Statistics, Data, and Statistical Thinking

1
Chapter 1

• Statistics, Data, and Statistical Thinking

2
The Science of Statistics

• Statistics the science of data
• Collection
• Evaluation (classification, summary, organization
  and analysis)
• Interpretation (drawing conclusions based on the
  data.)

3
Types of Statistical Applications

• Descriptive Statistics summarize or describe
  the important characteristics of a known set of
  population data
• Inferential Statistics use sample data to make
  inferences (or generalizations) about a population

4
Fundamental Elements of Statistics

• Experimental Unit object of interest
• example graduating senior
• Population the set of units we are interested
  in learning about
• example all 1450 graduating seniors at State
  U
• Variable characteristic of an individual
  population unit
• example age at graduation

5
Fundamental Elements of Statistics

• Sample subset of population
• example 100 graduating seniors at State U
• Statistical Inference generalization about a
  population based on sample data
• example The average age at graduation is 21.9
  (based on sample of 100)
• Measure of reliability statement about the
  uncertainty associated with an inference

6
Types of Data

• Quantitative Data
• measured on a naturally occurring scale
• equal intervals along scale (allows for
  meaningful mathematical calculations)
• data with absolute zero (zero means no value) is
  ratio data (bank balance, grade)
• Data with relative zero (zero has value) is
  interval data (temperature)

7
Types of Data

• Qualitative Data
• measured by classification only
• Non-numerical in nature
• Meaningfully ordered categories identify ordinal
  data (best to worst ranking, age categories)
• Categories without a meaningful order identify
  nominal data (political affiliation, industry
  classification, ethnic/cultural groups)

8
Fundamental Elements of Statistics

• Elements of Descriptive Statistical Problems
• population/sample of interest
• investigative variables
• numerical summary tools (charts, graphs, tables)
• pattern identification in data

9
Fundamental Elements of Statistics

• Elements of Inferential Statistical Problems
• population of interest
• investigative variables
• sample taken from population
• inference about population based on sample data
• Reliability measure for the inference

10
Types of Data

• Different statistical techniques used for
  quantitative and qualitative data
• Qualitative and Quantitative data can be used
  together in some techniques
• Quantitative data can be transformed into
  Qualitative data through category creation
• Qualitative data cannot be meaningfully
  transformed into Quantitative data

11
Collecting Data

• Data Sources
• Published source books, journals, abstracts
• Primary vs. secondary
• Designed Experiment
• Often used for gathering information about an
  intervention
• Survey
• Data gathered through questions from a sample of
  people
• Observational Study
• Data gathered through observation, no interaction
  with units

12
Collecting Data

• Sampling
• Sampling is necessary if inferential statistics
  are to be used
• Samples need to be representative
• Reflect population of interest
• Random Sampling
• Most common sampling method to ensure sample is
  representative
• Ensures that each subset of fixed size is equally
  likely to be selected

13
The Role of Statistics in Critical Thinking

• Statistical literacy is necessary today to make
  informed decisions both at work and at home
• Requires statistical thinking to critically
  assess data and the inferences drawn from it
• Statistical thinking assists you in identifying
  research resulting from unethical statistical
  practices

14
The Role of Statistics in Critical Thinking

• Common Sources of Error in Survey Data
• Selection bias exclusion of a subset of the
  population of interest prior to sampling
• Nonresponse bias introduced when responses are
  not gotten from all sample members
• Measurement error inaccuracy in recorded data.
  Can be due to survey design, interviewer impact,
  or a transcription error

15
Summary

• 2 types of statistical applications in business
  Descriptive and Inferential
• 6 fundamental elements of statistics
• population
• experimental units
• variable
• sample
• inference
• measure of reliability

16
Summary

• 2 types of data Quantitative and Qualitative
• 4 Data collection methods
• published source
• designed experiment
• survey
• observation

17
Summary

• Sources of Error in Survey Data
• selection bias
• non-response bias
• measurement error