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Simple Boxplot: Comparing Variability of a Continuous Variable by Discrete Categories, Summaries of Statistics

Instructions on how to build a Simple Boxplot using SPSS software to compare the variability of a continuous variable (score on final exam) among different categories of a discrete variable (hour of class). The document also discusses the purpose of the graph and how it can be used for data exploration and hypothesis testing.

Typology: Summaries

2021/2022

Uploaded on 09/12/2022

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11
Simple Boxplot
PURPOSE OF GR APHS YOU ARE ABOUT TO BUILD
To compare the variability of a continuous variable categorized by a discrete variable
« 
11.1 introduction to the Simple Boxplot
First, we advise you not to be misled by what we consider to be a confusing
name especially when this graph is compared with the 1-D boxplot described
in the previous chapter. The simple boxplot discussed in this chapter is not
as “simple” as the 1-D boxplot. The simple boxplot is not more difficult to
build; however, it does convey considerably more information making it
much more complex than the 1-D boxplot.
The simple boxplot displays the same five statistics as you did in the
previous chapter (minimum, first quartile, median value, third quartile, and
maximum value). Recall that these statistics were calculated for a single con-
tinuous variable. In that chapter, we used a single continuous variable, but
the simple boxplot takes it a step beyond. The simple boxplot displays the
same five statistics but separates the continuous variable into the several
categories of a discrete variable. For an example of the simple boxplot, look
at Figure 11.1 that uses data describing 1,050 students in terms of test perfor-
mance (score on final exam) and hour of their class.
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Simple B oxplot

PURPOSE OF GRAPHS YOU ARE ABOUT TO BUILD

  • • To compare the variability of a continuous variable categorized by a discrete variable « 11.1^ introduction^ to^ the^ S^ imple^ B^ oxplot First, we advise you not to be misled by what we consider to be a confusing name especially when this graph is compared with the 1-D boxplot described in the previous chapter. The simple boxplot discussed in this chapter is not as “simple” as the 1-D boxplot. The simple boxplot is not more difficult to build; however, it does convey considerably more information making it much more complex than the 1-D boxplot. The simple boxplot displays the same five statistics as you did in the previous chapter (minimum, first quartile, median value, third quartile, and maximum value). Recall that these statistics were calculated for a single con- tinuous variable. In that chapter, we used a single continuous variable, but the simple boxplot takes it a step beyond. The simple boxplot displays the same five statistics but separates the continuous variable into the several categories of a discrete variable. For an example of the simple boxplot, look at Figure 11.1 that uses data describing 1,050 students in terms of test perfor- mance (score on final exam) and hour of their class.

chapter 11 Simple B oxplot 201

The authors have chosen the default vertical orientation for this graph. You see a discrete variable with its nine categories (hour of class) displayed on the horizontal axis. The continuous variable is score on the final exam (vertical axis), which ranges from 0 to 125. The - 5 value on the vertical axis represents a graph-editing procedure to eliminate the lower whiskers from landing directly on the horizontal axis. We can assure you that the professor did not issue minus points on the exams. Figure 11.1 shows nine separate box and whisker plots, each giving the same statistics as the 1-D boxplot in the previous chapter. In this figure, you see our information bubbles giving the values for just one of the nine catego- ries of this variable. For the 0800 hour (8 a.m.) class students scored between 0 and 115 points. The middle 50% scored between 55 and 95 points; thus, the interquartile range is 40 points (95 – 55). The median value for the entire grade distribution of the 0800 hour class is 76. We can say that the lowest scoring 25% earned between 0 and 55 points, while the highest scoring 25% earned between 95 and 115. Remember that the statistics given in the preceding paragraph are for only one class time. By carefully reading the graph, you have these same statistics for all nine class times. The major purpose of this graph is to permit a convenient way to visually compare all nine class times on these five statistics Figure 11.1 Simple Boxplot Displaying a Continuous (Scores) and Discrete (Time) Variable

chapter 11 Simple B oxplot 203

11.3 uSing SpSS to B uild the S imple B oxplot (^) « In this section, you will build the basic simple boxplot and then use the Chart Editor to make one similar in appearance to the graph shown in Figure 11.1.

