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© 2008 McGraw-Hill Higher Education The Statistical Imagination Chapter 3. Charts and Graphs: A Picture Says a Thousand Words

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© 2008 McGraw-Hill Higher Education Graphs and Charts: Pictorial Presentation of Data Graphs and charts provide a direct sense of proportion With graphics, visible spatial features substitute for abstract numbers

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© 2008 McGraw-Hill Higher Education Types of Graphs and Levels of Measurement For nominal/ordinal variables, use pie charts and bar charts For interval/ratio variables, use histograms and polygons (line graphs)

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© 2008 McGraw-Hill Higher Education Graphing and Table Guidelines Choose a design based on a variable’s level of measurement, study objectives, and targeted audience A good graphic simplifies, not complicates A good graph is self-explanatory Produce rough drafts and seek advice Adhere to inclusiveness and exclusiveness Provide a descriptive title and indicate the source of material Scrutinize computer generated graphics

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© 2008 McGraw-Hill Higher Education Pie Chart A circle that is dissected or sliced from its center point with each slice representing the proportional frequency of a category of a nominal/ordinal variable Pie charts are especially useful for conveying a sense of fairness, relative size, or inequality among categories

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© 2008 McGraw-Hill Higher Education Constructing a Pie Chart To determine the correct size of a “slice,” multiply a category’s proportional frequency by 360 degrees Use a protractor to cut the pie Percentages are placed on the pie chart for the sake of clarity

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© 2008 McGraw-Hill Higher Education Interpreting a Pie Chart Focus on the largest pie slice (i.e., the category with the highest percentage frequency) and comment on it Compare slices and comment on stark differences in sizes Compare the results to other populations Summarize with a main point

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© 2008 McGraw-Hill Higher Education Bar Chart A series of vertical or horizontal bars with the length of a bar representing the percentage frequency of a category of a nominal/ordinal variable Bar charts are especially useful for conveying a sense of competition among categories

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© 2008 McGraw-Hill Higher Education Constructing a Bar Chart Construct on two axes, the abscissa (horizontal) and the ordinate (vertical) Categories of a variable are situated on one axis, and markings for percentages on the other To determine the correct bar size for a category, compute its percentage frequency To compare several groups, use clustered bar charts

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© 2008 McGraw-Hill Higher Education Interpreting a Bar Chart Observe the heights of bars and comment on the tallest (i.e., the category with the highest frequency) Compare and rank heights of bars and comment on stark differences Compare the results to other populations Summarize with a main point

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© 2008 McGraw-Hill Higher Education Frequency Histogram A 90-degree plot presenting the scores of an interval/ratio variable along the horizontal axis and the frequency of each score in a column parallel to the vertical axis Similar to bar charts except columns may touch to account for real limits and the principle of inclusiveness

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© 2008 McGraw-Hill Higher Education Constructing a Histogram Work from a frequency distribution and calculate the real limits of each score of X. Draw the horizontal axis and label for X. Draw the vertical axis and label for frequency of cases Draw the columns with the height of a column representing the frequency of scores for a given real limit span of X The width of each column of the histogram will be the same

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© 2008 McGraw-Hill Higher Education Interpreting Frequency Histograms Observe the heights of columns and note the tallest (i.e., the score with the highest frequency) Look for clusters of columns and a “central tendency” Look for symmetry (balance) in the shape of the histogram Summarize with a main point

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© 2008 McGraw-Hill Higher Education Frequency Polygon A 90-degree plot with interval/ratio scores plotted on the horizontal axis and score frequencies depicted by the heights of dots located above scores and connected by straight lines Portrays a sense of trend or movement Especially useful for comparing two or more samples

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© 2008 McGraw-Hill Higher Education Constructing a Polygon Work from a frequency distribution Draw the horizontal axis and label for the variable X. Draw the vertical axis and label for the frequency or percentage of cases Place dots above the scores X at the height of the frequency or percentage frequency Connect the dots with straight lines, closing the ends to the baseline of the lower and upper real limits of the distribution

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© 2008 McGraw-Hill Higher Education Interpreting Polygons Look for peaks and comment on the tallest (i.e., the score with the highest frequency) Look for expanse of space under the line and for peaks and valleys Look for a “central tendency” Look for symmetry (balance) in the shape of the line graph Summarize with a main point

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© 2008 McGraw-Hill Higher Education Polygons with Two or More Groups When two or more groups (populations, samples, or subsamples) are plotted, compare their peaks and shapes Plot percentage frequencies to adjust for differing group sizes Look for contrasting central tendencies among the groups Note the presence or lack of overlap in the polygons of any two groups

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© 2008 McGraw-Hill Higher Education Graphs Reveal Outliers For a distribution of scores, an outlier (or deviant) score is one that stands out as markedly different from the others With a trained eye, outliers may be noted in a frequency distribution, but are easily detected with graphs

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© 2008 McGraw-Hill Higher Education Statistical Follies Graphs may be intentionally or mistakenly distorted Make sure any claimed differences in scores is real and not simply a distortion of the graphic Use computer graphics carefully and edit output. Rely on the computer as simply a drawing tool

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Chapter 2 Summarizing and Graphing Data

Chapter 2 Summarizing and Graphing Data

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