Data Basics Quiz: Variables & Studies

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Data Basics

• Variables can be numerical (numbers) or categorical (groups or bins)
• Numerical variables can be discrete (e.g., 1, 2, 3) or continuous (e.g., decimal places)
• Categorical data can be ordinal (e.g., natural ordering) or nominal (e.g., no natural ordering)
• Explanatory variables might affect the response variable
• Observational studies don't interfere with data, while experiments randomly assign subjects to treatments

Review Problem

• Problem A: Identify explanatory and response variables in a study of social media use and marriage satisfaction. Determine if it is an observational study or an experiment.
• Reasoning: Explain why one approach is more suited than the other, considering if researchers intervene or observe

Variable Type Example

• Problem: Categorize "Cooking Experience" (rated 1-5).
• Categorization: Categorical (1, 2, 3, 4, 5), Ordinal (ordinal scale)

Chapter 1.3

• Topic: Observational studies, sampling strategies

Sample Definition

• Research Question: Average fruit/vegetable consumption of Duke undergraduates
• Sample: 200 Duke Undergraduates
• Target Population: All currently enrolled Duke undergraduates
• Purpose of sampling: Estimate the average for the target population

Census

• A survey that includes every member in the entire population
• Census is time consuming and expensive
• Populations constantly change, making it difficult to keep track of
• Some characteristics may be hard to measure

Exploratory Analysis to Inference

• Sampling: Examining a small part of something (e.g., a spoonful of soup) to understand the entire thing.
• Exploratory analysis: Deciding the spoonful isn't salty enough
• Inference: Conclude that the whole soup needs salt.
• Representative Sample: A sample which accurately reflects the population.

Sampling Bias

• Non-response bias Subjects chosen may not participate (e.g., email survey to students, few reply)
• Voluntary response bias Participants with strong opinions may be overrepresented
• Convenience sample bias Subjects most easily accessible tend to be disproportionately included

Sampling Bias Example - Landon vs. FDR

• 1936 Presidential election.
• Magazine (Literary Digest) made predictions with a biased sample (readers, auto owners, phone users).
• Prediction was wrong, magazine was discredited.

The Literary Digest Poll

• Poll: Surveyed about 10 million Americans, receiving responses from approximately 2.4 million
• Results: Predicted Landon as an overwhelming winner, with FDR only receiving 43% of the votes
• Reality: FDR won with 62% of the votes

Literary Digest Poll - What Went Wrong?

• Surveyed: The magazine's own readers, automobile owners, and telephone users
• Issues: These groups tend to be higher income and lean Republican
• Negative Impact: The poll's results significantly misrepresented the actual population

Survey on Parking Policy

• Issue: School district considering a change to high school student parking policy.
• Survey: Sent out 6000 surveys by mail to parents
• Response: 1200 completed
• Results: 960 agreed with change, 240 disagreed.
• Evaluations:
  • Some mailings might not have reached parents
  • Strong support for the change
  • Possible majority of parents could disagree with change
• Potential Bias: Not all parents responded.

Obtaining Good Samples

• Almost all statistical methods are based on implied randomness.
• Observational data not randomly gathered may not give reliable estimates or errors.

Types of Samples

• Simple Random Sample (SRS): Individual cases randomly selected from the population without any connection between them.
• Stratified Sample: Population divided into subgroups (strata) and SRS is used on each group.
• Cluster Sample: Population grouped into clusters. SRS is used to select clusters, then observations in these clusters.
• Multistage Sample: Combination of sampling techniques like SRS and cluster sampling

Practice Problem - Household Survey

• Context: Survey in suburban area, diverse neighborhoods (large homes, apartments).
• Least Effective Approach: Cluster sampling.

Practice Problem - Cats on YouTube

• Context: Estimating percentage of cat videos on YouTube.
• Sample: 1000 videos randomly selected
• Observation: Each video selected
• Variable: Whether or not a video is a cat video
• Sample Statistic The percentage (2%) of videos in the sample that were cat videos
• Population Parameter: The proportion of all videos on YouTube that are cat videos.