basic statistical review eps 625 – intermediate statistics robert a. horn, ph.d
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Basic Statistical Review
EPS 625 – Intermediate Statistics
Robert A. Horn, Ph.D.
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The Decision TreeType of Data
Qualitative(Categorical -
Nominal)
Quantitative(Ordinal and Continuous)
Type of Categorization
One Categorical Variable
Two Categorical Variables
Chi-Square – Goodness-of-Fit
Chi-Square – Contingency
Table
Type of Question
Relationship Differences
Number of Predictors
One Multiple
Multiple Regression
Measurement
Ordinal - Ranks Continuous
Spearman’s Rho Primary Interest
Degree of Relationship
Form of Relationship
Pearson’s Correlation
Regression
Number of Groups
Single(One)
Multiple
z TestSingle Sample
( Known)
t TestSingle Sample
( NOT Known)
Relation Between Samples
Dependent(Correlated)
Number of Independent
Variables
Assumptions MetAssumptions
NOT MetOne Multiple
Assumptions MetAssumptions
NOT MetFactorial ANOVA
Two
Relation Between Samples
Dependent(Correlated)
Independent
Assumptions MetAssumptions
NOT MetAssumptions Met
Assumptions NOT Met
Dependent-Samples t
WilcoxonIndependent-
Samples tMann-Whitney U
Repeated-Measures ANOVA
Friedman
One-Way ANOVA F Test
Kruskal-Wallis
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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
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Measurement Scales
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Key Terms Variables
Categorical (Nominal – Ordinal) Discrete Qualitative Frequency
Continuous (Interval – Ratio) Quantitative Measurement
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Key Terms Independent (Predictor) Variable
Active (experimental) Attribute (measured)
Dependent (Criterion) Variable Extraneous Variable
Confounding Third Variable
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Key Terms Descriptive Statistics
Measures of Central Tendency Mean, Median, Mode
Measures of Variability Range, Standard Deviation, Variance
Inferential Statistics Parametric Nonparametric
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Frequency Distributions
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Graphing Data – Constructing a Graph
Y axis
X axis
Origin = 0Independent Variable
Dependent Variable(Frequencies)
ThreeThree--QuarterQuarter--High RuleHigh RuleThe height of the Y axis shouldbe approximately three-quarters
the length of the X axis.
Y axis
X axis
Origin = 0Independent Variable
Dependent Variable(Frequencies)
ThreeThree--QuarterQuarter--High RuleHigh RuleThe height of the Y axis shouldbe approximately three-quarters
the length of the X axis.
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Distorting DataThrough Graphing
Good Housekeeping seal
YesNo
Mean P
refe
rence
15
14
13
12
11
10
9
8
7
6
5
4
3
2
10
Good Housekeeping seal
YesNo
Mean P
refe
rence
14
13
12
11
10
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Bar Graphs (Categorical Data)
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Histograms (Continuous Data)
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Stem-and-Leaf Displays
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Boxplots
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Describing Distributions Symmetric (Normal Distribution) Modality
Unimodal, Bi-Modal, Multi (tri)-Modal Skewness
Negative, Normal (Symmetrical), Positive Kurtosis
Platykurtic, Mesokurtic (Normal), Leptokurtic Linearity
Linear or Curvilinear
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Describing Distributions
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Describing Distributions
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Describing Distributions
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The Normal Distribution
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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.
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Common Statistical Symbols X A Raw Score Mean of a Sample Mean of a Population s Standard Deviation of a Sample Standard Deviation of a
Population s 2 Variance of a Sample 2 Variance of a Population
X
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Key Terms Probability
= Level of Significance p = Probability (Sig.)
Confidence Intervals Effect Size
d Family r Family
Standard Scores z
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Hypothesis Testing
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Non-Directional (two-tailed)
R egion of R etention
R egion of R ejectionR egion of R ejection
p < p <
p >
Critica l Value Critica l Value
Retain H 0
Reject H 0 Reject H 0
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Directional (one-tailed – negative end)
Region of Retention
Region of Rejection
p <
p >
Critical Value
Retain H0
Reject H0
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Directional (one-tailed – positive end)
Region of Retention
Region of Rejection
p <
p >
Critical Value
Retain H0
Reject H0
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Statistical Results and APA
t(9) = 5.08, p < .05, d = 1.61
| = Single Space
NOT
t(9)=5.08,p<.05,d=1.61F(2,57)=9.75,p<.01,2=.42
F(2, 57) = 9.75, p < .01, 2 = .42