
Graphing your data is a crucial step in understanding and communicating its meaning. A cluttered graph can be overwhelming and make it difficult to identify patterns or trends.
Keep your graph simple and clear by limiting the number of data points displayed. This will help you avoid visual overload and make it easier for others to understand your findings.
Using too many colors can make a graph look messy and confusing. Stick to a maximum of 3-4 colors to highlight key information without overwhelming the viewer.
A clear and simple graph can make all the difference in getting your message across.
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Choosing the Right Graph
Graphing data can be a bit overwhelming, especially when you have to choose the right type of graph to use. A good graph should help you understand the distribution of your data, and there are many types of plots that can achieve this.
One key point to consider is the type of data you're working with. If you have qualitative data, you're limited in how you can graph it due to its non-numerical nature.
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For quantitative data, such as a person's weight, frequency distributions can be a great way to organize and understand the data. This can help you identify outliers, which are observations that don't fit the rest of the data.
A good graph should provide a clear view of the distribution of the data points. This is where violin plots and box plots come in handy. A violin plot shows the distribution of data in each condition, while a box plot shows the median, variability, and outliers.
Here are some key characteristics of effective graphs:
- Provide a clear view of the distribution of the data points
- Include the median and variability
- Highlight outliers
By considering these factors and choosing the right type of graph, you can effectively communicate your findings and gain insights from your data.
Line Graphs Beyond Frequency
Line graphs are a great way to show changes over time. They're perfect for displaying ordered variables on both the X- and Y-axes.
A line graph can be used to compare changes over time, making it easier to see trends and patterns. This is especially useful when you have data that shows a steady progression, like medical costs in Figure 30.
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Line graphs are generally better than bar charts for comparing changes over time. While bar charts can be used in this situation, line graphs provide a clearer visual representation of the data.
Line graphs should only be used when both the X- and Y-axes display ordered variables, not qualitative variables. Using a line graph with categorical variables on the X-axis can be misleading.
Line graphs can be used to show percent increases and decreases, making it easy to see which components are trending upward or downward. For example, Figure 30 shows how medical costs had a steadier progression than other components of the CPI.
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Graph Checklist
Choosing the right graph for your data is crucial to effectively communicate your findings. A good graph should be easy to understand and provide a clear picture of the data.
To create a good graph, you need to select the appropriate graph type for the data you are displaying. This is where things can get tricky, but don't worry, I've got you covered. According to the Graph Checklist, you should have selected the appropriate graph type for the data you are displaying.
A graph should have a title to provide context and clarity. This might seem obvious, but it's surprising how many graphs I've seen without a title. A good graph title should be concise and informative.
Have you placed the independent variable on the x-axis and the dependent variable on the y-axis? This is a fundamental concept in graphing, and it's essential to get it right. If you haven't, it's time to go back to the drawing board.
Labeled axes are also crucial to creating a good graph. You should have labeled the axes correctly and specified the units of measurement. This will help your audience understand the data and make informed decisions.
A graph should have the proper scale, with the appropriate high and low values on the axes. This will ensure that your data is accurately represented and easy to read.
Here is a summary of the key points to check when creating a good graph:
Choose Y-axis Wisely
The Y-axis is more than just a vertical line on your graph. It's a crucial element that can make or break the effectiveness of your visualization. As Edward Tufte pointed out, the visualization expert, a proper presentation of all the data can be persuasive. In fact, he argued that with a proper presentation of all the data, the engineers could have been much more persuasive.
To choose the right Y-axis, you need to consider the type of data you're working with. If you have numerical data, you should place the dependent variable on the Y-axis. This is because numerical data is often represented by a continuous scale, and the Y-axis is the perfect place to show this.
A good Y-axis should have clear and concise labels, including units of measurement. For example, if you're measuring the voltage of batteries, your Y-axis should include units of measurement like volts (V). This will help your audience understand the data and make informed decisions.
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Here are some tips to keep in mind when choosing your Y-axis:
- Place the dependent variable on the Y-axis
- Use clear and concise labels, including units of measurement
- Avoid using different axis scaling to distort the message of your dataset
By following these tips, you can create a Y-axis that effectively communicates your data and helps your audience understand the results of your experiment. Remember, the Y-axis is not just a vertical line on your graph – it's a crucial element that can make or break the effectiveness of your visualization.
Line Display Trends
Line charts are perfect for displaying trends because they show an overall trend swiftly and concisely, making it hard to misinterpret.
Their popularity stems from their ability to demonstrate trends for different categories over the same period of time, aiding comparison.
