Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Chapter 3. Statistical Refresher Scales of Measurement -Measurement: The act of assigning numbers or symbols to characteristics of objects, events, or people according to rules (i.e., length) -Scale: A set of numbers or other symbols assigned to events or objects according to empirical basis/rule (outcome of measurement) (a) Nominal Scale: Categorization or classification (i.e., suicidal or not) (b) Ordinal Scale: Rank-ordering characteristics (i.e., extremely happy, moderately happy, happy, unhappy). (c) Interval Scale: Contain equal intervals between numbers (i.e., the difference between 1 and 2 is equal to the difference between 13 and 14). But no absolute zero (i.e., IQ score) (d) Ratio Scale: Has a true zero point (i.e., length, weight). Describing Data 1. Frequency distributions: Listing all scores alongside the number of times each score occurred. (a) Grouped Frequency distribution: Listing test-score-intervals or class intervals alongside the number of times each class interval occurred. (b) Histogram: A graph describing data with class intervals (i.e., 21-30, 31-40, etc.) on the x-axis and the number of times each class interval occurred on the y-axis. (c) Bar graph: A graph describing data with some categorization on the x-axis and the number of times each class (i.e., men vs. women) occurred. (d) Frequency Polygon: A graph describing data with connecting points where test scores or class intervals on x-axis meet frequencies of the scores or intervals on the y-axis. 2. Central Tendency (a) Mean: Arithmetic average. (b) Median: A middle score in a distribution (when even frequency, add and divide by 2). (c) Mode (i.e., bimodal): The most frequently occurring score. 3. Measures of variability (The extent to which scores in a distribution are scattered or dispersed?) (a) Range: The difference between the highest and lowest scores. (i.e., Interquartile vs. Semi-interquartile range) (b) Standard deviation: The standard distance between a raw score and the population mean. The square root of the average squared deviations about the mean. (S.D = Root of [Sigma (X-population)square / n] (c) Standard error: The standard distance between a sample mean and the population mean. (S.E = S.D / n) (d) Variation: Squared S.D. (e) Skewness: The nature and extent to which symmetry is absent. Positively (when high scores are relatively few) or negatively (when low scores are relatively few) skewed (f) Kurtosis: The steepness of a distribution (Leptokurtic, Mesokurtic, Platykurtic) 4. Standard Scores -A standard score is a raw score that has been converted from one scale into another scale that is more widely used, interpretable, and has some arbitrary mean and standard deviation). -Why do we need standard scores? (a) The raw scores have no meaning, no information about test-taker’s relative performance. (b) Compare raw scores between tests. 5. Normal curve: a bell-shaped, smooth, mathematically defined curve highest at the center and the gradually tapered on both sides approaching x-axis asymptotically (it is approaching but not touching it). (i.e., 34%, 68%, 95%) (a) Z score (= X – mean / s) (mean=0, sd=1): -The difference between a particular raw score and the mean divided by the standard deviation. – -The z score expresses a score in terms of the number of standard deviation units the raw score is below or above the mean of the distribution. (b) T score = Another form of Z scores but different mean and s.d. (mean=50, sd=10). sd units Z scores T scores IQ scores % -3sd -3 20 55 2.27 -2sd -2 30 70 13.59 -1sd -1 40 85 34.13 0 0 50 100 +1sd +1 60 115 34.13 +2sd +2 70 130 13.59 +3sd +3 80 145 2.27