Statistics Distributions and Tests Summary

Test/Distribution to Use (AP Stats)

  • One proportion
    • Test/Function to Use: 1-PropZTest (hypothesis test), 1-PropZint (confidence interval), checks a claim about a single population proportion.
  • Two proportions
    • Test/Function to Use: 2-PropZTest, 2-PropZInt, compares proportions from two independent populations.
  • One mean, population SD unknown
    • Test/Function to Use: T-Test, T-Interval, used when the population standard deviation is unknown and sample size is small.
  • Two means, population SD unknown
    • Test/Function to Use: 2-SampT Test, 2-SampTInt, compares means from two independent groups when population standard deviations are unknown.
  • Matched pairs (like before/after)
    • Test/Function to Use: T-Test on differences, analyzes the mean difference between paired observations.
  • Goodness of fit (one categorical variable)
    • Test/Function to Use: x²-GOF-Test, tests if an observed distribution fits a hypothesized distribution.
  • Homogeneity (two populations, one categorical variable)
    • Test/Function to Use: x²-Test, checks if the distribution of categorical variables is the same across different populations.
  • Independence (one population, two categorical variables)
    • Test/Function to Use: x²-Test, determines if two categorical variables are independent within a population.
  • Linear regression slope
    • Test/Function to Use: LinRegTTest, assesses if there is a significant linear relationship between two variables.

Sample Type

  • Simple Random Sample
    • Key Idea: Everyone has an equal chance; each member of the population is equally likely to be chosen.
  • Stratified Sample
    • Key Idea: Random from each group; the population is divided into subgroups (strata) and random samples are taken from each stratum.
  • Cluster Sample
    • Key Idea: Random whole groups; the population is divided into clusters and whole clusters are randomly selected.
  • Systematic Sample
    • Key Idea: Every nth person; selecting every nth member from a list or sequence.
  • Multistage Sample
    • Key Idea: Combining multiple sampling methods; using a combination of different sampling techniques.
  • Convenience Sample
    • Key Idea: Easiest to reach; selecting individuals who are easiest to reach.
  • Voluntary Response Sample
    • Key Idea: People opt-in; individuals choose to participate themselves.

Normal Distribution

  • Use when: Data is normal or sample is large (CLT).
  • Situation: Less than x
    • Calculator Function: normalcdf(-1E99, x, μ, σ)
  • Situation: Greater than x
    • Calculator Function: normalcdf(x, 1E99, μ, σ)
  • Situation: Between a and b
    • Calculator Function: normalcdf(a, b, μ, σ)
  • Situation: Percentile (find x)
    • Calculator Function: invNorm(area, μ, σ)

Key Words & Function Match

  • Key Phrase: "Exactly"
    • Function/Tip: pdf
  • Key Phrase: "At least"
    • Function/Tip: 1 - cdf
  • Key Phrase: "At most"
    • Function/Tip: cdf
  • Key Phrase: "More than"
    • Function/Tip: 1 - cdf
  • Key Phrase: "Less than"
    • Function/Tip: cdf (x-1 for strict less than)
  • Key Phrase: "First success"
    • Function/Tip: geometric
  • Key Phrase: "Between"
    • Function/Tip: normalcdf(a, b)
  • Key Phrase: "Percentile"
    • Function/Tip: invNorm(area)

Binomial Distribution (Fixed # of Trials)

  • Use when: Fixed number of trials, 2 outcomes (success/failure), same probability, independent.
  • Situation: Exactly x
    • Calculator Function: binompdf(n, p, x)
  • Situation: At most x
    • Calculator Function: binomcdf(n, p, x)
  • Situation: At least x
    • Calculator Function: 1 - binomcdf(n, p, x-1)
  • Situation: More than x
    • Calculator Function: 1 - binomcdf(n, p, x)
  • Situation: Less than x
    • Calculator Function: binomcdf(n, p, x−1)

Geometric Distribution(Until 1st Success)

  • Use when: Trials until 1