# Triage: Which Inferential Stats Case Should I Use?

Copyright © 2007–2020 by Stan Brown

Copyright © 2007–2020 by Stan Brown

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**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

**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.

**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.)

**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.

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.

**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.

**How many populations are there?**

**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.

**27 July 2013**: Note that binomial data yield counts.- (intervening changes suppressed)
**Nov 2007**: First version on the Web.

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