W7- OB Notes Part 3
2-1 Types of Data and Information
Descriptive statistics encompasses both population and sample datasets.Important factors for selecting the appropriate graph:
Type of data: Different types of data require different graphical representations.
Information required: Understand what you are trying to convey through the graph.
Variables and Values:
Definition of a Variable: A characteristic of a population or sample, denoted by uppercase letters (X, Y, Z).
Example: Student grade, stock price.
Values of a Variable: The range of possible values.
Example: Student marks can range from 0 to 100.
Data: Observed values of a variable.
Example: {67, 74, 71, 83, 93, 55, 48, 82, 68, 62}.
2-1a Types of Data
Interval Data:
Real numbers (e.g., heights, weights) which allow for meaningful arithmetic operations.
Also known as quantitative or numerical data.
Example: Heights of students in a class (e.g., 150 cm, 160 cm, etc.)
Nominal Data:
Categorical values that cannot be ranked or ordered (e.g., marital status).
Known as qualitative or categorical data.
Example: Types of pets owned (e.g., Dog, Cat, Bird).
Ordinal Data:
Categorical but ranked data (e.g., grades A, B, C, D, F).
Numerical ratings can be assigned to ranked categories.
Example: Customer satisfaction levels rated as Excellent, Good, Fair, Poor.
2-1b Hierarchy of Data
Interval Data:
All calculations valid. Can be treated as ordinal or nominal.
Example: Analyzing temperature data allows for averaging, unlike nominal data.
Ordinal Data:
Represents ranking; calculations valid based on ordering.
Can only be treated as nominal.
Example: Survey responses can show preferences but do not quantify the difference between ranks.
Nominal Data:
Arbitrary numbers for categories can only perform frequency calculations.
Example: Gender data can show representation but cannot be averaged.
2-2 Describing a Set of Nominal Data
Graphical & Tabular Techniques for Nominal Data:
Calculate frequency of variable values.
Use frequency distribution tables to summarize data.
Relative frequency distribution lists proportions.
Example 2.1 – Frequency Distribution
Survey Data: Work status based on responses from a survey.Categories include:
Working full time
Working part time
Temporarily not working
Unemployed
Retired
Student
Keeping house
Other
Graphical Representation of Nominal Data
Bar Chart:
Used to display frequencies; the height of the bars reflects frequency.
Example: A bar chart illustrating the number of respondents in each work status category.
Pie Chart:
Shows relative frequencies as segments of a circle. Good for showing proportionate data.
Example: A pie chart displaying that 48.3% of survey participants are working full-time with other segments denoting part-time, unemployed, etc.
Example Insights:
In the survey, 48.3% worked full-time; others varied across categories, demonstrating the workforce composition.
2-3 Describing Relationships
2-3a Tabular Method
Cross-Classification Table:
Summarizes relationships between two nominal variables using frequencies.
Example 2.4 – Newspaper Readership Survey
Cross-tabulation combines values of newspaper read and occupation (blue-collar, white-collar, professional).
Investigates if relations exist based on frequency counts.
Graphing the Relationship
Bar Charts can be used to visualize the relationship between two nominal variables.
Example: A bar chart showing the frequency of newspaper readership among different occupational categories helps in understanding preferences.
Representation helps in understanding similarities and differences across categories.
Chapter Summary
Descriptive Methods: Summarize data to extract relevant information.
Discussed graphical techniques for nominal data, including bar charts and pie charts.
Bivariate methods used for analyzing relationships between two nominal variables through cross-classification tables.
Appendices
Appendix 2.A: Detailed outputs and instructions for frequency distributions and bar charts using XLSTAT.
Appendix 2.B: Instructions and outputs for similar analyses in Stata.