BASIC STATISTICSPURPOSE 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 StatisticsLEVELS / SCALES OF MEASUREMENTMEASUREMENT•The application of rules for assigning numbers to objects•The assignment of numerical value, quantitative value to things or eventsPROPERTIES OF SCALES1.Magnitude•Property of “moreness”•Eg.5ftistallerthan 4ft•Eg.1stplace isgreaterthan3rdplace2.Equal Intervals•Difference between two points on the scale has same meaning as the differencebetween two other points on the scale.•Eg.scores80 and 90 and110and1203.Absolute Zero•Nothing of the property being measured exists.•Eg. Temperature K, ExtraversionSCALES / LEVELS OF MEASUREMENT1.Nominal•Tells a difference exists2.Ordinal•Direction of the difference3.Interval•Direction &magnitude of the difference4.Ratio•Direction, magnitude, & ratio of the differencePROPERTIES OF SCALESMAGNITUDEEQUALINTERVALABSOLUTEZERONOMINALNoNoNoORDINALYesNoNoINTERVALYesYesNoRATIOYesYesYesWhy 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 TSTANDARD 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 standardscore 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 thecorresponding raw score is above or below the mean.CHARACTERISTICS OF Z SCORES1.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 studiesSTANINE 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 = 2DEVIATION IQ•MEAN = 100, SD = 15SUMMARYOFSTANDARD SCORES-3sd-2sd-1sdMEAN+1 sd+2 sd+3 sdZ score-3-2-10+1+2+3T score20304050607080
Stanine-11357911IQ score557085100115150145NORMSNORMS•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 definedsample of individuals.