1 / 38

Topics: Descriptive Statistics

Topics: Descriptive Statistics. A road map Examining data through frequency distributions Measures of central tendency Measures of variability The normal curve Standard scores and the standard normal distribution. The Role of Description. Description as a purpose of research

katima
Download Presentation

Topics: Descriptive Statistics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Topics: Descriptive Statistics • A road map • Examining data through frequency distributions • Measures of central tendency • Measures of variability • The normal curve • Standard scores and the standard normal distribution

  2. The Role of Description • Description as a purpose of research • Choosing the right statistical procedures

  3. Raw Data: Overachievement Study

  4. Frequency Distributions • A method of summarizing and highlighting aspects of the data in a data matrix, showing the frequency with which each value occurs. • Numerical Representations: a tabular arrangement of scores • Graphical Representations: a pictorial arrangement of scores

  5. Numerical Frequency Distributions • Ungrouped Frequency Distributions • Grouped Frequency Distributions • Relative Frequency Distributions • Cumulative Frequency Distributions

  6. Tabular Frequency Distributions Single-Variable (“Univariate”)

  7. Frequency Distribution: Major MAJOR Valid Cum Value Label Value Frequency Percent Percent Percent PHYSICS 1.00 5 12.5 12.5 12.5 CHEMISTRY 2.00 4 10.0 10.0 22.5 BIOLOGY 3.00 7 17.5 17.5 40.0 ENGINEERING 4.00 5 12.5 12.5 52.5 ANTHROPOLOGY 5.00 5 12.5 12.5 65.0 SOCIOLOGY 6.00 4 10.0 10.0 75.0 ENGLISH 7.00 7 17.5 17.5 92.5 DESIGN 8.00 3 7.5 7.5 100.0 ------- ------- ------- Total 40 100.0 100.0 Valid cases 40 Missing cases 0

  8. Frequency Distribution: Major Group MAJORGRP Valid Cum Value Label Value Frequency Percent Percent SCIENCE & ENGINEERIN 1.00 21 52.5 52.5 52.5 SOCIAL SCIENCE 2.00 9 22.5 22.5 75.0 HUMANITIES 3.00 10 25.0 25.0 100.0 ------- ------- ------- Total 40 100.0 100.0

  9. Frequency Distribution: SAT SAT Valid Cum Value Frequency Percent Percent 1000.00 2 5.0 5.0 5.0 1025.00 1 2.5 2.5 7.5 1050.00 2 5.0 5.0 12.5 1060.00 1 2.5 2.5 15.0 1075.00 1 2.5 2.5 17.5 1080.00 1 2.5 2.5 20.0 1085.00 1 2.5 2.5 22.5 1090.00 2 5.0 5.0 27.5 1100.00 7 17.5 17.5 45.0 1120.00 2 5.0 5.0 50.0 1125.00 3 7.5 7.5 57.5 1130.00 1 2.5 2.5 60.0 1150.00 5 12.5 12.5 72.5 1160.00 2 5.0 5.0 77.5 1175.00 3 7.5 7.5 85.0 1185.00 1 2.5 2.5 87.5 1200.00 5 12.5 12.5 100.0 ------- ------- ------- Total 40 100.0 100.0 Valid cases 40 Missing cases 0

  10. Grouped Frequency Distribution: SAT

  11. Graphical Frequency Distributions • Bar Graphs • Histograms • Stem and Leaf • Frequency Polygons • Pie Chart

  12. Graphical Frequency Distributions:Single-Variable (“Univariate”)

  13. Bar Chart: Major

  14. Histogram: SAT(From Grouped Data)

  15. Frequency Polygon Overlay: SAT(From Grouped Data)

  16. Frequency Polygon: SAT(From Grouped Data)

  17. Frequency Polygon: SAT Scores(From Ungrouped Data)

  18. Cumulative Frequency Polygon: SAT Scores

  19. Stem and Leaf: SAT

  20. Stem and Leaf: SAT SAT Stem-and-Leaf Plot Frequency Stem & Leaf 3.00 10 . 002 8.00 10 . 55678899 13.00 11 . 0000000222223 11.00 11 . 55555667778 5.00 12 . 00000 Stem width: 100.00 Each leaf: 1 case(s)

  21. Graphical Frequency Distributions Two-Variable (“Joint” or “Bivariate”)

  22. Relative Frequency Polygon: GPAComparison of Majors

  23. Relative Frequency Polygon: GPA Comparison of Gender

  24. What Can Be Seen in Frequency Distributions • Shape • Central Tendency • Variability

  25. Shapes of Frequency Polygons

  26. Shapes of Distributions

  27. Descriptive Statistics • Central Tendency • Mode • Median • Mean • Variability • Range • Standard Deviation • Variance

  28. Definitions: Measures of Central Tendency • Mean: • “Arithmetic mean” • “Center of gravity” such that the “weight” of the scores above the mean exactly balances the “weight” of the scores below the mean • Median: • The number that lies at the midpoint of the distribution of scores; divides the distribution into two equal halves • Mode: • Most frequently occurring score

  29. Mean, Median, Mode:SAT Scores by Gender

  30. Mean, Median, Mode:SAT Scores by Area

  31. Relative Position of Mode, Median, and Mean

  32. Definitions:Measures of Variability • Range: • Difference between highest and lowest score • Inter-quartile Range: • The spread of the middle 50% of the scores • The difference between the top 25% (Upper Quartile-Q3) and the lower 25% (Lower Quartile-Q1) • Standard Deviation: • The average dispersion or deviation of scores around the mean (measured in original score units) • Variance: • The average variability of scores (measured in squared units of the original scores (square of the standard deviation)

  33. Range, Interquartile Range, and Standard Deviation: SAT Scores by Area

  34. Range, Interquartile Range, and Standard Deviation: SAT Scores by Gender

  35. Properties of Normal Distribution • Bell-shaped (unimodal) • Symmetric about the mean • Mode, median, and mean are equal (though rarely occurs) • Asymptotic (curve never touches the abscissa)

  36. Normal Curve Areas Under the Curve .3413 .3413 .1359 .1359 68% .0214 .0214 95% .0013 .0013 99% -3s -2s -1s +1s +2s +3s X

  37. Definitions: Standard Scores • Standard Scores: scores expressed as SD away from the mean (z-scores) • Obtained by finding how far a score is above or below the mean and dividing that difference by the SD • Changes mean to 0 and SD to 1, but does not change the shape (called Standard Normal Distribution)

  38. Uses of Standard Normal Distribution • What proportion of scores falls between the mean and a given raw score • What proportion of scores falls above or below a given raw score • What proportion of scores falls between two raw scores • What raw score fall above (or below) a certain percentage of scores

More Related