.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/statistics/ANCOVA.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code. .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_statistics_ANCOVA.py: ANCOVA ====== Analysis of covariance for univariate data. Example 1 --------- Based on [1]_, `Exercises `_ (page 8). .. GENERATED FROM PYTHON SOURCE LINES 14-28 .. code-block:: Python # Author: Christian Brodbeck from eelbrain import * y = Var([2, 3, 3, 4, 3, 4, 5, 6, 1, 2, 1, 2, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 2, 3], name="Growth Rate") genotype = Factor(range(6), repeat=4, name="Genotype") hours = Var([8, 12, 16, 24], tile=6, name="Hours") .. GENERATED FROM PYTHON SOURCE LINES 29-30 Show the model .. GENERATED FROM PYTHON SOURCE LINES 30-32 .. code-block:: Python print(hours * genotype) .. rst-class:: sphx-glr-script-out .. code-block:: none intercept Hours Genotype Hours x Genotype ----------------------------------------------------------------------------- 1 8 1 0 0 0 0 8 0 0 0 0 1 12 1 0 0 0 0 12 0 0 0 0 1 16 1 0 0 0 0 16 0 0 0 0 1 24 1 0 0 0 0 24 0 0 0 0 1 8 0 1 0 0 0 0 8 0 0 0 1 12 0 1 0 0 0 0 12 0 0 0 1 16 0 1 0 0 0 0 16 0 0 0 1 24 0 1 0 0 0 0 24 0 0 0 1 8 0 0 1 0 0 0 0 8 0 0 1 12 0 0 1 0 0 0 0 12 0 0 1 16 0 0 1 0 0 0 0 16 0 0 1 24 0 0 1 0 0 0 0 24 0 0 1 8 0 0 0 1 0 0 0 0 8 0 1 12 0 0 0 1 0 0 0 0 12 0 1 16 0 0 0 1 0 0 0 0 16 0 1 24 0 0 0 1 0 0 0 0 24 0 1 8 0 0 0 0 1 0 0 0 0 8 1 12 0 0 0 0 1 0 0 0 0 12 1 16 0 0 0 0 1 0 0 0 0 16 1 24 0 0 0 0 1 0 0 0 0 24 1 8 0 0 0 0 0 0 0 0 0 0 1 12 0 0 0 0 0 0 0 0 0 0 1 16 0 0 0 0 0 0 0 0 0 0 1 24 0 0 0 0 0 0 0 0 0 0 .. GENERATED FROM PYTHON SOURCE LINES 33-34 Estimate the ANCOVA: .. GENERATED FROM PYTHON SOURCE LINES 34-36 .. code-block:: Python test.ANOVA(y, hours * genotype) .. raw:: html

	SS	df	MS	F	p
Hours	7.06	1	7.06	54.90^***	< .001
Genotype	27.87	5	5.57	43.36^***	< .001
Hours x Genotype	3.15	5	0.63	4.90^*	.011
Residuals	1.54	12	0.13
Total	39.62	23

.. GENERATED FROM PYTHON SOURCE LINES 37-38 Plot the slopes: .. GENERATED FROM PYTHON SOURCE LINES 38-41 .. code-block:: Python p = plot.Regression(y, hours, genotype) .. image-sg:: /auto_examples/statistics/images/sphx_glr_ANCOVA_001.png :alt: ANCOVA :srcset: /auto_examples/statistics/images/sphx_glr_ANCOVA_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 42-45 Example 2 --------- Based on [2]_ (p. 118-20) .. GENERATED FROM PYTHON SOURCE LINES 45-56 .. code-block:: Python y = Var([16, 7, 11, 9, 10, 11, 8, 8, 16, 10, 13, 10, 10, 14, 11, 12, 24, 29, 10, 22, 25, 28, 22, 24]) cov = Var([9, 5, 6, 4, 6, 8, 3, 5, 8, 5, 6, 5, 3, 6, 4, 6, 5, 8, 3, 4, 6, 9, 4, 5], name='cov') a = Factor([1, 2, 3], repeat=8, name='A') .. GENERATED FROM PYTHON SOURCE LINES 57-58 Full model, with interaction .. GENERATED FROM PYTHON SOURCE LINES 58-61 .. code-block:: Python plot.Regression(y, cov, a) test.ANOVA(y, cov * a) .. image-sg:: /auto_examples/statistics/images/sphx_glr_ANCOVA_002.png :alt: ANCOVA :srcset: /auto_examples/statistics/images/sphx_glr_ANCOVA_002.png :class: sphx-glr-single-img .. raw:: html

