Types of Data: Nominal, Ordinal, Interval/Ratio

Importance of Data in Statistical Analysis

• Data collection helps in understanding phenomena or processes.
• Observations: Each entity we collect data on (e.g., person, business, product, period).
• Variables: Measurements of interest (e.g., age, sex, chocolate preference).
• Data Storage: Rows as observations, columns as variables in a spreadsheet.

Levels of Measurement

• Determines appropriate summary statistics, graphs, and analyses.

Nominal Data

• Basic level, also called categorical or qualitative.
• Examples: Sex, preferred chocolate type, color.
• Characteristics: Descriptions/labels with no order.
• Storage: Words/text or numerical codes (order not implied by numbers).
• Summary: Use frequency or percentage; mean/average not applicable.
• Graphs: Pie chart, column/bar chart, or stacked column/bar chart (column chart preferred).

Ordinal Data

• Examples: Rank, satisfaction, fanciness.
• Characteristics: Meaningful order, unequal intervals between values.
• Summary: Frequencies; mean calculation debated but used in behavioral research.
• Warning: Mean calculation should be justified.
• Graphs: Best shown as column/bar chart (pie chart not suitable).

Interval/Ratio Data

• Measured rather than classified/ordered.
• Examples: Number of customers, weight, age, size.
• Also known as scale, quantitative, or parametric.
• Characteristics: Can be discrete (whole numbers) or continuous (fractional numbers).
• Summary: Mean, median, standard deviation usually suitable.
• Graphs: Bar chart or histogram, data often grouped; box plots illustrate summary stats; line charts for data over time.

Example: Helen's Choconutties Survey

• Data collected from a sample of 50 customers.
• Variables: Age, sex, grocery spending, chocolate bars bought per week, chocolate preference, satisfaction with Choconutties, likelihood of buying a box.
• Data entry: Rows for customers, columns for variables.
• Analysis:
  • Preferred chocolate type (nominal): Pie/bar chart.
  • Satisfaction and likelihood (ordinal): Column chart; summary stats provided contextually.
  • Age, grocery spending, chocolate bars (interval/ratio): Bar chart/histogram; meaningful statistics like mean age (38 years), mean grocery spending ($192), mean chocolate bars (3.3 per week).

Conclusion

• Type of analysis depends on the level of measurement.
• Further details available in the video, "Choosing the Test".