### Abstract

Statistical hypothesis testing plays a central role in applied research to determine whether theories or expectations are supported by the data or not. Such expectations are often formulated using order constraints. For example an executive board may expect that sales representatives who wear a smart watch will respond faster to their emails than sales representatives who don't wear a smart watch. In addition it may be expected that this difference becomes more pronounced over time because representatives need to learn how to use the smart watch effectively. By translating these expectations into statistical hypotheses with equality and/or order constraints we can determine whether the expectations receive evidence from the data. In this chapter we show how a Bayesian statistical approach can effectively be used for this purpose. This Bayesian approach is more flexible than the traditional p-value test in the sense that multiple hypotheses with equality as well as order constraints can be tested against each other in a direct manner. The methodology can straightforwardly be used by practitioners using the freely downloadable software package BIEMS. An application in a human-computer interaction is used for illustration.

Original language | English |
---|---|

Title of host publication | Modern statistical methods for HCI |

Editors | J Robertson, M Kaptein |

Publisher | Springer |

Pages | 199-227 |

ISBN (Print) | 978-3-319-26631-2 |

DOIs | |

Publication status | Published - 2016 |

### Publication series

Name | Human-Computer Interaction Series |
---|---|

Publisher | SPRINGER |

ISSN (Print) | 1571-5035 |

### Keywords

- MODEL SELECTION
- P-VALUES
- RATIO

### Cite this

*Modern statistical methods for HCI*(pp. 199-227). (Human-Computer Interaction Series). Springer. https://doi.org/10.1007/978-3-319-26633-6_9

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*Modern statistical methods for HCI.*Human-Computer Interaction Series, Springer, pp. 199-227. https://doi.org/10.1007/978-3-319-26633-6_9

**Bayesian testing of constrained hypotheses.** / Mulder, J.

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Scientific

TY - CHAP

T1 - Bayesian testing of constrained hypotheses

AU - Mulder, J.

PY - 2016

Y1 - 2016

N2 - Statistical hypothesis testing plays a central role in applied research to determine whether theories or expectations are supported by the data or not. Such expectations are often formulated using order constraints. For example an executive board may expect that sales representatives who wear a smart watch will respond faster to their emails than sales representatives who don't wear a smart watch. In addition it may be expected that this difference becomes more pronounced over time because representatives need to learn how to use the smart watch effectively. By translating these expectations into statistical hypotheses with equality and/or order constraints we can determine whether the expectations receive evidence from the data. In this chapter we show how a Bayesian statistical approach can effectively be used for this purpose. This Bayesian approach is more flexible than the traditional p-value test in the sense that multiple hypotheses with equality as well as order constraints can be tested against each other in a direct manner. The methodology can straightforwardly be used by practitioners using the freely downloadable software package BIEMS. An application in a human-computer interaction is used for illustration.

AB - Statistical hypothesis testing plays a central role in applied research to determine whether theories or expectations are supported by the data or not. Such expectations are often formulated using order constraints. For example an executive board may expect that sales representatives who wear a smart watch will respond faster to their emails than sales representatives who don't wear a smart watch. In addition it may be expected that this difference becomes more pronounced over time because representatives need to learn how to use the smart watch effectively. By translating these expectations into statistical hypotheses with equality and/or order constraints we can determine whether the expectations receive evidence from the data. In this chapter we show how a Bayesian statistical approach can effectively be used for this purpose. This Bayesian approach is more flexible than the traditional p-value test in the sense that multiple hypotheses with equality as well as order constraints can be tested against each other in a direct manner. The methodology can straightforwardly be used by practitioners using the freely downloadable software package BIEMS. An application in a human-computer interaction is used for illustration.

KW - MODEL SELECTION

KW - P-VALUES

KW - RATIO

U2 - 10.1007/978-3-319-26633-6_9

DO - 10.1007/978-3-319-26633-6_9

M3 - Chapter

SN - 978-3-319-26631-2

T3 - Human-Computer Interaction Series

SP - 199

EP - 227

BT - Modern statistical methods for HCI

A2 - Robertson, J

A2 - Kaptein, M

PB - Springer

ER -