Unit 4: Statistics & Test Construction

 Scales of Measurement: Nominal Scale: A set of categories for classifying people or objects (e.g., eye color, gender, political affiliation) Ordinal Scale: A scale indicating the order or relative position of items or people based on some criterion (i.e., 1st place, 2nd, 3rd, etc.) Interval Scale: Scale with equal distances between points, but with no true zero point (e.g., temperature, most psychological tests) Ratio Scale: Scale with equal distances between points and with a true zero point, thus we can say something is twice as much as something else (e.g., inches of rainfall, distance in miles, etc.)              Measures of Central Tendency Mean: Arithmetical average calculated by dividing a sum of values by the total number of cases Median: Point that divides a set of scores in half. Mode: The most frequent score in a distribution of scores *Of these three measures, the MEAN is most affected by outliers or extreme scores.                    Measures of Variation Range: Difference between the largest and smallest scores in a distribution. Variance: A statistical average of the amount of dispersion around the mean in a distribution of the scores.  It is the Standard Deviation squared. Standard Deviation: A statistical measure of the amount of dispersion in a set of scores.  Specifically, it is the square root of the average squared deviations from the mean of a set of scores.  It is simply the square root of the variance. *Of the three measures, the STANDARD DEVIATION is most affected by outliers.                    Distributions of Scores Normal Curve: Hypothetical, bell-shaped distribution of scores that occurs when a normal distribution is plotted as a frequency polygon. In a normal distribution, the mean, median, and mode are all equal and divide the distribution in half (the 50th percentile). Percentile Rank: Reflects the percentage of subjects who score lower than the subject in question The Normal Distribution Positively Skewed Distribution: A distribution where most scores are clustered at the lower end of the curve, with a few very high scores creating a long "tail" to the right.  The mean is greater than the median, and the median is greater than the mode. Negatively Skewed Distribution: A distribution where most scores are clustered at the upper end of the curve, with a few very low scores creating a long "tail" to the left.  The mean is less than the median, and the median is less than the mode. NEXT PAGE
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