Measures of Central Tendency

KNR 445Statisticst-testsSlide 1Standard ScoresComparing scores across (normal) distributions z-scores1

KNR 445CT/Spread & Z-scoresSlide 2Assessing the relative position of a single scoreMove from describing a distribution to looking at how a single score fits into the groupRaw Score: a single individual value i.e. 36 in exam scoresHow do we interpret this value how good is it?1

KNR 445CT/Spread & Z-scoresSlide 3Describe the typical and the spread, and the number of casesMinimal StatisticsMeanSDN

Z-SCORE: identifies a score as above or below the mean AND expresses a score in units of SDE.g. z-score = 1.00 (1 SD above mean)z-score = -2.00 (2 SD below mean)1

KNR 445CT/Spread & Z-scoresSlide 4Z-score = 1.0: GRAPHICALLY

Z = 184% of scores smaller than this1

KNR 445CT/Spread & Z-scoresSlide 5Calculating z-scores

Calculate Z for each of the following situations:

1234

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KNR 445CT/Spread & Z-scoresSlide 6Other features of z-scoresMean of distribution of z-scores = 0 (i.e. 0 = 0 SD)SD of distribution of z-scores = 1since SD is unit of measurementz-score distribution is same shape as raw score distribution123

KNR 445CT/Spread & Z-scoresSlide 7Z-scores can compare scores from different distributionsMarys scoreSAT Exam 550 (mean 500 SD 100)Geralds scoreACT Exam 24 (mean 18 SD 6)Who scored higher?Mary: (550 500)/100 = ?Gerald: (24 18)/6 = ?1234

KNR 445CT/Spread & Z-scoresSlide 8Z-scores & the normal curveFor any z-score, we can calculate the percentage of scores between it and the mean; all scores below it & all above itApplet demos:http://psych.colorado.edu/~mcclella/java/normal/normz.htmlhttp://psych.colorado.edu/~mcclella/java/normal/handleNormal.htmlhttp://psych.colorado.edu/~mcclella/java/normal/tableNormal.html1

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8KNR 445CT/Spread & Z-scoresSlide 9Finding z-scores in PASW

Choose this option

KNR 445CT/Spread & Z-scoresSlide 10

Finding z-scores in PASWSlide the variable over that you want converted to z-scoresAnd choose this

KNR 445CT/Spread & Z-scoresSlide 11Finding z-scores in PASW

The z-scores pop up in the data window as a new variable1

KNR 445CT/Spread & Z-scoresSlide 12Finding z-scores in Excel

First compute the average for the variable1

KNR 445CT/Spread & Z-scoresSlide 13Finding z-scores in Excel

Then the SD1

KNR 445CT/Spread & Z-scoresSlide 14

Finding z-scores in ExcelThen stick in the relevant formula in the first cell (note use of $)1

2KNR 445CT/Spread & Z-scoresSlide 15Finding z-scores in Excel

Then just copy down1