Analysis of covariance | Wikipedia audio article

This is an audio version of the Wikipedia Article:
en.wikipedia.org/wiki/Analysis_of_covariance


00:00:40 1 Uses
00:00:54 1.1 Increase power
00:01:21 1.2 Adjusting preexisting differences
00:01:49 2 Assumptions
00:02:16 2.1 Assumption 1: linearity of regression
00:02:43 2.2 Assumption 2: homogeneity of error variances
00:03:11 2.3 Assumption 3: independence of error terms
00:03:38 2.4 Assumption 4: normality of error terms
00:04:05 2.5 Assumption 5: homogeneity of regression slopes
00:04:33 3 Conducting an ANCOVA
00:04:46 3.1 Test multicollinearity
00:05:14 3.2 Test the homogeneity of variance assumption
00:05:41 3.3 Test the homogeneity of regression slopes assumption
00:06:08 3.4 Run ANCOVA analysis
00:06:36 3.5 Follow-up analyses
00:07:03 4 Power considerations
00:07:30 5 See also



Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago.

Learning by listening is a great way to:
increases imagination and understanding
improves your listening skills
improves your own spoken accent
learn while on the move
reduce eye strain

Now learn the vast amount of general knowledge available on Wikipedia through audio (audio article). You could even learn subconsciously by playing the audio while you are sleeping! If you are planning to listen a lot, you could try using a bone conduction headphone, or a standard speaker instead of an earphone.

Listen on Google Assistant through Extra Audio:
assistant.google.com/services/invoke/uid/0000001a1…
Other Wikipedia audio articles at:
youtube.com/results?search_query=wikipedia+tts
Upload your own Wikipedia articles through:
github.com/nodef/wikipedia-tts
Speaking Rate: 0.7155195924224225
Voice name: en-GB-Wavenet-D


"I cannot teach anybody anything, I can only make them think."
Socrates


SUMMARY
=======
Analysis of covariance (ANCOVA) is a general linear model which blends ANOVA and regression. ANCOVA evaluates whether the means of a dependent variable (DV) are equal across levels of a categorical independent variable (IV) often called a treatment, while statistically controlling for the effects of other continuous variables that are not of primary interest, known as covariates (CV) or nuisance variables. Mathematically, ANCOVA decomposes the variance in the DV into variance explained by the CV(s), variance explained by the categorical IV, and residual variance. Intuitively, ANCOVA can be thought of as 'adjusting' the DV by the group means of the CV(s).The ANCOVA model assumes a linear relationship between the response (DV) and covariate (CV):





y

i
j


=
μ
+

τ

i


+

B

(

x

i
j


−


x
¯


)
+

ϵ

i
j


.


{\displaystyle y_{ij}=\mu +\tau _{i}+\mathrm {B} (x_{ij}-{\overline {x}})+\epsilon _{ij}.}

In this equation, the DV,




y

i
j




{\displaystyle y_{ij}}
is the jth observation under the ith categorical group; the CV,




x

i
j




{\displaystyle x_{ij}}
is the jth observation of the covariate under the ith group. Variables in the model that are derived from the observed data are



μ


{\displaystyle \mu }
(the grand mean) and





x
¯




{\displaystyle {\overline {x}}}
(the global mean for covariate



x


{\displaystyle x}
). The variables to be fitted are




τ

i




{\displaystyle \tau _{i}}
(the effect of the ith level of the IV),



B


{\displaystyle B}
(the slope of the line) and




ϵ

i
j




{\displaystyle \epsilon _{ij}}
(the associated unobserved error term for the jth observation in the ith group).
Under this specification, the a categorical treatment effects sum to zero




(


∑

i


a



τ

...