Basic Statistics.docx - BASIC STATISTICS \u2022 PURPOSE OF STATISTICS A goal of statistics is to make inferences or generalizations about a population \u2022

# Basic Statistics.docx - BASIC STATISTICS u2022 PURPOSE OF...

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BASIC STATISTICS PURPOSE OF STATISTICS A goal of statistics is to make inferences, or generalizations, about a population. Purpose of statistics: Description Descriptive Statistics Making Inference Correlational Statistics Inferential Statistics LEVELS / SCALES OF MEASUREMENT MEASUREMENT The application of rules for assigning numbers to objects The assignment of numerical value, quantitative value to things or events PROPERTIES OF SCALES 1. Magnitude Property of “moreness” Eg.5ftistallerthan 4ft Eg.1stplace isgreaterthan3rdplace 2. Equal Intervals Difference between two points on the scale has same meaning as the difference between two other points on the scale. Eg.scores80 and 90 and110and120 3. Absolute Zero Nothing of the property being measured exists. Eg. Temperature K, Extraversion SCALES / LEVELS OF MEASUREMENT 1. Nominal Tells a difference exists 2. Ordinal Direction of the difference 3. Interval Direction &magnitude of the difference 4. Ratio Direction, magnitude, & ratio of the difference PROPERTIES OF SCALES MAGNITUDE EQUALINTERVAL ABSOLUTEZERO NOMINAL No No No ORDINAL Yes No No INTERVAL Yes Yes No RATIO Yes Yes Yes Why is it important? It defines the mathematical operations we can apply to the data. Eg. Nominal = can you use correlational stats? Which one? STANDARD SCORES
Z-score, T-scores, Stanine, Deviation IQ, McCall’s T STANDARD SCORES (Z-SCORES) Tells where the score lies Z-score = X–Mean/SD MEAN = 0andSD = 1 If the standard score is POSITIVE, then the score is greater than the mean, if the standard score is NEGATIVE, then the score is less than the mean. Z = (-), X < Mean; Z = (+), X > Mean It is easier to interpret. It is not the scores per se. A z score is a transformed score that designates how man standard deviation units the corresponding raw score is above or below the mean. CHARACTERISTICS OF Z SCORES 1. The z scores have the same shape as the set of raw scores. 2. The mean of the z scores is always equivalent to zero. 3. The standard deviation ofzscoresisalwaysequivalentto1. T SCORES / MCCALL’S T MEAN = 50, SD=10 System developed in 1939 by W.A. McCall Originally intended to develop a system to derive equal units on mental quantities Came from Thorndike’s studies STANINE SYSTEM Converts any set of scores into a transformed scale which rangesfrom1to9 Comes from the words “standard nine” The scale is standardized to have a MEAN = 5 and SD = 2 DEVIATION IQ MEAN = 100, SD = 15 SUMMARY OF STANDARD SCORES -3sd -2sd -1sd MEAN +1 sd +2 sd +3 sd Z score -3 -2 -1 0 +1 +2 +3 T score 20 30 40 50 60 70 80
Stanine -1 1 3 5 7 9 11 IQ score 55 70 85 100 115 150 145 NORMS NORMS Refer to the performances by defined groups on particular tests The norms for a test are based on the distribution of scores obtained by some defined sample of individuals.