Descriptive Statistics
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Descriptive Statistics
Data is plural.
Datum is singular
All data is not equal.
Measurement systems:
1. Nominal: has the property of identity (0=female, 1=male)
2. Ordinal: has the properties of identity and order (ranked data the units are not even in amount of property)
3. Interval: has the properties of identity, order, and additivity (the units are equal in amount of property)
4. Ratio: has the properties of identity, order, additivity, and absolute zero (like 0 degrees Kelvin)
Measures of Central Tendency
Mean: average
Median: middle most number
Mode: the most common number
In a normal distribution, the mean, median and mode are the same (50th percentile). Most items in nature are equally distributed. Income is NOT normally distributed.
Measures of Variability
Standard deviation (extent to which the scores cluster around the mean)
Variance (SD squared)
Range (highest minus lowest scores)
| -2 standard dev | -1 standard dev | 0 | +1 standard dev | +2 standard
dev |
| 70 | 85 | 100 (WISC-IV) | 115 | 130 |
| MR (with other behaviours) |
68 % of scores fall here | Gifted Education. |
| 2nd percentile | 16th percentile | 50th percentile | 84th percentile | 98th percentile |
| 96% of scores fall here |
| -2 | -1 | 0 (Z-Score) |
+1 | +2 |
| 30 | 40 |
50 (T-Score) | 60 | 70 |
| 300 | 400 | 500 (SAT) |
600 | 700 |
Scores of 70 represent Mild Mental Retardation
Scores of 55 represent Moderate Mental Retardation (below first percentile)
99.74% of scores fall between -3 and +3 standard deviations.
Remember: you cant score in the 100th percentile. (99 is the highest because that is the percent of cases that fall below.)
Mean and standard deviation of the SAT is 500 (on each test) and 100.
Stanine (Standard Nine) originates from military use.
Example computation of a standard deviation from raw scores:
| X | X-Xbar | (X Xbar)squared |
85 | 31 (85-54=31) | 961 (31 squared) |
80 | 26 | 676 |
| 70 | 16 | 256 |
| 60 | 6 | 36 |
| 55 | 1 | 1 |
| 50 | -4 | 16 |
| 45 |
-9 | 81 |
| 40 | -14 | 196 |
| 30 | -24 | 576 |
| 25 | -29 | 841 |
| 540 (mean = 54) | | 3640 (Sum above) |
Variance = {sum(X-Xbar)}squared/n = 364
SD = square root of the above = 19.08
We now know the mean and standard deviation of our set of scores. (54 and 19.08)
Normal Curve Equivalent (NCE) has a mean of 50 and a standard deviation of 21.06. (not all that useful)
Age Equivalent and Grade Equivalent scores assume that all school districts curriculums are equal, and that they move kids through the grade levels equally. In actuality, these concepts are not universal.
Reliability consistency, stability over testing occasions and time spans.
Three types
1. Test-retest reliability
2. Internal consistency a measure of reliability based on the average inter-correlations of the items on the test (do the odds correlate with the evens?).
3. Alternate form reliability two versions of the test correlate.
Filed under: EDC 512-513 Cognitive Assessment and Practicum
Copyright: September, 2003 - David Profitt
