Qualitative variable

Introduction to iMac Study

  • In August 1988, Apple introduced the iMac computer, aiming to understand its impact on market share.

  • Analysis sought to determine if the iMac attracted new customers or primarily previous Macintosh owners.

  • A sample of 500 iMac customers was interviewed and categorized into three groups:

    • Previous Macintosh owners

    • Previous Windows users

    • New computer purchasers

Graphical Methods for Displaying Data

  • The section explores various graphical methods to effectively represent the qualitative data collected from interviews.

Qualitative Data

  • Definition: Data that occupies non-numerical categories without a pre-established order.

  • Example: The category of former Windows users does not have a natural positional relation to Macintosh owners.

Pie Charts

  • A pie chart represents different categories as slices of a pie, with the area of each slice proportional to the percentage of responses.

  • In the iMac study:

    • Majority of purchasers were Macintosh owners.

    • 12% were former Windows users.

    • 17% were buying a computer for the first time.

  • Effectiveness: Pie charts are suitable for presenting relative frequencies of a small number of categories.

  • Limitations:

    • Not recommended for large numbers of categories.

    • Can be confusing when comparing different surveys or experiments.

  • Edward Tufte's Critique:

    • Tufte criticized the use of multiple pie charts, suggesting that they can lead to poor design decisions.

  • Caution on Small Samples:

    • If pie charts are based on small observations, labeling slices with percentages can be misleading.

    • Example: If only five individuals were surveyed, and three were Windows users, a 60% label could mislead.

    • Recommendation: Instead of percentages, display actual frequencies (e.g., three).

Bar Charts

  • Alternative method for representing frequencies of categories.

  • The bar chart shows:

    • Frequencies on the y-axis.

    • Type of computer previously owned on the x-axis.

  • Comparison Across Surveys:

    • Bar charts excel at illustrating differences between two distributions, unlike pie charts.

  • Example: An illustration of users playing card games at Yahoo on two different days:

    • More players on Wednesday than Sunday.

    • Consistent number of Pinochle players on both days, but significantly more Hearts players on Wednesday.

  • Design Tip: Avoid excessive embellishments in graphs that may obscure important information.

    • Example: 3D bar charts can hinder clarity relative to 2D bar charts.

    • Example: Using images instead of plain bars can exaggerate differences.

Misleading Graphs

  • Distortion in Graphs:

    • Edward Tufte's concept of lie factor arises when the illustrated size effect in a graph exceeds or falls below the actual data.

    • A lie factor greater than 1.05 or less than 0.95 is considered unacceptable.

  • Bar Charts with Non-Zero Baselines:

    • The baseline, representing the minimum value of a category, should normally be set to zero.

    • Adjusting the baseline (e.g., setting it to 50) can distort perception of differences.

Line Graphs

  • Guideline: Avoid line graphs when dealing with qualitative variables on the x-axis.

  • Line graphs visually represent data as bars connected by lines, which can suggest a numerical order that doesn't exist.

  • Example: The misleading representation of card game data using a line graph implies a natural order among categories.

Conclusion

  • Both pie charts and bar charts can effectively display qualitative data.

  • Bar charts are favored for larger category sets, while pie charts work better for fewer categories.

  • Importance of avoiding misleading graphs to ensure accurate data representation.