For instance, a line chart can visualize sales figures by age group for multiple product lines, allowing you to see at a glance which age group is buying the most of each product.
This can be particularly useful for identifying the biggest customers, as seen in the example where 34-45 year old buyers of PDAs are the largest customer base, followed by 19-24 year old buyers of cell phones.
Line charts are a valuable tool for business use cases, providing a clear and concise way to display trends and aid comparison.
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Beyond Frequencies: Choosing the Right Graph
A graph is a powerful tool to help you understand and communicate complex data. But, with so many types of graphs out there, it can be overwhelming to choose the right one.
There are many different types of plots that we can use, each with its own advantages and disadvantages. For example, a bar graph is great for comparing different trials or experimental groups, but it's not the best choice if your independent variable is not numerical.
A line graph, on the other hand, is perfect for showing changes over time, but it's only suitable when both the X- and Y-axes display ordered variables. This is why it's essential to consider the type of data you're working with and what you want to communicate before choosing a graph.
Here are some popular graph types and their uses:
Remember, the key is to choose a graph that effectively communicates your message and helps your audience understand your data. By considering the type of data and the story you want to tell, you can select the right graph and make a lasting impression.
Graphing Quantitative Variables
Graphing quantitative variables is a crucial step in understanding the data you've collected. These variables are measured on a numeric scale, such as height, weight, or temperature. Quantitative variables are distinguished from categorical variables, which don't involve measuring or ordering.
To portray distributions of quantitative variables, you can use various types of graphs, including bar charts, histograms, frequency polygons, stem and leaf displays, box plots, and line graphs. Some graph types, like stem and leaf displays, are best suited for small to moderate amounts of data, while others, like histograms, are better for large amounts of data.
A scatter plot is used to show the relationship between two variables, and can be a good choice if you're trying to understand the relationship between two quantitative variables.
Histograms
Histograms are a great way to display the shape of a distribution, and they're especially useful when you have a large amount of data.
A histogram is a graphic version of a frequency distribution, and it consists of bars of equal width drawn adjacent to each other with both a horizontal and vertical axis. The horizontal axis is labeled with what the data represents, and the vertical axis is labeled with frequency or relative frequency.
The class intervals in a histogram are represented by bars, and the height of each bar corresponds to its class frequency. This means that the taller the bar, the more data points fall within that class interval.
To create a histogram, you need to decide on the width of the class intervals, also known as the bin width. The choice of bin width determines the number of class intervals, and it affects the shape of the histogram. It's a good idea to experiment with different choices of width to see which one works best.
A grouped frequency distribution, like the one shown in Table 4, can be used to simplify large datasets. By grouping scores together, you can create a more manageable table that still conveys the shape of the distribution.
The grouped frequency distribution in Table 4 shows how the scores on a psychology test are distributed. The class intervals are grouped in 10s, and each group has the same width. This makes it easy to see the shape of the distribution and identify any patterns or outliers.
Here's a breakdown of the class intervals in Table 4:
By looking at this table, you can see the distribution of the scores and how they're grouped together. This can be a helpful way to visualize the data and identify any patterns or outliers.
Graphing Quantitative Variables
A statistical graph is a tool that helps you learn about the shape or distribution of a sample or a population. Graphs can be a more effective way of presenting data than a mass of numbers because we can see where data clusters and where there are only a few data values.
Some common types of graphs used to summarize and organize quantitative data are the dot plot, the bar graph, the histogram, the stem-and-leaf plot, the frequency polygon, the pie chart, and the box plot. You'll briefly learn about bar graphs, histograms, and frequency polygons in this lesson.
A bar graph shows the difference in means, but doesn't show us how much spread there is in the data around these means. This is a limitation of bar graphs, as knowing the spread of the data is essential to determine whether a difference between groups is large enough to be important.
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There are many different types of plots that we can use, each with their own advantages and disadvantages. In general, we prefer using a plotting technique that provides a clearer view of the distribution of the data points.
Some effective ways to show data that provide a good feel for the distribution of the data include violin plots and box plots. A violin plot plots the distribution of data in each condition, while a box plot shows the median, a measure of variability, and any outliers.
A good data analysis chart should answer "yes" to every question on the data analysis checklist. This includes having sufficient data to know whether your hypothesis is correct, accurate data, and a chart that specifies units of measurement for all data.
Here are some common types of graphs used for quantitative data:
Funnel Display
Funnel Display is a powerful tool to visualize the progress of customers through a sales process. It typically depicts a pipeline of decreasing values.
A funnel chart is a specific type of visualization that brings conversation rates to life at each step. This allows you to quickly see where people are dropping out of the process.
