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- 1. Descriptive Statistics Notes from McMillan & Schumacher
- 2. Statistics â€¢ Methods of organizing and analyzing quantitative data â€¢ Tools designed to help researcher organize and interpret numbers derived from measuring a trait or variable â€¢ International language that only manipulates numbers â€¢ Numbers do not interpret themselves â€¢ Meaning derived from the research design
- 3. Categories of Statistics Descriptive and Inferential Descriptive Statistics â€¢ Summarize, organize, and reduce large numbers of observations to a few numbers â€¢ Describe or characterize the data â€¢ Assigning numbers to things in order to differentiate one thing from another
- 4. Inferential Statistics â€¢ Use to make inferences or predictions from the sample to the population â€¢ Depend on descriptive statistics â€¢ Estimation of population characteristics from sample â€¢ Experimental Designs â€“ True Experimental â€“ random assignment â€“ Quasi Experimental â€“ Pre-test/post-test, time series â€“ Single subject
- 5. Descriptive to Inferential Descriptive Statistics Of Sample Population Sample Estimate Population Based on Descriptive Statistics
- 6. Scales of Measurement Nominal â€“ Categories (sex, ethnicity, party) Ordinal â€“ Rank order (percentile norms) Interval â€“ Equal difference between #s Ratio â€“ Equal amounts from zero
- 7. Nominal Scale of Measurement â€¢ Nominal - Name â€¢ Categories and Classifications â€¢ Naming of mutually exclusive categories â€¢ People, events, phenomena â€¢ Eye color, gender, political party, group â€¢ No order or value implied â€¢ Assign number for coding - arbitrary â€¢ Numbers do not represent quantity or degree
- 8. Ordinal Scale of Measurement â€¢ Ordinal â€“ by ranked order â€¢ Categories rank-ordered from highest to lowest â€“ Equal = â€“ Greater than > â€“ Less than < â€¢ Ranking by grade point average, percentile, achievement test score, social class
- 9. Interval Scale of Measurement â€¢ Shares characteristics with ordinal â€¢ Equal intervals between each category â€¢ Equal difference between variables or attributes being measures â€¢ Constant unit of measurement â€¢ Difference between 5&6 = 18&19 â€¢ Year, Centigrade, Fahrenheit
- 10. Ratio Scale of Measurement â€¢ Most refined type of measurement â€¢ Ordinal and Interval â€¢ Numbers can be compared by ratios â€¢ Numbers represent equal amounts from absolute zero â€¢ Age, dollars, time, speed, class size â€¢ Most educational measurement â€“ not ratio
- 11. Graphic Portrayals of Data â€¢ Frequency Distribution â€“ f â€¢ Number of times each score was attained â€¢ Rank order and then tally â€¢ Show most/least occurring scores â€¢ General Shape of Distribution â€¢ Outliers
- 12. Histograms and Bar Graphs â€¢ Graphic way of representing frequency distribution â€¢ Histogram â€“ frequencies rank- ordered â€¢ Bar Graph â€“ order arbitrary
- 13. Frequency Polygon â€¢ Illustrates frequency distribution â€¢ Single points rather than bars are graphed â€¢ Normal curve â€“ curves the straight lines
- 14. Measures of Central Tendency â€¢ Mean â€“ â€“ arithmetic average of all scores â€¢ Median â€“ â€“ point which divides a rank-ordered distribution into halves that have an equal number of scores â€“ 50% above and 50% below â€¢ Mode â€“ score that occurs most frequently
- 15. Relationships among Measures of Central Tendency â€¢ Normal Distribution â€“ Mean, median, and mode about the same â€“ Bell shaped symmetrical curve â€“ Large numbers â€“ normal distribution â€¢ Skewed Distribution â€“ Positively skewed â€“ Most scores at low end â€“ Negatively skewed â€“ Most scores at high end â€“ Lower numbers distributed unevenly
- 16. Normal Distribution
- 17. Bell Curve â€“ Normal Distribution Mean = Median = Mode0 100 Normal curve â€“ theoretical distribution used to transform data and calculate many statistics
- 18. Positively Skewed Mode Mean Median0 100 Most of the scores are at the low end of the distribution
- 19. Negatively Skewed Mean Median Mode 0 100 Most of the scores are at the high end of the distribution
- 20. Measures of Variability â€¢ Shows how spread out the distribution of the scores is from the mean of the distribution â€“ dispersion of scores â€¢ How much, on average, does each score differ from the mean? â€¢ Variability measures â€“ Range â€“ highest and lowest (no mean) â€“ Standard Deviation â€“ numerical index indicating average variability of scores
- 21. Standard Deviation â€¢ Indicates the amount on average that the set of scores deviates from the mean
- 22. SD in Normal Distribution -1 SD0 100 34% 34% +1 SD 68% +1 SD = 84th percentile -1 SD = 16th percentile 50% below the mean 50% above the mean
- 23. Box and Whisker Plot â€¢ Use to give picture of variability â€¢ Size of rectangular box â€“ 25th to 75th percentiles â€¢ Whiskers draw from ends of box to 10th and 90th percentiles
- 24. Standard Scores â€¢ Makes it easier to analyze several distributions if means and standard deviations are different for each distribution â€¢ Raw scores converted to standard scores â€¢ Provide constant normative or relative meaning â€¢ Obtained from the mean and standard deviation of the raw score distribution
- 25. The Z-Score â€¢ Most basic standard score â€¢ Mean of 0 â€¢ Standard deviation of 1 â€¢ Z-score of +1 = 84th percentile â€¢ Z-score of â€“1 = 16th percentile â€¢ Example â€“ IQ tests 100 = mean 15/16 = standard deviation
- 26. Scatterplot â€¢ Graphic representation of relationship of variables â€¢ Relationships â€“ Positive â€“ Negative â€“ None â€“ Curvilinear
- 27. Correlation Coefficient â€¢ Calculated number representing the relationships between variables â€¢ Range from â€“1.00 to +1.00 â€¢ High Positive Relationship (.85 .90. 96) â€¢ Low Positive Relationship (.15 .20 . 08) - 1 +10 High negative High positive
- 28. Types of Correlation Coefficients â€¢ See Table 7.5 â€“ page 172 â€¢ Most common â€“ Pearson product-moment â€¢ r â€¢ Both continuous â€“ Spearman â€¢ rs â€¢ Both rank-ordered
- 29. Example of Correlation - SPSS

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