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Basic Statistical Review
EPS 625 – Intermediate Statistics
Robert A. Horn, Ph.D.
The Decision Tree
Type of Data
Qualitative
(Categorical Nominal)
Quantitative
(Ordinal and
Continuous)
Type of
Categorization
Type of Question
One Categorical
Variable
Two Categorical
Variables
Relationship
Differences
Chi-Square –
Goodness-of-Fit
Chi-Square –
Contingency
Table
Number of
Predictors
Number of
Groups
One
Multiple
Measurement
Multiple
Regression
Ordinal - Ranks
Continuous
Spearman’s Rho
Primary Interest
Degree of
Relationship
Form of
Relationship
Pearson’s
Correlation
Regression
Single
(One)
z Test
Single Sample
( Known)
t Test
Single Sample
( NOT Known)
Two
Multiple
Relation
Between
Samples
Relation
Between
Samples
Dependent
(Correlated)
Independent
Number of
Independent
Variables
Dependent
(Correlated)
Assumptions Met
Assumptions
NOT Met
Assumptions Met
Assumptions
NOT Met
Assumptions Met
Assumptions
NOT Met
DependentSamples t
Wilcoxon
IndependentSamples t
Mann-Whitney U
RepeatedMeasures
ANOVA
Friedman
One
Multiple
Assumptions Met
Assumptions
NOT Met
One-Way
ANOVA F Test
Kruskal-Wallis
Factorial ANOVA
Key Terms


Sample

Statistic

Representative of the population

Commonly symbolized with Roman Letters
Population



Parameter
Commonly symbolized with Greek Letters
Sampling


Random Sample
Random Assignment
Measurement Scales
Key Terms

Variables

Categorical (Nominal – Ordinal)




Discrete
Qualitative
Frequency
Continuous (Interval – Ratio)


Quantitative
Measurement
Key Terms

Independent (Predictor) Variable




Active (experimental)
Attribute (measured)
Dependent (Criterion) Variable
Extraneous Variable


Confounding
Third Variable
Key Terms

Descriptive Statistics

Measures of Central Tendency


Measures of Variability


Mean, Median, Mode
Range, Standard Deviation, Variance
Inferential Statistics


Parametric
Nonparametric
Frequency Distributions
Graphing Data –
Constructing a Graph
Y axis
Three-Quarter-High Rule
The height of the Y axis should
be approximately three-quarters
the length of the X axis.
Dependent Variable
(Frequencies)
X axis
Independent Variable
Origin = 0
Distorting Data
Through Graphing
15
14
14
13
12
13
11
10
9
8
12
Mean Preference
7
11
10
No
Good Housekeeping seal
Yes
6
5
4
3
2
1
0
No
Good Housekeeping seal
Yes
Bar Graphs
(Categorical Data)
Histograms
(Continuous Data)
Stem-and-Leaf Displays
Boxplots
Describing Distributions


Symmetric (Normal Distribution)
Modality


Skewness


Negative, Normal (Symmetrical), Positive
Kurtosis


Unimodal, Bi-Modal, Multi (tri)-Modal
Platykurtic, Mesokurtic (Normal), Leptokurtic
Linearity

Linear or Curvilinear
Describing Distributions
Describing Distributions
Describing Distributions
The Normal Distribution
Summation Notation ()



One of the most common symbols in statistics
is the uppercase Greek letter sigma, (),
which is the standard notation for
summation.
It is readily translated as “add up, or sum,
what follows.”
The general rule, which always applies, is to
perform operations within parentheses before
performing operations outside parentheses.
Common Statistical Symbols

X A Raw Score

X



s



s2

2
Mean of a Sample
Mean of a Population
Standard Deviation of a Sample
Standard Deviation of a Population
Variance of a Sample
Variance of a Population
Key Terms

Probability




Confidence Intervals
Effect Size



 = Level of Significance
p = Probability (Sig.)
d Family
r Family
Standard Scores


z

Hypothesis Testing
Non-Directional
(two-tailed)
Directional
(one-tailed – negative end)
Directional
(one-tailed – positive end)
Statistical Results and APA
t(9) = 5.08, p < .05, d = 1.61
F(2, 57) = 9.75, p < .01,
2

| = Single Space
NOT
t(9)=5.08,p<.05,d=1.61
F(2,57)=9.75,p<.01,2=.42
= .42