The beauty of a funnel chart is that it shows the number of people at each demand stage, from initial website visit to every touchpoint until a final sale. This makes it easy to identify areas where customers are getting lost in the process.
Funnel charts are often used to display sales figures, making them a valuable tool for businesses to track their sales progress.
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Graphing Variables
Graphing variables is an essential skill for anyone working with data. Qualitative variables can be summarized by frequency, but they're limited in graphing due to their non-numerical nature.
To graph quantitative variables, researchers often use frequency distributions, which help identify outliers – observations that don't fit the rest of the data. Outliers can be due to mistakes or indicate unusual events.
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A frequency distribution is a way to organize scores in order from highest to lowest and group similar scores together. This helps researchers spot outliers and understand the data better.
Line graphs are a type of graph that's particularly useful for showing changes over time. They're created by joining the tops of bar graphs with lines, making it easier to see trends and patterns. Line graphs are best used when both the X and Y axes display ordered variables.
Avoid using pie charts, as they can be misleading and hard to interpret. Instead, opt for line graphs or other types of graphs that are designed for showing changes over time or multiple variables.
Bubble charts are another type of graph that can be useful for showing multiple variables. They depict the weight of values by circle circumference size, making it easy to see which categories are most significant.
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Graphing Beyond Frequency
Graphing Beyond Frequency is a crucial aspect of presenting quantitative data. A good graph should provide a clear view of the distribution of the data points, rather than just showing frequencies.
Bar charts are particularly effective for showing change over time. They can display quantitative information beyond just frequency counts, making them a versatile tool for data visualization.
A bar chart can show the percent change in price for streaming services, as seen in Figure 24. The graph illustrates price reduction due to market competition and restructuring of service tiers.
Bar charts can also be used to compare the means of different experimental conditions, but we don't recommend them for this purpose. Box plots should be used instead, as they provide more information about the distribution of data without taking up more space.
A box plot, like the one shown in Figure 27, can reveal more about the distribution of movement times than a bar chart. It highlights the median, variability, and outliers, giving a clearer picture of the data.
There are several types of plots that can be used to present quantitative data, each with its own advantages and disadvantages. Some options include violin plots, which show the distribution of data in each condition, and box plots, which highlight the median, variability, and outliers.
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Here's a comparison of different plotting techniques:
By choosing the right plot type, you can effectively communicate the story behind your data and provide a clear view of the distribution of the data points.
Break Down Simply
Bar charts are a great way to break down complex data into simple, easy-to-understand categories. They're perfect for comparing several different values, especially when some of these are broken into color-coded categories.
One of the key benefits of bar charts is that they allow you to see the differences between categories at a glance. As Edward Tufte notes, a good bar chart should have plain bars, without fancy graphics or 3D effects that can distort the data.
Bar charts are also great for showing the relative importance of different categories. For example, in a bar chart, the height of each bar represents the value of that category, so you can easily see which categories are the most valuable.
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In some cases, you may want to use a bar chart to show the difference between two or more groups. This can be especially helpful when you want to compare the means of two groups, but also want to see how the data is distributed.
Here are some examples of bar charts that can be used to break down complex data:
- Bar graph in panel A of Figure 31, which shows the difference in means between men and women in the NHANES dataset
- A bar chart with color-coded categories, such as the one shown in Example 5, which compares the sales figures for different product lines in different age groups
Data Visualization Best Practices
To create effective data visualizations, you should start by asking yourself if your data is sufficient to answer your hypothesis. If not, you're better off not creating a chart at all.
A good data visualization should have accurate data, summarized with averages if necessary, and units of measurement specified for all data. This will help you and your audience understand the data quickly.
You should also verify that all calculations are correct, and consider the user's perspective when designing your visualization. This means thinking about how they will navigate and interact with the data.
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Here are some key questions to ask yourself when creating a data visualization:
Focusing on Function and User Experience
Focusing on Function and User Experience is crucial in data visualization.
To start, you need to identify the function of your data visualization, which is the trend, pattern, or vital piece of information you're trying to convey at a glance.
Consider the user, how they navigate and interact with the data, and what they need to take away from it.
Just like a well-designed building, a good data visualization should be clean and beautiful.
Here are some key considerations to keep in mind:
- Start with the function: identify the trend, pattern, or vital piece of information you're trying to convey.
- Consider the user: think about how they will navigate and interact with the data.
- Make it clean and beautiful: a good data visualization should be visually appealing.
By focusing on the function and user experience, you can create a data visualization that effectively communicates your message and engages your audience.