  • • Open 1991 U.S. General Social Survey.sav (found in the SPSS Sample files).
  • • Click Graphs , then click Chart Builder to open Chart Builder window.
  • • Click Boxplot , click and drag the Simple Boxplot (the first icon) to the Chart preview panel.
  • • Click and drag Race of Respondent to the X-Axis box.
  • • Click and drag Age of Respondent to the Y-Axis box.
  • • Click OK (the basic graph now appears in the Output Viewer ).
  • • Double click the graph to open the Chart Editor.
  • • Click any number on the y -axis.
  • • In the Properties window, click the Scale tab , then in the Range panel, change Major Increment to 10.
  • • Click Apply.
  • • Click the Show Grid Lines icon (the fifth icon from the right).
  • • In the Properties window, click the Lines tab , and in the Lines panel, click the black arrow beneath Weight and click 0.25 , then click the black arrow beneath Style then click the first dotted line.
  • • Click Apply.
  • • Click on any whisker of a boxplot (a faint line appears around all whiskers).
  • • If Properties window is not open, click the Properties Window icon.
  • • In the Properties window, click the Lines tab , and in the Lines panel, click the black arrow beneath Weight , then click 2.
  • • Click Apply.
  • • Click any boxplot box (a faint frame appears around all boxes).
  • • In the Properties window, make sure that the Fill & Border tab is highlighted.
  • • In the Color panel, click the white rectangular box.
  • • In the Color panel, click the black arrow beneath Pattern , and click the first pattern in the second row.
  • • Click Apply.
  • • Click the X in the upper right-hand corner of the Chart Editor (graph is moved to the Output Viewer ).

204 Building SpSS graphS to underStand data

  • • Click the graph (a frame appears around the graph), and then click and grab the lower right corner of the frame (marked by a small black square), hover the mouse pointer until you see a double- headed arrow , and move it diagonally up and to the left to reach the approximate size of the graph in Figure 11.2. Figure 11.2 Simple Boxplot for a Discrete (Race) and Continuous (Age) Variable « 11.4^ interpretation^ of^ the^ S^ imple^ B^ oxplot This section repeats those questions presented earlier (Section 11.2.1) but this time with the answers provided by the information presented in the graph just built. 11.4.1 Questions and Answers for the Simple Boxplot The information to answer the following questions may be found in Figure 11.2.
  1. What are the median ages, ranked from lowest to highest, for the three race categories? The youngest median age of 36 years is for the “Other” race category, next is for “Black” at 39, and finally, the oldest median age is for the “White” category at 42.

206 Building SpSS graphS to underStand data

Figure 11.3 Review Exercise: Simple Boxplot for Degrees Centigrade and Alloy Figure 11.4 Review Exercises: Simple Boxplot for Resale Value and Vehicle Type

  1. Open car_sales.sav and select the discrete variable named type and labeled Vehicle type. The continuous variable is named resale and labeled 4-year resale value. Build the simple boxplot as in Figure 11.4 and answer the following questions. Questions: (a) Which distribution approximates the normal distribu- tion? ( b) Which of the two distributions has the highest median resale value and what is this value? (c) What are the highest resale values for trucks and automobiles when outliers and extremes are excluded? (d) What is the inter- quartile range for automobiles? (e) What are the minimum and maximum values for the resale value of the middle 50% of the trucks?

chapter 11 Simple B oxplot 207

Figure 11.5 Review Exercises: Simple Boxplot for Current Salary and Gender

  1. Open Employee data.sav , and select gender as the discrete variable. Select the continuous variable named Salary and labeled Current salary. Build the simple boxplot in Figure 11.5 and answer the following questions. Questions: (a) What is the value of the most extreme value in the male salary distribution? ( b) What is the most extreme salary for the females? (c) If you exclude the outliers and extremes, what are the highest and lowest salaries for the males? (d) Excluding the outliers and extremes, what are the high and low salaries for females? (e) What are the median salaries for males and females?
  2. Open credit_card.sav from the SPSS Sample file, and select Type of transaction as the discrete variable. Select the continuous variable named spent and labeled Amount spent. Build the simple boxplot in Figure 11.6 and answer the following questions. Questions: (a) What type of transaction has the largest interquartile range, and what is that value? ( b) Which type of transaction recorded the highest expenditure as measured by the median, and what was that amount? (c) Which type of transaction recorded the highest expenditure, and what

chapter 11 Simple B oxplot 209

Figure 11.7 Review Exercise: Simple Boxplot for Amount Spent and Gender