	SS	df	MS	F	p
cov	199.54	1	199.54	32.93^***	< .001
A	807.82	2	403.91	66.66^***	< .001
cov x A	19.39	2	9.70	1.60	.229
Residuals	109.07	18	6.06
Total	1112.00	23

.. GENERATED FROM PYTHON SOURCE LINES 62-63 Drop interaction term .. GENERATED FROM PYTHON SOURCE LINES 63-67 .. code-block:: Python plot.Regression(y, cov) test.ANOVA(y, a + cov) .. image-sg:: /auto_examples/statistics/images/sphx_glr_ANCOVA_003.png :alt: ANCOVA :srcset: /auto_examples/statistics/images/sphx_glr_ANCOVA_003.png :class: sphx-glr-single-img .. raw:: html

	SS	df	MS	F	p
A	807.82	2	403.91	62.88^***	< .001
cov	199.54	1	199.54	31.07^***	< .001
Residuals	128.46	20	6.42
Total	1112.00	23

.. GENERATED FROM PYTHON SOURCE LINES 68-71 ANCOVA with multiple covariates ------------------------------- Based on [3]_, p. 139. .. GENERATED FROM PYTHON SOURCE LINES 71-76 .. code-block:: Python # Load data form a text file ds = load.txt.tsv('Fox_Prestige_data.txt', delimiter=' ', skipinitialspace=True) ds.head() .. raw:: html

#	id	education	income	women	prestige	census	type
0	GOV.ADMINISTRATORS	13.11	12351	11.16	68.8	1113	prof
1	GENERAL.MANAGERS	12.26	25879	4.02	69.1	1130	prof
2	ACCOUNTANTS	12.77	9271	15.7	63.4	1171	prof
3	PURCHASING.OFFICERS	11.42	8865	9.11	56.8	1175	prof
4	CHEMISTS	14.62	8403	11.68	73.5	2111	prof
5	PHYSICISTS	15.64	11030	5.13	77.6	2113	prof
6	BIOLOGISTS	15.09	8258	25.65	72.6	2133	prof
7	ARCHITECTS	15.44	14163	2.69	78.1	2141	prof
8	CIVIL.ENGINEERS	14.52	11377	1.03	73.1	2143	prof
9	MINING.ENGINEERS	14.64	11023	0.94	68.8	2153	prof

.. GENERATED FROM PYTHON SOURCE LINES 77-81 .. code-block:: Python # Variable summary ds.summary() .. raw:: html

Key	Type	Values
id	Factor	GOV.ADMINISTRATORS, GENERAL.MANAGERS, ACCOUNTANTS... (102 cells)
education	Var	6.38 - 15.97
income	Var	611 - 25879
women	Var	0 - 97.51
prestige	Var	14.8 - 87.2
census	Var	1113 - 9517
type	Factor	prof:31, bc:44, wc:23, NA:4

Fox_Prestige_data.txt: 102 cases

.. GENERATED FROM PYTHON SOURCE LINES 82-90 .. code-block:: Python # Exclude cases with missing type ds2 = ds[ds['type'] != 'NA'] # ANOVA test.ANOVA('prestige', '(income + education) * type', data=ds2) .. raw:: html

	SS	df	MS	F	p
income	1131.90	1	1131.90	28.35^***	< .001
education	1067.98	1	1067.98	26.75^***	< .001
type	591.16	2	295.58	7.40^**	.001
income x type	951.77	2	475.89	11.92^***	< .001
education x type	238.40	2	119.20	2.99	.056
Residuals	3552.86	89	39.92
Total	28346.88	97

.. GENERATED FROM PYTHON SOURCE LINES 91-96 References ---------- .. [1] Crawley, M. J. (2005). Statistics: an introduction using R. J Wiley. .. [2] Rutherford, A. (2001). Introducing ANOVA and ANCOVA: A GLM Approach. Sage. .. [3] Fox, J. (2008) Applied Regression Analysis and Generalized Linear Models, Second Edition. Sage. .. _sphx_glr_download_auto_examples_statistics_ANCOVA.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: ANCOVA.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: ANCOVA.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: ANCOVA.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_