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Ordinal Scale: This scale puts order into categories. It only ranks categories by
ability, but there is no specific quantification between categories. It is only placement, e.g., judging a swimming race without a stopwatch, i.e., there is no quantitiy to
determine the difference between ranks. KEY: placement without quantification.
• Most statistical methods are based on assumption that a distribution of scores is normal and that the distribution can be graphically represented by the normal curve (bell-shaped).
• Normal distribution is theoretical and is based on the assumption that the distribution contains an infinite number of scores.
• describe the middle characteristics of the data (distribution of scores); represent scores in a distribution around which other scores seem to center
Score that represents the exact middle of the distribution; the fiftieth percentile; the score that 50% of the scores are above and 50% of the scores are below.
Characteristics• Not affected by extreme scores.• A measure of position.• Not used for additional statistical calculations.
• Most useful and sophisticated measure of variability.• Describes the scatter of scores around the mean.• Is a more stable measure of variability than the range or
quartile deviation because it depends on the weight of each score in the distribution.
• Lowercase Greek letter sigma is used to indicate the the standard deviation of a population; letter s is used to indicate the standard deviation of a sample.
• Since you generally will be working with small samples, the formula for determining the standard deviation will include (N - 1) rather than N.
1. Is the square root of the variance, which is the average of the squared deviations from the mean. Population variance is represented as F2 and the sample variance is represented as s2.
2. Is applicable to interval and ratio data, includes all scores, and is the most reliable measure of variability.3. Is used with the mean. In a normal distribution, one standard deviation added to the mean and one standard deviation subtracted from the mean includes the middle 68.26% of the scores.
T-ScoresT-scale• Has a mean of 50.• Has a standard deviation of 10.• May extend from 0 to 100.• Unlikely that any t-score will be beyond 20 or 80
(this range includes plus and minus 3 standard deviations).FormulaT-score = 50 + 10 (X - X) = 50 + 10z sFigure 2.9 shows the relationship of z-scores, T-scores, and the normal curve.
4. Add the value found in step 3 to the mean and each subsequent number until you reach the T-score of 80.5. Subtract the value found in step 3 from the mean and each decreasing number until you reach the number 20.6. Round off the scores to the nearest whole number.
*For some scores, lower scores are better (timed events).