Measures of Central Tendency

KNR 445Statisticst-testsSlide 1VariabilityMeasures of dispersion or spread

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KNR 445CT/Spread & Z-scoresSlide 2Variability definedMeasures of Central Tendency provide a summary level of performanceRecognizes that performance (scores) vary across individual casesVariability quantifies the spread of performance (how scores vary)parameter or statistic1

KNR 445CT/Spread & Z-scoresSlide 3To describe a distributionMeasure of Central TendencyMean, Mode, MedianVariabilityhow scores clustermultiple measuresRange, Interquartile rangeMean of Absolute Deviations, Variance, Standard Deviation1

KNR 445CT/Spread & Z-scoresSlide 4The Range# of hours spent watching TV p/wk2, 5, 7, 7, 8, 8, 10, 12, 12, 15, 17, 20Range = (Max - Min) Score20 - 2 = 18 Very susceptible to outliersDependent on sample size1

KNR 445CT/Spread & Z-scoresSlide 5Semi-Interquartile rangeWhat is a quartile??Rank values from largest to smallestDivide sample into 4 partsQ1 , Q2 , Q3 => Quartile Points (25th, 50th & 75th percentiles)Interquartile Range = Q 3 - Q 1SIQR = IQR / 2Related to the MedianFor ordinal data, or skewed interval/ratio1234

KNR 445CT/Spread & Z-scoresSlide 6Standard DeviationMost commonly accepted measure of spreadTake the mean, then add up the deviations of all numbers from the meanE.g. take 3 values as a distribution3,4,5Mean is 4First: 3-4 = -1, 4-4 = 0, 5-4 = 1. Then square these deviations, and add them up.Then divide by the number of values in the original distribution (3)Then take the square root of this.Your answer?The final number is an estimate of the typical (standard) difference (deviation) between a score and the meanWhy square deviations and square root them again?1234

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KNR 445CT/Spread & Z-scoresSlide 7Key points about SDSD small data clustered round meanSD large data scattered from the meanAffected by extreme scores (as per mean)Consistent (more stable) across samples from the same population just like the mean - so it works well with inferential stats (where repeated samples are taken)13

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KNR 445CT/Spread & Z-scoresSlide 8Reporting descriptive statistics in a paper1. Descriptive statistics for vertical ground reaction force (VGRF) are presented in Table 3, and graphically in Figure 4. 2. The mean ( SD) VGRF for the experimental group was 13.8 (1.4) N/kg, while that of the control group was 11.4 ( 1.2) N/kg.12

KNR 445CT/Spread & Z-scoresSlide 9SD and the normal curve607080X = 70SD = 1034%34%About 68% ofscores fallwithin 1 SDof mean12

KNR 445CT/Spread & Z-scoresSlide 10About 68% ofscores fallbetween 60 and 70The standard deviation and the normal curve607080X = 70SD = 1034%34%1

KNR 445CT/Spread & Z-scoresSlide 1170About 95% ofscores fallwithin 2 SDof mean60805090X = 70SD = 10The standard deviation and the normal curve1

KNR 445CT/Spread & Z-scoresSlide 1270About 95% ofscores fallbetween 50 and 9060805090X = 70SD = 10The standard deviation and the normal curve1

KNR 445CT/Spread & Z-scoresSlide 13The standard deviation and the normal curve70About 99.7% of scores fall within 3 S.D. of the mean60805090X = 70SD = 10401001

KNR 445CT/Spread & Z-scoresSlide 14The standard deviation and the normal curve70About 99.7% of scores fall between 40 and 10060805090X = 70SD = 10401001

KNR 445CT/Spread & Z-scoresSlide 15What about = 70, SD = 5?What approximate percentage of scores fall between 65 & 75?What range includes about 99.7% of all scores?

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KNR 445CT/Spread & Z-scoresSlide 16Descriptive statistics for a normal populationnMeanSDAllows you to formulate the limits (range) including a certain percentage (Y%) of all scores. Allows rough comparison of different sets of scores.

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KNR 445CT/Spread & Z-scoresSlide 17Interpreting The Normal TableArea under Normal CurveSpecific SD values (z) including certain percentages of the scoresValues of Special Interest1.96 SD = 47.5% of scores (95%)2.58 SD = 49.5% of scores (99%)http://psych.colorado.edu/~mcclella/java/normal/tableNormal.htmlhttp://davidmlane.com/hyperstat/z_table.htmlInfo on using tables:http://www.statsoft.com/textbook/sttable.html1