Descriptive Statistics

Descriptive Statistics

  • Descriptive statistics is the first true statistics topic, differing from research in general or quantitative methods.
  • Descriptive statistics describes a sample.
  • It doesn't infer anything about a larger population; it's merely a description of a particular sample.
  • Descriptive statistics are considered basic and don't allow for inferring larger meanings.

Course Structure

  • The course progresses from basic to sophisticated analyses.
  • Descriptive statistics are the most basic type of analysis.
  • Descriptive statistics are present in research articles in the methods section.
  • They describe the sample, including: the number of participants, the sample size, their mean age, their mean experience, and other relevant traits.
  • Descriptive statistics don't enable life-changing analysis.
  • Descriptive statistics allow a researcher to describe their sample so that a reader can make judgments about the sample's quality and representativeness.

Statistical Vocabulary

  • Parameter: A characteristic of an overall population.
  • Statistic: A characteristic of a sample.
  • Population mean uses the Greek symbol μ (mu).
  • Overall population is denoted by an uppercase N.
  • Sample is denoted by a lowercase n.
  • Sample mean is denoted by X̄ (X bar).

Population vs. Sample

  • Population: A large group of individuals.
  • Sample: Individuals pulled from the population, ideally randomly.
  • Population mean: Represented by μ.
  • Sample size: Represented by nn.
  • Sample mean: Extracted from the sample.
  • Sample mean: Represented by X̄ is used to infer the population mean even though it often deviates from the actual parameter.

Descriptive vs. Inferential Statistics

  • Descriptive statistics describe a group.
  • Inferential statistics make inferences from the sample to the population.
  • Descriptive statistics describe the sample mean while inferential statistics allow one to extrapolate conclusions for the larger population.

Measuring Things

  • Descriptive statistics helps us in the next leap to inferential statistics, where we're actually making meaningful analysis.
  • Descriptive statistics allow us to look at a distribution of scores.