This chapter discusses data exploration techniques including preparing data for analysis through data reduction, coding, and descriptive statistics. Graphic and descriptive techniques are used to summarize and describe data numerically and graphically. Common graphs discussed are frequency distributions, scatterplots, line graphs, bar graphs, and box-and-whisker plots which can show relationships between variables and the distribution of data. Checks for invalid, missing, and outlier data are recommended before conducting inferential statistical analyses.

1. Research Methods, 9th Edition
Theresa L. White and Donald H. McBurney
Chapter 14
Data Exploration Part 1: Graphic
and Descriptive Techniques

2. Preparing Data for Analysis
 Once the data is collected:
 Put the data into a summary data sheet.
 Do preliminary statistics and plots.
 Check for invalid data
 Check for missing data
 Check for wild data
 Describe data numerically.
 Describe data graphically.
 Perform inferential statistics.

3. Data Reduction
 Process of transcribing data from individual
data sheets to a summary form or data file.

4. Data Reduction
 謄錄到資料表
 Contain all the data in a matrix format
 Rows indicated subjects
 Columns indicate variables
 上頁案例 :
 某一教授開設 ES 課程，有兩個班級，分別是
早上 8 點、 11 點上課，他每門課考了 2 次考試
，每次考試總分為 20 分。他要分析這兩個班級
考試成績差異。

5. Coding Guide
 List that specifies the variables of the study,
columns that the variables occupy in the data
file, and their possible values.
 Located either on summary form, in notebook,
or both!

6. 建立 料 —法資 檔 1 直接在 SPSS
建立
 案例
雲林科技大學 SPSS 研習營

8. 料資 編碼
 答案 成 字或其他符將 轉換 數 號，以利分析
 常 受 者回 可分成有限的將 訪 應 類別 ( 分類 )
 分類是指根 某 ， 一 料分成據 項變數 將 組資 幾個
部分，亦即 用 分 料的程序運 規則區 資
 分 可能 牲某些 料 ， 也能提升 料類 犧 資 細節 卻 資
分析效率
 封 式、 放式 卷皆閉 開 問 須編碼

9. 表編碼 (codebook) 設計
 表也編碼 稱為 架編碼 構 (coding scheme)
 包含每 研究 ， 描述如何 用 於個 變數 並 應 編碼規則 變數
上。
 研究者利用 表，使 料 入更精 、更有效率編碼 資 輸 確
 表也可包含各 料在 料 中位置編碼 變數資 資 檔
 是否 化， 表 包含無論 電腦 編碼 應 卷 、 名問 題號 變數 稱
、 在 入媒 中（變數 輸 體 SPSS 料 、資 檔 EXCEL ）所
位、各 描述、各 述、 料 料 型佔欄 選項 問題敘 資 資 類 （
字或字串）數
 可 表是否正預試 檢測編碼 確

10. 表 例編碼 範
雲林科技大學 SPSS 研習營
Data source: http://metaconnects.org/survey-analysis

11. 編碼表範例編碼表範例

13. 雲林科技大學 SPSS 研習營

14. 統計分類
 Descriptive statistics
 Summarize a set of data
 Inferential statistics
 Help us to draw conclusions about populations

15. Descriptive statistics
 常用的敘述統計量 :
 Average (measures of central tendency)
 Variability (measure of variability)

16. Measures of Central Tendency
Descriptive statistic that is the average of the
distribution.
 Mode = Most common score
 Median = Middlemost score
 Mean = Sum of all the scores divided by
the number of scores.

17. Measures of Central Tendency
 中位數
 不受到其他值與中位數之差距，只在乎高於、
低於中位數之個數
 平均數
 對於極端質敏感

18. Measures of Variability
 Range
 Highest score – Lowest score
 Percentile
 Score below which a certain number of cases in a
distribution fall
 Interquartile Range
 75th
percentile – 25th
percentile
 Q3 – Q1
 Semi-interquartile range
 (Q3 – Q1)/2

19. Measures of Variability

20. Measures of Variability
 值域
 高度不穩定
 由兩個極端值決定
 標準差
 也容易受到 outlier 影響
 變異數、標準差…最常用

21. Most Common Measures of
Variability
 Variance
 Average of the squared deviations from the
mean.

 Standard Deviation
 Square root of the variance.

