Statistical Analysis for Education and Psychology Researchers

sample standard deviation) is df=n−1, where n is the number of xi scores in the sample
(sample size).

Interpretation of Quantiles

Most computer statistical packages are able to provide a range of data plotting facilities
and descriptive statistics. PROC UNIVARIATE in SAS provides comprehensive
summary statistics which are divided into four sections, moments, quantiles, extremes
and if appropriate, missing values.
Consider once again the A-level data set. To obtain descriptive statistics for the
variable age in years the following SAS code is submitted:

proc univariate;

var agey;

run;

The VAR statement lists the variables to be summarized. The output produced by this
code is as follows:
Variable=AGEY AGE IN YEARS
Moments
N 114 Sum Wgts 114
Mean 19.1769 Sum 2186.167
Std Dev 1.180186 Variance 1.392839
Skewness 3.601622 Kurtosis 20.44996
USS 42001.29 CSS 157.3908
CV 6.154207 Std Mean 0.110535
T:Mean=0 173.4924 Pr>|T| 0.0001
Num^=0 114 Num>0 114
M (Sign) 57 Pr>=|M| 0.0001
Sgn Rank 3277.5 Pr>=|S| 0.0001
Quantiles (Def =5)
100% Max 27.16667 99% 24.25
75% Q3 19.5 95% 20.75
50% Med 18.91667 90% 20.33333
25% Q1 18.58333 10% 18.25
0% Min 16.75 5% 18.16667
1% 17.83333
Range 10.41667
Q3−Q1 0.916667
Mode 18.75
Extremes
Lowest Obs Highest Obs
16.75 ( 95) 20.91667 ( 69)
17.83333 ( 56) 21.08333 ( 15)
18.08333 ( 106) 21.75 ( 104)

Statistical analysis for education and psychology researchers 72