### 统计代写|Generalized linear model代考广义线性模型代写|Describing Distribution Shapes: A Caveat

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|Generalized linear model代考广义线性模型代写|Frequency Polygons

Another alternative to the histogram is a box plot (also called a box-and-whisker plot), which is a visual model that shows how spread out or compact the scores in a dataset are. An example of a box plot is shown in Figure 3.21, which represents the age of the subjects in the Waite et al. (2015) study. In a box plot, there are two components: the box (which is the rectangle at the center of the figure) and the fences (which are the vertical lines extending from the box). The middle $50 \%$ of scores are represented by the box. For the subject age data from the Waite et al. (2015) dataset, the middle $50 \%$ of scores range from 21 to 31 , so the box shown in Figure $3.21$ extends from 21 to 31 . Inside the box is a horizontal line, which represents the score that is in the exact middle, which is 24 . The lower

fence extends from the bottom of the box to the minimum score (which is 18). The upper fence extends from the top of the box to the maximum score (which is 38 ).

The example in Figure $3.21$ shows some useful characteristics of box plots that are not always apparent in histograms. First, the box plot shows the exact middle of the scores. Second, the box plot shows how far the minimum and maximum scores are from the middle of the data. Finally, it is easy to see how spread out the compact the scores in a dataset are. Figure $3.21$ shows that the oldest subjects in the Waite et al. (2015) study are further from the middle of the dataset than the youngest subjects are. This is apparent because the upper fence is much longer than the lower fence-indicating that the maximum score is much further from the middle $50 \%$ of scores than the minimum score is.
Like frequency polygons, box plots have the advantage of being useful for displaying multiple variables in the same picture. This is done by displaying box plots side by side. Formatting multiple box plots in the same figure makes it easy to determine which variable(s) have higher means and wider ranges of scores.

## 统计代写|Generalized linear model代考广义线性模型代写|Stem-and-Leaf Plots

Another visual model that some people use to display their data is the stem-and-leaf plot, an example of which is shown on the right side of Figure 3.23. This figure shows the age of the subjects from Table 3.1. The left column is the tens place (e.g., the 2 in the number 20 ), and the other columns represent the ones place (e.g., the 0 in the number 20) of each person’s age. Each digit on the right side of the visual model represents a single person. To read an individual’s score, you take the number in the left column and combine it with a number on the other side of the graph. For example, the youngest person in this sample was 18 years old, as shown by the 1 in the left column and the 8 on the right side of the model. The next youngest person was 19 years old (as represented by the 1 in the left column and the 9 in the same row on the right side of the visual model). The stem-and-leaf also shows that seven people were between 20 and 25 years old and that the oldest person was 38 years old. In a way, this stemand-leaf plot resembles a histogram that has been turned on its side, with each interval 10 years wide.

Stem-and-leaf plots can be convenient, but, compared to histograms, they have limitations. Large datasets can result in stem-and-leaf plots that are cumbersome and hard to read. They can also be problematic if scores for a variable span a wide range of values (e.g., some scores in single digits and other scores in double or triple digits) or precisely measured variables where a large number of subjects have scores that are decimals or fractions.

Before personal computers were widespread, stem-and-leaf plots were more common because they were easy to create on a typewriter. As computer software was created that was capable of generating histograms, frequency polygons, and box plots automatically, stem-and-leaf plots gradually lost popularity. Still, they occasionally show up in modern social science research articles (e.g., Acar, Sen, \& Cayirdag, 2016, p. 89; Linn, Graue, \& Sanders, 1990, p. 9; Paek, Abdulla, \& Cramond, 2016, p. 125).

## 统计代写|Generalized linear model代考广义线性模型代写|Line Graphs

Another common visual model for quantitative data is the line graph. Like a frequency polygon, line graphs are created by using straight-line segments to connect data points to one another. However, a line graph does not have to represent continuous values of a single variable (as in a frequency polygon and histogram) or begin and end with a frequency of zero. Line graphs can also be used to show trends and differences across time or across nominal or ordinal categories.

Since their invention over 200 years ago, line graphs have been recognized as being extremely useful for showing trends over time (Friendly \& Denis, 2005). When using it for this purpose, the creator of the line graph should use the horizontal axis to indicate time and the vertical axis to indicate the value of the variable being graphed. An example of this type of line graph is shown in Figure 3.24, which shows the murder rates in the five most populous Canadian provinces over the course of 5 years. Line graphs are also occasionally used to illustrate differences among categories or to display several variables at once. The latter purpose is common for line graphs because bar graphs and histograms can get too messy and complex when displaying more than one variable.

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## MATLAB代写

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