KNR 445
Statistics
t-tests
Slide 1
Variability
Measures of dispersion or
spread
1
KNR 445
CT/Spread &
Z-scores
Slide 2
Variability defined
 Measures of Central Tendency provide a summary
1
level of performance
 Recognizes that performance (scores) vary across
individual cases
 Variability quantifies the spread of performance
(how scores vary)
 parameter or statistic
KNR 445
CT/Spread &
Z-scores
Slide 3
To describe a distribution
 Measure of Central Tendency
 Mean, Mode, Median
1
 Variability
 how scores cluster
 multiple measures
 Range, Interquartile range
 Mean of Absolute Deviations, Variance, Standard Deviation
KNR 445
CT/Spread &
Z-scores
Slide 4
The Range
 # of hours spent watching TV p/wk
 2, 5, 7, 7, 8, 8, 10, 12, 12, 15, 17, 20
 Range = (Max - Min) Score
 20 - 2 = 18
 Very susceptible to outliers
 Dependent on sample size
1
KNR 445
CT/Spread &
Z-scores
Slide 5
1
2
Semi-Interquartile range
 What is a quartile??
 Rank values from largest to smallest
 Divide sample into 4 parts
 Q1 , Q2 , Q3 => Quartile Points (25th, 50th & 75th
percentiles)
 Interquartile Range = Q 3 - Q 1
 SIQR = IQR / 2
4
3
 Related to the Median
 For ordinal data, or skewed interval/ratio
KNR 445
CT/Spread &
Z-scores
Slide 6
Standard Deviation
 Most commonly accepted measure of spread
 Take the mean, then add up the deviations of all
numbers from the mean
 E.g. take 3 values as a “distribution”
1
2
3
4
7
 3,4,5
 Mean is 4
5
 First: 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?
6
 The final number is an estimate of the typical (standard)
difference (deviation) between a score and the mean
 Why square deviations and square root them again…?
KNR 445
CT/Spread &
Z-scores
Slide 7
1
2
3
Key points about SD
 SD small  data clustered round mean
 SD large  data scattered from the mean
 Affected 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)
Reporting descriptive statistics in a
paper
KNR 445
CT/Spread &
Z-scores
Slide 8

1
2
1. “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.”
KNR 445
CT/Spread
& Z-scores
Slide 9
SD and the normal curve
1
X = 70
SD = 10
34%
60
2
About 68% of
scores fall
within 1 SD
of mean
34%
70
80
KNR 445
CT/Spread
& Z-scores
Slide 10
The standard deviation and the
normal curve
About 68% of
scores fall
between 60
and 70
X = 70
SD = 10
34%
60
34%
70
1
80
KNR 445
CT/Spread
& Z-scores
Slide 11
The standard deviation and the
normal curve
About 95% of
scores fall
within 2 SD
of mean
X = 70
SD = 10
1
50
60
70
80
90
KNR 445
CT/Spread
& Z-scores
Slide 12
The standard deviation and the
normal curve
About 95% of
scores fall
between 50
and 90
X = 70
SD = 10
1
50
60
70
80
90
The standard deviation and the
normal curve
KNR 445
CT/Spread
& Z-scores
Slide 13
About 99.7%
of scores fall
within 3 S.D.
of the mean
X = 70
SD = 10
1
40
50
60
70
80
90
100
The standard deviation and the
normal curve
KNR 445
CT/Spread
& Z-scores
Slide 14
About 99.7%
of scores fall
between 40
and 100
X = 70
SD = 10
1
40
50
60
70
80
90
100
KNR 445
CT/Spread &
Z-scores
Slide 15
1
What about X = 70, SD = 5?
 What approximate percentage of scores fall
between 65 & 75?
2
 What range includes about 99.7% of all scores?
3
Descriptive statistics for a normal
population
KNR 445
CT/Spread &
Z-scores
Slide 16
 n
 Mean
1
 SD
 Allows you to formulate the limits (range) including a
certain percentage (Y%) of all scores. Allows rough
comparison of different sets of scores.
KNR 445
CT/Spread &
Z-scores
Slide 17
Interpreting The Normal Table
 Area under Normal Curve
 Specific SD values (z) including certain percentages of
the scores
 Values of Special Interest
1
 1.96 SD = 47.5% of scores (95%)
 2.58 SD = 49.5% of scores (99%)

http://psych.colorado.edu/~mcclella/java/normal/tableNormal.html
 http://davidmlane.com/hyperstat/z_table.html
 Info on using tables:

http://www.statsoft.com/textbook/sttable.html