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Basic Statistical Review

This detailed review focuses on fundamental statistical concepts critical for intermediate statistics, covering key terms such as sample, population, and parameter distinctions. It explores measurement scales, variable types, and various descriptive statistics, including measures of central tendency and variability. Additionally, it explains inferential statistics, probability, hypothesis testing, and essential graphing techniques. By learning about these concepts, students can enhance their understanding of data analysis, improve their research skills, and apply statistical methods accurately across various disciplines.

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Basic Statistical Review

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

  2. The Decision Tree

  3. 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

  4. Measurement Scales

  5. Key Terms • Variables • Categorical (Nominal – Ordinal) • Discrete • Qualitative • Frequency • Continuous (Interval – Ratio) • Quantitative • Measurement

  6. Key Terms • Independent (Predictor) Variable • Active (experimental) • Attribute (measured) • Dependent (Criterion) Variable • Extraneous Variable • Confounding • Third Variable

  7. Key Terms • Descriptive Statistics • Measures of Central Tendency • Mean, Median, Mode • Measures of Variability • Range, Standard Deviation, Variance • Inferential Statistics • Parametric • Nonparametric

  8. Frequency Distributions

  9. Graphing Data – Constructing a Graph

  10. Distorting DataThrough Graphing

  11. Bar Graphs (Categorical Data)

  12. Histograms (Continuous Data)

  13. Stem-and-Leaf Displays

  14. Boxplots

  15. 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

  16. Describing Distributions

  17. Describing Distributions

  18. Describing Distributions

  19. The Normal Distribution

  20. 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.

  21. 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

  22. Key Terms • Probability •  = Level of Significance • p = Probability (Sig.) • Confidence Intervals • Effect Size • d Family • r Family • Standard Scores • z • 

  23. Hypothesis Testing

  24. Non-Directional (two-tailed)

  25. Directional (one-tailed – negative end)

  26. Directional (one-tailed – positive end)

  27. 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

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