Basic Statistical Review EPS 625 – Intermediate Statistics Robert A. Horn, Ph.D.

The Decision Tree

Key Terms Sample Population Sampling 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 Inferential 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

Distorting Data Through Graphing

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

Key Terms Probability Confidence Intervals Effect Size Standard Scores  = Level of Significance p = Probability (Sig.) Confidence Intervals Effect Size 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 = .42 | = Single Space NOT t(9)=5.08,p<.05,d=1.61 F(2,57)=9.75,p<.01,2=.42