TC3 → Stan Brown → Statistics → Inferential Cases
Updated 23 Mar 2014 (What’s New?)

Inferential Statistics Cases

Copyright © 2007–2014 by Stan Brown, Oak Road Systems

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.
NUMERIC DATA
Required: n ≥ about 30 or normal with no outliers.
0One pop. mean, known σ
(Do you really know σ?)
μ CI: ZInterval; HT: Z-Test
SS: MATH200A part 5
1★One pop. mean, unknown σ μ CI: TInterval; HT: T-Test
SS: MATH200A part 5
1SOne pop. standard dev. σ CI and HT: MATH200B part 5 (not TI-89)
3★Mean difference for paired data μd Requirements apply to the differences.
CI: TInterval using the differences; HT: T-Test using the differences
4★Difference of 2 indep. pop. means, unpaired data μ1, μ2
μ1−μ2
Requirements apply to each sample.
CI: 2-SampTInt; HT: 2-SampTTest
4STwo pop. standard dev. σ12 CI: n/a; HT: 2-SampFTest
8Equality of several pop means μ1, μ2, μ3, ... CI: undefined; HT: ANOVA; see also One-Way ANOVA
9Linear correlation coefficient ρ or r CI and HT: MATH200B part 6
TI 89 HT: LinRegTTest
10BSlope of regression line β1 CI and HT: MATH200B part 7
TI-89 CI: LinRegTInt; TI-89 HT: LinRegTTest
10YPredicted values of y μy|xj, yj MATH200B part 7 (not TI-89)
YES/NO COUNTS — INFERENCES ABOUT PROPORTIONS
2★One pop. proportion p CI requires ≥ 10 successes and ≥ 10 failures in sample
CI: 1-PropZInt
HT requires expected successes npo ≥ 10 and failures nnpo ≥ 10
HT: 1-PropZTest
HT w/ small samples: MATH200A part 3 or binomcdf
SS: MATH200A part 5
5★Difference of 2 pop. proportions p1, p2
p1p2
CI requires ≥ 10 successes and ≥ 10 failures in each sample
CI: 2-PropZInt
HT: 2-PropZTest
HT requires ≥ 10 successes and ≥ 10 failures in each sample, or n1, n1n1, n2, n2n2 all ≥ 10 using pooled
SS: MATH200A part 5
CATEGORY COUNTS — INFERENCES ABOUT MODELS
Required: all expected values ≥ about 5.
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
7★Independence or homogeneity
(in 2-way table)
none CI: undefined; HT: χ²-Test or MATH200A part 7
TI-89 HT: Chi2 2-way

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