11.7: Critical Analysis
- Page ID
- 64754
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)When critically analyzing visual representations of data, it is important to observe any overall impressions or trends. Because the interpretation of visual representations of data have a large degree of subjectivity, small details in plots and graphs should not be overinterpreted. Another important issue is to determine whether the visual representation has been manipulated to cover up a trend, or perhaps make a trend appear where one does not really exist in the data.
The key questions when critically analyzing bar charts frequency distributions are:
- How do the frequencies compare to one another?
- Has the horizontal axis been ordered in a way to make it appear that there is a trend in the frequencies?
- Has the horizontal axis been ordered in a way to emphasize a comparison between two categories?
- Is the vertical axis properly scaled so that it starts at zero and has a range large enough to accommodate the data but not de-emphasize differences between categories?
The key questions when critically analyzing pie charts are:
- Do some responses have higher frequencies than others?
- Do some responses have lower frequencies than others?
- Are the frequencies of all the responses about the same?
- For a sequence of pie charts, is there a trend in the frequencies of the responses or do all the pie charts appear to be similar?
- Have the pie charts been manipulated to emphasize or de-emphasize the frequencies for some responses, such as using a three-dimensional pie chart?
The key questions when critically analyzing line graphs are:
- Is there a trend in time in the graph or is the line constant throughout the time period?
- Are there times when there are peaks or valleys in the graph?
- If more than one line is represented in the graph, how do the trends between the lines compare? Do they peak at similar times? Are there valleys at similar times?
- Is the vertical axis properly scaled so that it starts at zero and has a range large enough to accommodate the data but not de-emphasize trends or differences?
The key questions when critically analyzing histograms are:
- How do the frequencies compare to one another?
- Is there a trend in the frequencies?
- Are there gaps in the histogram where no data was observed in some classes?
- How many modes does the histogram have?
- If the histogram is unimodal, is it symmetric, skewed left, or skewed right?
- Is the vertical axis properly scaled so that it starts at zero and has a range large enough to accommodate the data but not de-emphasize differences between classes?
The key questions when critically analyzing scatterplots are:
- Does the plot show an association between the two variables?
- Are there areas of the scatterplot where few data points were observed?
- Are there any points far away from the clod of points that would be an outlier?
- Are the axes properly scaled?