22. Tables
Table: a display of data in a matrix format

23. Graphs
Graph: a representation of data by spatial relationships in a
diagram

24. Table, Graph
 Help us summarize data and understand the
relationships between variables.
 A picture is worth a thousand words
 表 :
 水平軸— X 軸，常呈現自變數值
 垂直軸— Y 軸，常呈現依變數值

25. Frequency Table
 The professor wants to see how many people
earned each test score.

26. Frequency Distribution
 Graph that shows how many scores fall into
particular bins, or divisions of the variable
Histogram

27. Frequency Distribution
Frequency Polygon
 A frequency distribution in which the
frequencies are connected by straight lines

28. The Shape of Distributions
Normal Negative
Skew
Positive
Skew
 前一頁是哪一型 ?

29. The Shape of Distributions
 前一頁圖
 A
 mode = median=mean
 B (left skew)
 mode __ median__mean
 C (right skew)
 mode __ median__mean

30. Cumulative Frequency Distribution
a = Normal Curve
b = Positively Skewed
c = Negatively Skewed
 A frequency distribution that
shows the number if scores
that fall at or below a certain
score

31. Scattergram
 A graph showing the responses of a
number of individuals on two variables;
visual display of correlational data

32. Scattergram
 Often used with correlation coefficient
 A correlation is a statistic indicating the
strength of the relationship between two
variables
 Prediction of one of the variables can be
achieved with regression

33. Correlation Coefficient
 Measures strength of association between variables.
 Does NOT indicate causation
 Most commonly used is Pearson’s r
 Value is between – 1.0 and +1.0
Scattergram of Paired Values of x and y; (a) r = +1.00, (b) r=−1.00, (c) r = 0.50, (d) r = 0, and (e) r = 0

34. Correlation Coefficient
 Correlation
 Less than 0.2: weak
 0.2-0.4: moderately weak
 0.4-0.6: moderate
 0.6-0.8: moderately strong
 0.8-1: strong
 Pearson correlation coefficient is a measure of a linear
(straight-line) function.
 It can not reflect the curvilinear relationship

35. Regression
 Predicting the value of one variable from
another from the equation for a line
 Slope of the line (m) reflects
 Correlation
 Scale of measurement for the two variables
 Squaring the correlation (determination
coefficient) yields a goodness of fit measure

36. Regression
 determination coefficient
 The proportion of the variability in y that is
accounted by x

37. Line Graph
 A graphical representation using lines to show
relationships between quantitative variables
 Y-axis is the dependent variable
 X-axis is the independent variable

38. Bar Graph
 Used to represent categorical data

39. Frequency Data and Graphs
Test Score as a Function of Class Membership
Frequency Distribution of Test Scores by
Class Membership

40. Time Series Graph
 X-axis represents the passage of time
Time-Series Graph Cumulative Record

41. Indicating Variability
 Error Bars
 Vertical lines above and below each point or
bar on a graph that show +/- one standard
deviation from the mean.

42. Box and Whisker Plot
 Graph based on median and percentiles rather than mean
and standard deviation.

43. Box and Whisker Plot
 Data source:
http://www.bbc.co.uk/schools/gcsebitesize/maths/statistics/repre
sentingdata3hirev6.shtml

44. Checking for Problem Data
 Invalid Data
 Outside the range of possible values
 Find and correct
 Missing Data
 Empty cells
 If necessary, replace with code
 Outliers
 Possible, but improbable answers
 Check to see if they are different enough to
remove

45. Style Guide for Figures
 Be clear
 Use black ink
 Label both axes
 Label units of measurement
 Provide a caption for the figure
 Beware of chartjunk (parts that aren’t
necessary to understand the chart)