Testing hypotheses for differences between linear regression lines

Stanley J. Zarnoch

doi:10.2737/SRS-RN-17

Treesearch

Testing hypotheses for differences between linear regression lines

Informally Refereed

Authors:

Stanley J. Zarnoch

Year:

2009

Type:

Research Note

Station:

Southern Research Station

DOI:

https://doi.org/10.2737/SRS-RN-17

Source:

Res. Note SRS-17. Asheville, NC: U.S. Department of Agriculture, Forest Service, Southeastern Forest Experiment Station. 20 p.

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Download (PDF 4.26 MB): https://research.fs.usda.gov/download/treesearch/33218.pdf

Abstract

Five hypotheses are identified for testing differences between simple linear regression lines. The distinctions between these hypotheses are based on a priori assumptions and illustrated with full and reduced models. The contrast approach is presented as an easy and complete method for testing for overall differences between the regressions and for making pairwise comparisons. Use of the Bonferroni adjustment to ensure a desired experimentwise type I error rate is emphasized. SAS software is used to illustrate application of these concepts to an artificial simulated dataset. The SAS code is provided for each of the five hypotheses and for the contrasts for the general test and all possible specific tests.

Keywords

Contrasts, dummy variables, F-test, intercept, SAS, slope, test of conditional error

Citation

Zarnoch, Stanley J. 2009. Testing hypotheses for differences between linear regression lines. Res. Note SRS-17. Asheville, NC: U.S. Department of Agriculture, Forest Service, Southeastern Forest Experiment Station. 20 p.