BrownMath.com → Statistics → Inferential Cases
Updated 29 Dec 2014

# Inferential Statistics Cases

Summary: This table organizes procedures for inferential statistics into a chart of Cases. (The Case numbers are useful for reference, although they are not standard statistics terminology.) The ones marked with ★ are covered in the textbook, and most of the rest are covered in separate optional Web pages. All links are live in the online version of this page.

See also: While you’re getting used to the cases, practice with the interactive Triage: Which Inferential Stats Case Should I Use?
Case Number
and Description
Pop.
Param.
TI-83/84/89 Procedures
(CI=conf int, HT=hypothesis test, SS=sample size)
All require random sample or randomization, and 10n ≤ N; additional requirements are noted in each case.
NUMERIC DATA
0One pop. mean, known σ
(Do you really know σ?)
μ Required: n ≥ about 30 or normal with no outliers.
CI: `ZInterval`; HT: `Z-Test`
SS: MATH200A part 5
1★One pop. mean, unknown σ μ Required: n ≥ about 30 or normal with no outliers.
CI: `TInterval`; HT: `T-Test`
SS: MATH200A part 5
1SOne pop. standard dev. σ Population must be ND, not just roughly normal.
CI and HT: MATH200B part 5 (not TI-89)
3★Mean difference for paired data μd Required: n ≥ about 30, or differences are normal with no outliers.
CI: `TInterval` using the differences; HT: `T-Test` using the differences
4★Difference of 2 indep. pop. means, unpaired data μ1, μ2 or
μ1−μ2
Required: in each sample, n ≥ about 30 or normal with no outliers.
CI: `2-SampTInt`; HT: `2-SampTTest`
4STwo pop. standard dev. σ12 Both populations must be ND, not just roughly normal.
CI: n/a; HT: `2-SampFTest`
8Equality of several pop means μ1, μ2, μ3, ... CI: n/a; HT: `ANOVA`; see One-Way ANOVA for procedure and requirements.
9Linear correlation coefficient ρ or r Required: for any given x, population of y is ND.
CI and HT: MATH200B part 6
TI 89 HT: `LinRegTTest`
10BSlope of regression line β1 Required: residuals are ND.
CI and HT: MATH200B part 7
TI-89 CI: `LinRegTInt`; TI-89 HT: `LinRegTTest`
10YPredicted values of y μy|xj, yj Required: residuals are ND.
MATH200B part 7 (not TI-89)
YES/NO COUNTS — INFERENCES ABOUT PROPORTIONS
2★One pop. proportion p CI: `1-PropZInt`; requires ≥ 10 successes and ≥ 10 failures in sample.
HT: `1-PropZTest`; requires expected successes npo ≥ 10 and expected failures nnpo ≥ 10.
HT w/ small samples: MATH200A part 3 or `binomcdf`
SS: MATH200A part 5
5★Difference of 2 pop. proportions p1, p2
p1p2
CI: `2-PropZInt`; each sample requires ≥ 10 successes and ≥ 10 failures.
HT: `2-PropZTest`; requires same as CI. If that’s not met, use pooled to test that n1, n1n1, n2, n2n2 are all ≥ 10.
SS: MATH200A part 5
CATEGORY COUNTS — INFERENCES ABOUT MODELS
6★Goodness of fit (GOF) or multinomial none CI: undefined; HT: MATH200A part 6
TI-89 HT: `Chi2 GOF` or Testing Goodness of Fit on TI-89
Required: every expected value ≥ about 5.
7★Independence or homogeneity
(in 2-way table)
none CI: undefined; HT: `χ²-Test` or MATH200A part 7
TI-89 HT: `Chi2 2-way`
Required: every expected value ≥ about 5.

## What’s New

• 29 Dec 2014: Move requirements for numeric data and category counts from the section heads to the individual cases. (Requirements for yes/no counts were already that way.)
• (intervening changes suppressed)
• 10 Nov 2007: New document, inspired by Dabes and Janik [full citation at http://BrownMath.com/swt/sources.htm#so_Dabes1999].