Data Visualization
Data visualization is a crucial step in understanding and communicating your data's insights. A good data visualization should answer "yes" to every question on the Data Analysis Checklist, which includes having sufficient data to know whether your hypothesis is correct, accurate data, and correct calculations.
Edward Tufte, a visualization expert, has argued that a proper presentation of all the data can be more persuasive. He suggests showing a figure that highlights important facts, such as the relationship between the amount of O-ring damage and the temperature at takeoff.
A replotting of Tufte's damage index data can be a powerful tool for illustrating trends and patterns. This type of visualization allows you to see the trend in the data and the projected temperatures for a specific launch.
Area/scatter maps are another useful type of data visualization, particularly for geographic data. These maps show which locations are most significant to your business by visualizing data as points of color on a map.
To create a good area/scatter map, you should review your data and look for patterns and trends. This can be done by calculating an average for the different trials of your experiment, if appropriate, and clearly labeling all tables and graphs.
Here are some key things to keep in mind when creating an area/scatter map:
Comparing and Displaying Values
For side-by-side comparisons of different values, column charts are usually the best choice. This is because they allow you to easily compare values across different categories.
Column charts are particularly effective for showing change over time, especially when you want to draw attention to total figures rather than trends. However, when you want to highlight or contrast key figures and an overall trend, combining a line and column chart can be a great option.
Here are some common types of charts used for displaying values:
- Column charts: good for side-by-side comparisons and showing change over time.
- Line charts: good for depicting trends and comparing values over time.
- Treemaps: useful for displaying hierarchies and comparative value between categories and subcategories.
- Bar charts: can be used to present other kinds of quantitative information, not just frequency counts.
Frequency polygons are a graphical device for understanding the shapes of distributions, and they can be used to compare sets of data.
Compare Values Side-by-Side
Column charts are perfect for side-by-side comparisons of different values. They're also great for showing change over time, especially when you want to draw attention to total figures rather than trends.
Column charts are particularly useful when numbers don't move much from day to day, making it hard to spot trends with a line graph. For example, a chart showing total website page views vs. sessions on a series of dates can reveal insightful information about the concrete number of visitors to the website each day.
You can also combine a line and column chart to highlight or contrast key figures and an overall trend. This can open up new lines of inquiry, like which units are the most profitable, even when fewer are sold.
Bar charts can also be used to represent frequencies of different categories, making them perfect for qualitative data. They're great for comparing the results of different surveys or conditions within the same overall survey.
Frequency Polygons
Frequency polygons are a graphical device for understanding the shapes of distributions, serving the same purpose as histograms but especially helpful for comparing sets of data.
They are a good choice for displaying cumulative frequency distributions, and can be constructed from a frequency table.
A frequency polygon for 642 psychology test scores was constructed from the frequency table shown in Table 5, and it's clear that the distribution is not symmetric, with good scores trailing off more gradually than poor scores.
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The shape of the distribution can be easily discerned from the frequency polygon, with most scores between 65 and 115.
Frequency polygons are useful for comparing distributions by overlaying the frequency polygons drawn for different data sets, as shown in Figure 12.
This allows for the comparison of two distributions, such as the time it took to move a cursor to a small or large target on a screen, with the figure showing that it generally took longer to move the cursor to the small target.
Cumulative frequency polygons can also be plotted together, as shown in Figure 13, to further compare the distributions.
The difference in distributions for the two targets is again evident in the cumulative frequency polygon, making it a useful tool for comparing data.
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Treemaps
Treemaps are a powerful tool for visualizing hierarchies and comparative values between categories and subcategories. They do this by nesting color-coded rectangles inside each other, weighted to reflect their share of the whole.
This allows you to retain detail while getting an instant sense of which areas are most important overall. You can see at a glance which categories are most successful and which ones need more attention.
Treemaps are especially useful for displaying complex data in a way that's easy to understand. By using color and size to represent different values, you can quickly identify trends and patterns.
For example, a treemap can show you that AdWords is your most successful marketing channel, but also reveal that the US is your most valuable destination across all channels.
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Area/Scatter Maps
Area/Scatter Maps are a powerful tool for visualizing geographic data. They show you where your business is most significant by representing data as points of color on a map, with circle size indicating values.
These maps can instantly reveal which locations are driving the most conversions for your business. For example, a map might show website visitors by location, with color indicating the percentage of conversions.
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Scatter charts, a type of area/scatter map, present categories of data by circle color and the volume of data by circle size. They're used to visualize the distribution of and relationship between two variables.
Scatter charts can help you identify patterns and trends in your data, like the number of units sold and revenue brought in. This can lead to insights like the most frequent and profitable clients being men, as seen in a chart breaking down product lines by gender and sales data.
