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**RE: ANCOVA - contrast / hypothesis testing**Dec 10, 2019 11:12 AM | Athina Aruldass -

*University of Cambridge*RE: ANCOVA - contrast / hypothesis testing

Hi again Andrew

Pls ignore my first 2 questions from above (I was very confused and my brain just broke...).

For Q3 - this is the design matrix I eventually came up with :

1 0.3

1 2.2

1 0.3

1 4

1 0.9

columns : 1st - intercept, 2nd - inflammation

contrast : [0 -1] , stat test : t-test (not one sample t-test)

Hyp : testing for negative correlation between inflammation score and FC

I went on to perform this over 3 groups with this design matrix (after being warned that my initial design was rank deficient) :

1 0 0.3

1 -1 2.2

1 0 0.3

1 1 4

1 0 0.9

columns : 1st - intercept, 2nd - group with 3 levels (g1 : -1, g2 : 0, g3 : 1), 3rd - inflammation

contrast : [0 0 -1] , stat test : t-test

Hyp : testing for negative correlation between inflammation score and FC whilst controlling for group

++++++++ Questions +++++++++

1) Are the above design matrices correct ?

2) If I were to add a group*inflammation interaction column for the 3-group design would the design matrix then look like this

1 0 0.3 0

1 -1 2.2 -2.2

1 0 0.3 0

1 1 4 4

1 0 0.9 0

columns : 1st - intercept, 2nd - group with 3 levels (g1 : -1, g2 : 0, g3 : 1), 3rd - inflammation , 4th - group*inflammation

contrast : [0 0 0 -1] , stat test : t-test (not one sample)

If this is correct - what could one then infer / hypothesise for ? I quoted your reply to another query on interaction effect (with 2 groups) posted on the forum -

" The contrast [0 0 0 1] whether the the slope of the age-connectivity relationship is steeper in the group coded with 1, whereas [0 0 0 -1] will tester whether the slope is less steep.

In other words it is testing whether the age effect is stronger or weaker in one of the particular groups. "

(i) Would the above translate to my exp. (with age = inflammation) ?

(ii) Could I infer anything more specific for groups coded 0 and -1 ?

(iii) Would I have to perform a post-hoc pairwise ie. with 2 groups, interaction effect analyses ?

Please and many thanks - Athina.

Pls ignore my first 2 questions from above (I was very confused and my brain just broke...).

For Q3 - this is the design matrix I eventually came up with :

1 0.3

1 2.2

1 0.3

1 4

1 0.9

columns : 1st - intercept, 2nd - inflammation

contrast : [0 -1] , stat test : t-test (not one sample t-test)

Hyp : testing for negative correlation between inflammation score and FC

I went on to perform this over 3 groups with this design matrix (after being warned that my initial design was rank deficient) :

1 0 0.3

1 -1 2.2

1 0 0.3

1 1 4

1 0 0.9

columns : 1st - intercept, 2nd - group with 3 levels (g1 : -1, g2 : 0, g3 : 1), 3rd - inflammation

contrast : [0 0 -1] , stat test : t-test

Hyp : testing for negative correlation between inflammation score and FC whilst controlling for group

++++++++ Questions +++++++++

1) Are the above design matrices correct ?

2) If I were to add a group*inflammation interaction column for the 3-group design would the design matrix then look like this

1 0 0.3 0

1 -1 2.2 -2.2

1 0 0.3 0

1 1 4 4

1 0 0.9 0

columns : 1st - intercept, 2nd - group with 3 levels (g1 : -1, g2 : 0, g3 : 1), 3rd - inflammation , 4th - group*inflammation

contrast : [0 0 0 -1] , stat test : t-test (not one sample)

If this is correct - what could one then infer / hypothesise for ? I quoted your reply to another query on interaction effect (with 2 groups) posted on the forum -

" The contrast [0 0 0 1] whether the the slope of the age-connectivity relationship is steeper in the group coded with 1, whereas [0 0 0 -1] will tester whether the slope is less steep.

In other words it is testing whether the age effect is stronger or weaker in one of the particular groups. "

(i) Would the above translate to my exp. (with age = inflammation) ?

(ii) Could I infer anything more specific for groups coded 0 and -1 ?

(iii) Would I have to perform a post-hoc pairwise ie. with 2 groups, interaction effect analyses ?

Please and many thanks - Athina.

## Threaded View

Title | Author | Date |
---|---|---|

Athina Aruldass |
Dec 5, 2019 | |

Athina Aruldass |
Dec 18, 2019 | |

Andrew Zalesky |
Dec 18, 2019 | |

Athina Aruldass |
Jan 5, 2020 | |

Andrew Zalesky |
Jan 6, 2020 | |

Athina Aruldass |
Dec 10, 2019 | |

Andrew Zalesky |
Dec 12, 2019 | |

Athina Aruldass |
Dec 8, 2019 | |

Andrew Zalesky |
Dec 6, 2019 | |