KNR 445 Statistics t-tests Slide 1 Standard Scores Comparing scores across (normal) distributions – “z- scores” 1

KNR 445 CT/Spread & Z-scores Slide 2 Assessing the relative position of a single score  Move from describing a distribution to looking at how a single score fits into the group  Raw Score: a single individual value  i.e. 36 in exam scores  How do we interpret this value – how good is it? 1

KNR 445 CT/Spread & Z-scores Slide 3 Describe the “typical” and the “spread”, and the number of cases Minimal Statistics  Mean  SD  N  Z-SCORE: identifies a score as above or below the mean AND expresses a score in units of SD  E.g.  z-score = 1.00 (1 SD above mean)  z-score = (2 SD below mean) 1

KNR 445 CT/Spread & Z-scores Slide 4 Z-score = 1.0: GRAPHICALLY Z = 1 84% of scores smaller than this 1

KNR 445 CT/Spread & Z-scores Slide 5 Calculating z-scores Calculate Z for each of the following situations:

KNR 445 CT/Spread & Z-scores Slide 6 Other features of z-scores  Mean of distribution of z-scores = 0 (i.e. 0 = 0 SD)  SD of distribution of z-scores = 1  since SD is unit of measurement  z-score distribution is same shape as raw score distribution 1 2 3

KNR 445 CT/Spread & Z-scores Slide 7 Z-scores can compare scores from different distributions  Mary’s score  SAT Exam 550 (mean 500 SD 100)  Gerald’s score  ACT Exam 24 (mean 18 SD 6)  Who scored higher? Mary: (550 – 500)/100 = ? Gerald: (24 – 18)/6 = ?

KNR 445 CT/Spread & Z-scores Slide 8 Z-scores & the normal curve  For any z-score, we can calculate the percentage of scores between it and the mean; all scores below it & all above it  Applet demos:   

KNR 445 CT/Spread & Z-scores Slide 9 Finding z-scores in PASW Choose this option…

KNR 445 CT/Spread & Z-scores Slide 10 Finding z-scores in PASW Slide the variable over that you want converted to z- scores And choose this

KNR 445 CT/Spread & Z-scores Slide 11 Finding z-scores in PASW The z-scores pop up in the data window as a new variable 1

KNR 445 CT/Spread & Z-scores Slide 12 Finding z-scores in Excel First compute the average for the variable 1

KNR 445 CT/Spread & Z-scores Slide 13 Finding z-scores in Excel Then the SD 1

KNR 445 CT/Spread & Z-scores Slide 14 Finding z-scores in Excel Then stick in the relevant formula in the first cell (note use of $) 1

2 KNR 445 CT/Spread & Z-scores Slide 15 Finding z-scores in Excel Then just copy down 1