Transcript Ch 5: Variability (skip p. 151-162)

Ch 5: Variability
(skip p. 151-162)
Wed, Feb 18th, 2004
Variability
 Describes spread/diversity of the
scores in distribution
 Options: range, interquartile range,
standard deviation, variance
 Range: difference betw highest &
lowest scores.
 Interquartile Range (IQR): width of
middle 50% of distribution
(cont.)
 IQR: Q1 is 25% percentile (score for
which 25% scores fall below it); Q3
is 75% percentile
– IQR = Q3 – Q1
– Less affected by outliers than range
– Box plot (in book) graphs the range,
25%, median, & 75% scores
Variance & SD
 Variance – average of squared deviations
from the mean
– Based on deviation scores, y-ybar, then square,
and take average
– Unit is squared original unit, so hard to
interpret
 Standard deviation – average deviation
from mean (square root of variance)
– Based on deviation scores  averaged
– SD calculated in original unit, so easier to
interpret
Calculating Variance, SD
 1) Start by finding “Sum of Squares” (SS)
SS =  (y-ybar)2
That is, sum up each scores’ (y) squared
deviation from the mean (ybar).
Example: (8, 12, 35, 17, 22, 11), N = 6
Ybar (mean) = 17.5
SS = (8-17.5)2 + (12-17.5)2 + (35-17.5)2 +
(17-17.5)2 + (22-17.5)2 + (11-17.5)2 = 489.5
 Note – must square the deviations, otherwise
they would sum to 0
(cont.)
 2) After finding SS, find variance:
S2y = SS / N-1 (for sample variance, for
population variance, use N as denom)
Here, S2y = 489.5 / 6-1= 97.9
 3) Find standard deviation:
Sy = sqrt (SS / N-1) …or sqrt(S2y )
Here, Sy = sqrt (489.5 / 6-1) = 9.89
Properties of Standard Dev
 1) Add/subtract a constant from each score
 doesn’t change the standard deviation
– The mean will change by that constant, but the
spread of the scores won’t change
 2) Mult/divide each score by constant &
standard dev changes by the same constant
– Because the mean will change by that constant,
your deviation scores will change consistently
too
Notes on Lab 10
 SPSS: follow step-by-step instructions for
using menus…note:
 To add constant to each score in data, use
“Compute” function
 Transform  Compute
Window pops up…under “Target variable” come
up w/new variable name (addthree), for
“Numeric Expression” – choose original variable
from list (e.g., age) then type in transformation
you want (e.g., age +3), hit OK
SPSS will add a new column in dataset with this
new transformed variable