Chapter 5: Organizing and Displaying Data

Learning Objectives Demonstrate techniques for showing data in graphical presentation formats Choose the best format to display the data Accurately interpret data presented on a graph or table

Introduction Once the data are collected, it is important to determine how to present the data concisely, accurately, and clearly. Should I describe the data in a text or use graphs and chart? – The amount of data to describe – The level of measurement – Audience characteristics

Grouping Data One of the most common ways of presenting data is a Frequency Distribution, a display of possible values and corresponding frequencies Example

Grouping Data Frequency distribution can be either ungrouped or grouped. – Ungrouped: suitable for categorical measurements, nominal or ordinal, and continuous measurements with a small range of data values – Grouped: suitable for continuous measurements with a large range of data values “Analyze > Descriptive Statistics > Frequencies”

Graphs and Charts Graphs and charts are good ways of displaying and describing the data Goal is to find the best chart or graph that shows the data in a meaningful, clear, and efficient manner. Level of measurement is an important factor to determine which graphs or charts should be used.

Graphs and Charts Discrete or Categorical Data – Bar chart: a typical chart that has response categories on the horizontal axis and the frequencies of each category on the vertical axis – Graph > Legacy Dialogues > Bar – Example

Graphs and Charts Discrete or Categorical Data – Pie chart: a circular chart where pieces within the chart represent a corresponding proportion of each category – Graph > Legacy Dialogues > Pie – Example

Graphs and Charts Continuous Data – When the data is measured on continuous levels of measurement, both bar chart and pie chart become inefficient in displaying the data – Better charts are histogram, stem and leaf plot, and box plot.

Graphs and Charts Histogram – Similar to a bar chart in structure – However, it organizes a group of data points into a number of intervals and the bar represents the frequency in corresponding intervals Graph > Legacy Dialogues > Histogram Example

Graphs and Charts Stem and leaf plot – Similar to a histogram, but it shows more information such as individual data values as well as the overall shape distribution – However, it shows more in Graph > Legacy Dialogues > Explore > “Plot” button Example

Graphs and Charts Box plot – Convey more information than both histogram and stem and leaf plot including overall distribution, the center of distribution, quartile, and any potential outliers – Good for comparison across groups Graph > Legacy Dialogues > Box plot” button Example

Graphs and Charts Box plot – Graph > Legacy Dialogues > Box plot” button – Example

Graphs and Charts Box plot – Middle line: Median (50 th percentile) – Lower edge: First quartile (25 th percentile) – Upper edge: Third quartile (75 th percentile) – Ends of the vertical lines: Whiskers Lower whisker: 1.5 times the interquartile range (IQR) from 25 th percentile Upper whisker: 1.5 times the interquartile range (IQR) from 75 th percentile – Any data point below lower whisker or above upper whisker can be treated as outliers

Other Graphs and Charts Line chart – Another choice for categorical data – Created by connecting dots, representing the data values of each category Graphs > Legacy Dialogues > Line Example

Other Graphs and Charts Scatter plot – A good choice to examine relationship between two continuous variables Graphs > Legacy Dialogues > Scatter/Dot Example

Best chart and format Ask yourself which level of measurement a variable was measured – Categorical: Bar chart, Pie chart or line chart – Continuous: Histogram, Stem and leaf plot, Box plot, or Scatterplot (2 variables) Ask yourself whether you provided enough information on each component of the graph – Clear Title – Clear named variable – etc

Best chart and format Independent variable on the horizontal axis and dependent variable on the vertical axis Present the graph on a proper scale