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 2019/4/16 Week 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 2019/4/16 Week 2

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) 2019/4/16 Week 2

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!! 2019/4/16 Week 2

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 2019/4/16 Week 2

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 2019/4/16 Week 2

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. 2019/4/16 Week 2

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. 2019/4/16 Week 2

Organizing the Data III Qualitative data － Nominal scales Quantitative data － Ordinal, interval, and ratio scales 2019/4/16 Week 2

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. 2019/4/16 Week 2

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 2019/4/16 Week 2

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. 2019/4/16 Week 2

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. 2019/4/16 Week 2

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 2019/4/16 Week 2

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 2019/4/16 Week 2

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. 2019/4/16 Week 2

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. 2019/4/16 Week 2