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.