What is a Sample

  • A sample is a subset of a larger population of items.

    • Used to make inferences about the population without examining every item.
    • The goal is to generalize from sample data to population characteristics.

Generalizing from a Sample

  • Generalization Argument Pattern:

    • N% of [Sample] has [Feature].
    • N% of [Population] has [Feature].
    • Example:
      • 30% of pregnancies at Gotham General Hospital (GGH) with women aged 20-24 are unplanned.
      • Therefore, 30% of pregnancies in women aged 20-24 in Gotham are unplanned.
    • Population: pregnancies in women aged 20-24 in Gotham.
    • Sample: pregnancies in women aged 20-24 at GGH.
    • Feature: unplanned[1]``[2].

Sample Size and Its Impact

  • Importance of Sample Size:

    • Larger sample sizes generally provide more reliable generalizations.
    • Sample size is indicated with ( n ).
    • Example:
      • 30% of pregnancies at GGH with women aged 20-24 (n=500) are unplanned.
      • Therefore, 30% of pregnancies in women aged 20-24 in Gotham are unplanned[3].

Precision and Accuracy

  • Understanding Precision vs. Accuracy:

    • Precision: Exactness or specificity of a statement.
    • Accuracy: Closeness of a statement to the truth.
    • Example:
      • Precise statements: “The speed of light is 155,286,903 m/s” and “The speed of light is 271,306,682 m/s.”
      • Accurate statement: “The speed of light is around 300,000,000 m/s” (true value: 299,792,458 m/s)[4]``[5].

Margin of Error and Confidence Level

  • Defining Margin of Error (MoE):

    • Quantifies the precision of a statistical estimate.
    • Presented as a range (e.g., ±4 points).
    • Larger MoE indicates lower precision.
    • Confidence level indicates the likelihood that the true population parameter lies within the MoE.
    • Example:
      • At GGH, 30% of pregnancies with women aged 20-24 (n=500) are unplanned (±4 pts).
      • Indicates a confidence level, typically 95% if not stated[6].

Identifying Sample Bias

  • Understanding Sample Bias:

    • A biased sample occurs when some characteristic of the sample makes the measured feature more (or less) common than in the entire population.
    • Examples of Bias:
      • Argument that 60% of the cities visited by airplane have a university implies that 60% of all cities have a university. This is biased due to the selection of cities with airports[7]``[8].

Unit 9 Skills

  • Key Skills to Develop:

    • Recognizing how changes in precision, MoE, confidence level, or sample size affect one another.
    • Evaluating the effect of sample size on the strength of an argument.
    • Identifying and explaining sample bias[9].