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Exploratory Data Analysis, Frequency Distributions and Percentiles

將地方圖案插入此投影片 選取 〔 插入 〕 功能表 〔 圖片 〕 指令 選取 〔 從檔案 〕 指令 選取你的標幟圖片檔案 按下 〔 確定 〕 調整標幟圖案大小 於標幟圖案內任意一處按一下 . 出現在標幟圖案外的白色小方塊即為可調整邊框 運用此法來調整物件大小 如果你在使用調整邊框之前按住 Ctrl 鍵，將維持你想調整之物件比例. Exploratory Data Analysis, Frequency Distributions and Percentiles. Statistics. The Data.

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Exploratory Data Analysis, Frequency Distributions and Percentiles

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  1. 將地方圖案插入此投影片 • 選取〔插入〕功能表 〔圖片〕指令 • 選取〔從檔案〕指令 • 選取你的標幟圖片檔案 • 按下〔確定〕 • 調整標幟圖案大小 • 於標幟圖案內任意一處按一下.出現在標幟圖案外的白色小方塊即為可調整邊框 • 運用此法來調整物件大小 • 如果你在使用調整邊框之前按住Ctrl 鍵，將維持你想調整之物件比例 Exploratory Data Analysis, Frequency Distributions and Percentiles Statistics Week 2

  2. The Data 5 20 6 19 18 17 7 8 16 15 17 8 15 14 10 11 15 11 12 14 15 13 12 11 11 12 13 11 10 9 Week 2

  3. Exploratory Data Analysis • A set of procedures for arranging and displaying numbers that allow the researcher to quickly organize, summarize, and interpret data collected from a research project. • Perhaps the most basic thing I have to say is…look at the data. Always, always plot up the data to see what the number say (Robert Bolles 1988, p. 83) Week 2

  4. Exploratory Data Analysis • You should always look at data to see what trends and patterns are evident. • Some statistics can be misleading. • REMEMBER－Garbage in, garbage out!! Week 2

  5. Goals of EDA • Organization, summarization, and interpretation • To know the characteristics of the data researchers collect • Measures of central tendency－The value or values that best represent the entire data set. • Measures of dispersion－how spread out or dispersed the data are. • The shape of the distribution • Relation between variables Week 2

  6. Exploratory data analysis can never be the whole story, but nothing else can serve as the foundation stone－－as the first step John Tukey 1977, p3 Week 2

  7. Organizing the Data I • First－Order the data • Stem-and-Leaf Plots • A graphical means of organizing data that allows for exploration of the data and its distribution while retaining the information of the original scores. Week 2

  8. Organizing the Data II • Frequency Distributions－ An organized set of numbers representing the frequency of observations that fall within a specific category or class of a variable. • Class － a mutually exclusive and nominal category that represents elements or subjects that share a common characteristic. Week 2

  9. Organizing the Data III • Qualitative data － Nominal scales • Quantitative data － Ordinal, interval, and ratio scales Week 2

  10. Organizing the Data IV • To know the relative position of the score (value of variable) • Percentile rank－the percentage of cases in a comparison group that achieve a score at or below a given score • Cumulative frequency－The total number of scores in a frequency distribution that are within and below a specified class. Week 2

  11. Organizing the Data V • Class width－The size of a class as determined by the difference between its upper and lower real limits. • Midpoint of a class－The number in the middle of the real limits of a class. • This number is considered to best represent the numbers in the class Week 2

  12. Grouped Frequency Distributions • A frequency distribution in which the values of the variable have been grouped into classes. • To make computation easier • To make the display more comprehensible • Loss information • How many classes should I have? • Based on your own decisions and on how you want to interpret the data. Week 2

  13. Creating the classes • Find the difference between the highest and the lowest scores and add 1 to obtain the total number of possible score values. • Divide this figure by the number of classes you want to use and round to a whole number. W • Add (W-1) to the minimum value of the lowest class to obtain the maximum score of the lowest class. • The nest higher class begins at the integer following the maximum score of the lower class. • Assign each obtained score to the class within which it is included. Week 2

  14. The Shape of Distribution I • Frequency histogram—A form of bar graph used with interval or ratio-scaled frequency. • Used only for interval and ratio scales • Each point on the graph represents the midpoint of the class. • Use odd numbers to set the class width Week 2

  15. The Shape of Distribution II • Normal distribution—A hypothetical frequency distribution with a characteristic bell-shaped form in which a large portion of scores is at or near the midpoint of the distribution. Skew Week 2

  16. The Shape of Distribution III • Kurtosis—The degree to which scores are clustered about one common area of a distribution or spread throughout the distribution. • Lepotkurtic refers to distributions where the scores are clustered close to a common point. • Platykurtic referst to a distribution where the scores are spread across the distribution. • Mesokurtic refers to a normally distributed set of data. Week 2

  17. The Shape of Distribution IV • Skew – The relative symmetry of a distribution of scores. • Positive skew refers to a distribution where the scores are clustered at the lower end of the scale, with a tail of scores at the upper end of the distribution. • Negative skew refers to a distribution where the scores are clustered at the upper end of the scale, with a tail of scores at the lower end of the distribution. Week 2

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