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.

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What type of data do you have?

• Numeric — Each individual contributes a number (discrete or continuous); typical inferences are about means. — go to Node 100
• Binomial — Each person answers a yes/no question, or each individual either has or doesn’t have a particular trait; you count yeses or successes; inferences are about proportions. — go to Node 200
• Categorical — Each individual has a non-numeric trait with multiple possible answers, like hair color or marital status. — 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 samples or populations are there?

• One — This includes the case where you have a fixed reference point in a different population. Example: “In 1990 the mean household income was $39,045. A recent survey of 500 households found a mean of. …” The recent survey is a sample, but the 1990 value is not a sample, just a number to test against. — go to Node 120
• Two, paired data — go to Case 3
  Caution: In paired data, you get two numbers from each individual or from each “team” (twins, husband/wife, etc.)
• Two, unpaired data — go to Case 4
  Caution: In unpaired data, you have two unrelated groups, and you get one number from each person in each group.
• 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
• Yes — go to Case 0
  Caution: Do you really know the standard deviation of the population? When “a survey found a mean of 800 and a standard deviation of 45”, that’s a sample standard deviation just like it’s a sample mean.

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 samples or populations are there?

• One — go to Case 2
  Caution: This includes the case where you have a fixed reference point in a different population. Example: “In 1990, 68% of Americans felt pessimistic about their financial future. A recent survey of 1500 Americans found that 1089 of them. …” The recent survey is a sample, but the 1990 value is not a sample, just a number to test against.
• Two — go to Case 5
• Three or more — go to Case 7
  This is a 2-way table, testing homogeneity or independence.

Node 300. Categorical data

How many populations are there?

• One — go to Node 350
• Two or more — go to Case 7 (test of homogeneity)

Node 350. Categorical data for one population

How many variables are there?

• One — go to Case 6
  Here you have one row or column of numbers, representing the number of individuals with each value of the trait. For example, if the trait is hair color then you would have an observed number of blonds, an observed number of brunets, an observed number of redheads, and so on. You test that against a model of expected percentages or ratios.
• Two — go to Case 7 (independence)
  Here you have a two-way table of one population. The rows represent levels of one trait, such as educational level, and the columns represent a second trait, such as marital status.