Area/scatter maps can show weaknesses in a marketing strategy at a glance, giving you valuable information on where to focus your efforts.
Show Proportions
Pie charts are great for illustrating the share each value makes up of the whole, they're far more intuitive than simply listing percentages that add up to 100%.
For a pie chart to be effective, you need to have six categories or fewer, any more than that and the chart will be too crowded, and the values too indistinct, to garner any insight.
Area charts, on the other hand, compare proportions and give a sense of the overall volume, as well as the proportion of this taken up by each category.
This makes them useful for imposing a reality check on your revenue estimations, and for assessing where cash flow really is tightest, rather than where in the year you’re simply bringing in the most cash.
Pie charts can also be used to quickly identify which campaigns bring in the biggest share of total leads, making them a valuable tool for marketing teams.
Understanding Data Relationships
Understanding data relationships is crucial when graphing your data. It's not just about visualizing a single variable, but about exploring the connection between two variables.
Research questions often involve investigating the relationship between two variables, such as performance on a test and gender. In most analyses, each variable has a role: the response variable (dependent variable) and the explanatory variable (independent variable).
To graph your data effectively, you should ask yourself if you have sufficient data to support your hypothesis. This is a key consideration when creating a good data analysis chart.
A good chart should provide clear and accurate summaries of the data, without misleading the viewer. This means specifying units of measurement for all data and verifying that all calculations are correct.
Scatter charts are particularly useful for visualizing the distribution of, and relationship between, two variables. They present categories of data by circle color and the volume of the data by circle size, making it easy to see patterns and trends.
To create an effective scatter chart, consider the following:
- Is there a clear relationship between the two variables?
- Are there any outliers or anomalies in the data?
- Can you see patterns or trends in the data?
By considering these factors and using scatter charts effectively, you can gain valuable insights into the relationships between your data and make informed decisions.
Common Mistakes to Avoid
Graphing your data can be a great way to visualize trends and patterns, but it's easy to make mistakes that can distort the message of your data. Three-dimensional figures are less clear than 2-d.
Using graphics that have nothing to do with the actual data can be misleading, like adding images to bar charts that don't help convey information. A distracting background texture can also take away from the data.
Setting the baseline to a value other than zero can distort the data, making it harder to understand. Normally, the baseline should be zero.
A line graph is essentially a bar graph with the tops of the bars represented by points joined by lines, but it's not suitable for qualitative variables. It can give the false impression that the variables are ordered numerically when they're actually ordered alphabetically.
Pie charts can be tricky to read, especially when comparing outcomes of two different surveys or experiments. They can be confusing when there are a large number of categories.
Here's a checklist to help you avoid common mistakes:
Which Viz?
When graphing your data, it's essential to choose the right visualization technique to effectively communicate your findings.
A bar graph can be useful for showing the difference in means between two groups, but it doesn't provide information about the spread of the data. In the case of the NHANES dataset, a bar graph only shows the difference in means between men and women in height, without giving us a sense of how much spread there is in the data.
A plot with bars and overlaid data points can make it clearer that the distributions of height for men and women are overlapping, but it's still hard to see due to the large number of data points. This was the case with the second plot in Figure 31.
We prefer using a plotting technique that provides a clearer view of the distribution of the data points. Two effective options are the violin plot and the box plot.
A violin plot, like the one in panel C of Figure 31, plots the distribution of data in each condition after smoothing it out a bit. This gives us a good idea of how the data is spread out.
A box plot, shown in panel D of Figure 31, shows the median, a measure of variability, and any outliers. This gives us a good feel for the distribution of the data.
Here's a quick comparison of the three options:
Ultimately, the choice of visualization technique depends on the specific characteristics of your data and the story you want to tell.
Frequently Asked Questions
Why graphing can be an important tool for analyzing data?
Graphing helps identify patterns, trends, and relationships within data, making it easier to understand and communicate complex information. By visualizing data, you can simplify analysis and present insights effectively to others.
What is the independent variable in the pill bug experiment?
The independent variable in the pill bug experiment is time, which is being measured and recorded. This variable is being manipulated to observe its effect on the dependent variable.
Sources
- https://statacumen.com/teach/S4R/PDS_book/graphing-relationships.html
- https://www.sciencebuddies.org/science-fair-projects/science-fair/data-analysis-graphs
- https://open.maricopa.edu/psy230mm/chapter/chapter-3-describing-data-using-distributions-and-graphs/
- https://stephanieevergreen.com/ways-to-show-change-over-time/
- https://www.sisense.com/blog/10-useful-ways-visualize-data-examples/
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