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Descriptive Statistics
Descriptive (describe)
 Frequencies
 Percents
 Measures
 mean
 median
 mode
of Central Tendency
Measures of Spread
 Nominal
data = number of responses in each
category (A’s = 4, B’s = 7, C’s = 21, D’s = 1, F’s=2)
 Other data = difference between responses for
the greatest and least numeric values (Age of
oldest is 104 and youngest is 18. Range =86 years)
Tertiles, Quartiles, Quintiles
 Interquartile Range (IQR)
 Range for the 25th to 75th
which captures the middle 50%
Measures of Spread
 Standard
Deviation – describes, on
average, how much individual values differ
from the mean
 Standard
Scores or Z-scores – describes
how many SD’s away from the sample
mean an individual score or response is
Normal Distribution
68% of individuals
95% of individuals
>99% of individuals
-3 SD
-2 SD
-1 SD
Inferential Statistics
Based on Probability
Tests of significance: are observed differences
real differences or simply the result of chance
 t-test:
test difference between means of two groups
(t statistic)
(Analysis of Variance): test difference among
three of more independent groups (F statistic)
Interpreting p-values or
probability value
Used to decide whether the results observed are
likely to reflect real differences between groups
The standard is to use α = 0.05 or 5% (1 in20)
 t = 1.11, p =0.042
 t = 1.02, p = 0.051
Probability that results observed have occurred by
chance alone
α = probability of Type I error (finding statistical
significance when in reality there is none)
Parametric and Non-Parametric
Parametric = DV is some measured quantity
(ratio or interval) so it makes sense to calculate
means and SD
 You
can draw bell curves through the data defined
by two parameters…the mean and SD….hence
parametric (beside, near)
Non-Parametric = DV is count or rankings so
means and SD have no meaning (e.g. The
average religion of Americans is 2.67)
Parametric Tests
ANOVA (analysis of variance)
Linear Regression or Multiple Linear Regression
ANCOVA (analysis of covariance) – combines
regression and analysis of variance
Non-Parametric Tests
Logistic Regression
Log-linear analysis