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MeanDifferenceCI

MeanDifferenceCI[list1,list2]

gives a confidence interval for the difference between the population means estimated from list1 and list2.

Details and Options

  • To use MeanDifferenceCI, you first need to load the Hypothesis Testing Package using Needs["HypothesisTesting`"].
  • MeanDifferenceCI[list1,list2] gives a confidence interval {min,max} centered at Mean[list1]-Mean[list2].
  • MeanDifferenceCI is based on a normal distribution if the population variances are assumed known.
  • If the variances for the two populations are assumed equal and unknown, the interval is based on Student's distribution with Length[list1]+Length[list2]-2 degrees of freedom.
  • If the population variances are not assumed known and not assumed equal, Welch's approximation for the degrees of freedom is used.
  • The following options can be given:
  • ConfidenceLevel 0.95probability associated with a confidence interval
    EqualVariances Falsewhether the unknown population variances are assumed equal
    KnownVariance Nonelist of variances of each population

Examples

open allclose all

Basic Examples  (1)Summary of the most common use cases

In[1]:=1
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https://wolfram.com/xid/0b4vblefar9g96-ngy175

The 95% confidence interval for the difference in two population means:

In[2]:=2
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https://wolfram.com/xid/0b4vblefar9g96-s6e
Out[2]=2

Options  (3)Common values & functionality for each option

ConfidenceLevel  (1)

In[1]:=1
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https://wolfram.com/xid/0b4vblefar9g96-70fdq

The 99% confidence interval:

In[2]:=2
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https://wolfram.com/xid/0b4vblefar9g96-oh6kdq
Out[2]=2

EqualVariances  (1)

In[1]:=1
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https://wolfram.com/xid/0b4vblefar9g96-uhrp1

A confidence interval assuming equal but unknown variances:

In[2]:=2
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https://wolfram.com/xid/0b4vblefar9g96-jvio5q
Out[2]=2

KnownVariance  (1)

In[1]:=1
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https://wolfram.com/xid/0b4vblefar9g96-efvlin

A confidence interval assuming known variances:

In[2]:=2
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https://wolfram.com/xid/0b4vblefar9g96-km8zxv
Out[2]=2
Wolfram Research (2007), MeanDifferenceCI, Wolfram Language function, https://reference.wolfram.com/language/HypothesisTesting/ref/MeanDifferenceCI.html.
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Wolfram Research (2007), MeanDifferenceCI, Wolfram Language function, https://reference.wolfram.com/language/HypothesisTesting/ref/MeanDifferenceCI.html.

Text

Wolfram Research (2007), MeanDifferenceCI, Wolfram Language function, https://reference.wolfram.com/language/HypothesisTesting/ref/MeanDifferenceCI.html.

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Wolfram Research (2007), MeanDifferenceCI, Wolfram Language function, https://reference.wolfram.com/language/HypothesisTesting/ref/MeanDifferenceCI.html.

CMS

Wolfram Language. 2007. "MeanDifferenceCI." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/HypothesisTesting/ref/MeanDifferenceCI.html.

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Wolfram Language. 2007. "MeanDifferenceCI." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/HypothesisTesting/ref/MeanDifferenceCI.html.

APA

Wolfram Language. (2007). MeanDifferenceCI. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/HypothesisTesting/ref/MeanDifferenceCI.html

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Wolfram Language. (2007). MeanDifferenceCI. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/HypothesisTesting/ref/MeanDifferenceCI.html

BibTeX

@misc{reference.wolfram_2025_meandifferenceci, author="Wolfram Research", title="{MeanDifferenceCI}", year="2007", howpublished="\url{https://reference.wolfram.com/language/HypothesisTesting/ref/MeanDifferenceCI.html}", note=[Accessed: 03-April-2025 ]}

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@misc{reference.wolfram_2025_meandifferenceci, author="Wolfram Research", title="{MeanDifferenceCI}", year="2007", howpublished="\url{https://reference.wolfram.com/language/HypothesisTesting/ref/MeanDifferenceCI.html}", note=[Accessed: 03-April-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_meandifferenceci, organization={Wolfram Research}, title={MeanDifferenceCI}, year={2007}, url={https://reference.wolfram.com/language/HypothesisTesting/ref/MeanDifferenceCI.html}, note=[Accessed: 03-April-2025 ]}

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@online{reference.wolfram_2025_meandifferenceci, organization={Wolfram Research}, title={MeanDifferenceCI}, year={2007}, url={https://reference.wolfram.com/language/HypothesisTesting/ref/MeanDifferenceCI.html}, note=[Accessed: 03-April-2025 ]}