
- Standard score tells you the number of standard deviation units above or below the mean a particular score is
Properties of Standard Scores
- Sign
- Negative – score is below the mean
- Zero – score is equal to the mean
- Positive – score is above the mean
- The mean of any set of standard scores will always be zero (
)
Uses of Standard Scores
- Standard scores allow us to make comparisons between scores from distributions that have different means and standard deviations
** Remember, when we convert to standard scores, M = 0 and SD = 1.0, so it is possible to compare two scores that were originally from two different distributions.
Standard Scores and the Normal Distribution
- Normal distributions have the following properties:
- Are bell shaped
- Are symmetrical around the mean
- Have Mean = Median = Mode
- There is a different normal distribution for every unique combination of M and SD, but all have the 3 properties above
- In any normal distribution, the proportion of scores falling above or below a given standard score is always the same.
- The proportion of scores that occur between two specific standard scores is the same for all normal distributions
Look at Figure 4.1 (p. 110)
- .3413, or about 34% of the scores fall between standard scores of 0 and 1(or 0 and -1)
- .6826, or about 68% of scores fall between standard scores of –1 and +1
- .9544, or about 95% of scores fall between –2 and +2
- .9974, or about 99% of scores fall between –3 and +3
**always same pattern above & below mean, because its symmetrical
- When we are talking about standard scores in a normal distribution, we call the standard scores z-scores
- Is computed the same way as before: 
- Appendix B (p. 563 -571) gives proportions falling under more specific proportions of the normal curve than are presented in Figure 4.1 (for many more z scores than the whole numbers listed in Figure 4.1)
This table gives us the following information:
- Column 1 – absolute value of z scores, starting w/.00 through 4.00
- Column 2 – the proportion of scores falling between any positive z score and its negative value
- Column 3 – the proportion of scores falling above a positive z or below a negative z
- Column 4 – the proportion of scores above its positive value and below its negative value (proportion falling in tails – also twice value in column 3)
- Column 5 – the proportion of scores between any z score an the mean (1/2 column 2)
- If we can assume a set of scores is normally distributed, we can use the table to find the percentage of scores in a given portion of the normal distribution.
***NOT all standard scores are normally distributed!!!!
Standard Scores and the Shape of the Distribution
- The process of standardizing scores does not change the fundamental shape of the distribution
- Standardization affects the central tendency and variability of the scores but not the skewness or kurtosis of scores
