Basic Statistical Review

EPS 625 – Intermediate Statistics

Robert A. Horn, Ph.D.

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

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 Mean, Median, Mode

Measures of Variability Range, Standard Deviation, Variance

Inferential Statistics Parametric Nonparametric

Frequency Distributions

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.

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

Bar Graphs (Categorical Data)

Histograms (Continuous Data)

Stem-and-Leaf Displays

Boxplots

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

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 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

Key Terms Probability

= Level of Significance p = Probability (Sig.)

Confidence Intervals Effect Size

d Family r Family

Standard Scores z

Hypothesis Testing

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

Directional (one-tailed – negative end)

Region of Retention

Region of Rejection

p <

p >

Critical Value

Retain H0

Reject H0

Directional (one-tailed – positive end)

Region of Retention

Region of Rejection

p <

p >

Critical Value

Retain H0

Reject H0

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