Triage: Which Inferential Stats Case Should I Use?

See also:  For a chart with many more tests, see Harvey Motulsky’s Intuitive Biostatistics: Choosing a Statistical Test (link verified 2007-12-01).

Start Here

Caution: These procedures all require simple random sampling.

What type of data do you have?

• Numeric (discrete or continuous) — go to Node 100
• Binomial (yes/no) — go to Node 200
• Categorical — go to Node 300

Node 100. Numeric data

What population parameter are you trying to make inferences about?

• Population mean(s) — go to Node 110
• Population standard deviation(s) or variance(s) — go to Node 150
• Population correlation coefficient — go to Case 9
  Requirement: Population values of y are normally distributed for any given x.
• Slope of regression line — go to Case 10B
  Requirement: Residuals are normally distributed.
• Predicted values of response variable — go to Case 10Y
  Requirement: Residuals are normally distributed.

Node 110. Numeric data, pop. mean(s)

How many populations are there?

• One — go to Node 120
• Two, paired data — go to Case 3
  Requirement: Sample size ≥ about 30, or differences are normally distributed with no outliers.
• Two, unpaired data — go to Case 4
  Requirements: 1. Samples are independent. 2. Each sample size ≥ about 30, or data are normally distributed with no outliers.
• Three or more — go to Case 8
  Requirements: 1. Samples are independent. 2. Data are normally distributed. 3. All populations have same σ. (The test is robust, so moderate departures from requirements 2 and 3 are okay, especially if sample sizes are equal or nearly equal.)

Node 120. Numeric data, one pop. mean

Do you know the standard deviation of the population?

• No — go to Case 1
  Requirement: Sample size ≥ about 30, or data are normally distributed with no outliers.
• Yes — go to Case 0
  Requirements: 1. You know the s.d. of the population. 2. Sample size ≥ about 30, or data are normally distributed with no outliers.

Node 150. Numeric data, pop. standard deviation(s) or variance(s)

How many populations are there?

• One — go to Case 1S
  Requirement: Population must be normally distributed, not just roughly normal.
• Two — go to Case 4S
  Requirements: 1. Samples are independent. 2. Populations must be normally distributed, not just roughly normal.

Node 200. Binomial (yes/no) data

How many populations are there?

• One — go to Case 2
  Requirements: 1. np̂(1−p̂) ≥ 10. (Some authors substitute: ≥ 5 yes and ≥ 5 no in sample.) 2. n ≤ 5% of population.
• Two — go to Case 5
  Requirements: 1. Samples are independent. 2. np̂(1−p̂) ≥ 10 for each sample. (Some authors substitute: ≥ 5 yes and ≥ 5 no in each sample.) 3. Each n ≤ 5% of population.
• Three or more — go to Case 7 (homogeneity)
  Requirements: 1. No E is zero. 2. No more than 20% of the E’s are < 5.

Node 300. Categorical data

How many populations are there?

• One — go to Node 350
• Two or more — go to Case 7 (homogeneity)
  Requirements: 1. No E is zero. 2. No more than 20% of the E’s are < 5.

Node 350. Categorical data for one population

How many variables are there?

• One — go to Case 6
  Requirements: 1. No E is zero. 2. No more than 20% of the E’s are < 5.
• Two — go to Case 7 (independence)
  Requirements: 1. No E is zero. 2. No more than 20% of the E’s are < 5.