z-scores
Are a standard score that indicates how
many standard deviations above or below the group mean a particular score falls.
Z-scores can be both positive and negative and are typically in fractions. See
the how z-scores distribute across a normal
distribution curve.
Formula for finding a z-score for any given score in a given dataset:
z = (x - Average)/stdev
x = subject value
Average = mean of sample scores (x/n)
Stdev = standard deviation of sample
*When using MSExcel, remember to use
absolute cell referencing ($Row$Column) for the cells containing the Average and
Stdev values*
*Shortcut -- the MSExcel fx STANDARDIZE is the z-score
formula*
T-scores
T-scores are another method of
standardizing scores. T-scores have the advantage that all scores are positve
whole numbers and range from 0 to 100 with 50 representing the Mean of the
group. In calculating T-scores, there are two formulas -- the formula used
depends on whether a smaller or a larger score is considered the better score.
See the how T-scores distribute across a normal
distribution curve
When a value above the mean is better (e.g., strong
= more weight lifted):
T=(10*(x - Average))/Stdev) + 50
When a value below the mean is better (e.g., faster
= less time):
T=(10*(Average - x))/Stdev) + 50
*When using MSExcel, remember to use absolute cell referencing ($Row$Column) for the cells containing the Average and Stdev values*
Percentile Rank Scores
Percentile rank scores provide the relative position of a given score
within a given dataset of scores. A percentile rank score indicates how many
scores are equal and below a specific score. Variables used in the calculation
are: frequency distribution, cumalative frequency, and percentile rank.
See the how percentile ranks (noted as cumulative
percentage on the diagram) distribute across a normal
distribution curve.
*When using MSExcel, remember to use
absolute cell referencing ($Row$Column) for the data array*
Percentiles
Percentiles are used to find a particular value within the range of a values
within a given dataset. For example, if values run from 5.26 to 5.92, then the
percentiles formula would provide an actual value between 5.26 and 5.92 for any
given percentage. E.g., the value at the 85th percentile within a dataset (n=20)
of scores ranging from 5.26 to 5.92 equals 5.84; at the 50th percentile, 5.58;
at the 0 percentile, 5.26; and the 100th percentile, 5.92.
*When using MSExcel, remember to use absolute cell referencing ($Row$Column) for the data array*