This

**preview**shows half of the first page. to view the full**2 pages of the document.**•communicating outcomes — there are 3 ways to examine &/or interpret

outcomes from an analysis:

(i) hypothesis testing — determine statistical vs. practical signiﬁcance

(ii) visual (graphic) display — see if there is pattern of the participant’s

behaviour across levels of factors (best to show interactions)

-interactions can overwhelm the looks of our main effect, thus you

need to look both at the graph & data

(iii) verbal description of relationship between factors — describe

relationships in terms of:

(a) additive or non-additive

(b) independent or dependent

(c) difference between differences

•points to remember:

(i) values in the cells of the data matrix are the means for each unique

experimental conditions

-the graphic ﬁgure displays these cell means, not values for X

(ii) you need at least 4 cells means to create a ﬁgure or table

-an APA-type graphic ﬁgure is required only if the interaction in

the study is statistically signiﬁcant

(iii) interpret main effects using the marginal means

-if marginal means for a speciﬁc factor are not statistically different,

then the main effect for that factor is not signiﬁcant !

(i.e. the levels of that factor are not differentially inﬂuencing the

participant’s behaviours)

-if marginal means for a speciﬁc factor are statistically different,

then there may be a main effect!

(i.e. participants may be responding to one level of the factor

differential than they are to the other level(s) of the same factor)

(iv) to interpret a data matrix for the presence of an interaction, look at

the values in the diagonals of the cell means

(v) hypothesis testing is the only way to conﬁrm the presence of a

signiﬁcant treatment effect

-data matrix & ﬁgures only provide a description

•interpreting data — for main effects &/or interactions:

(i) no main effect or interactions — there is no signiﬁant treatment

effects or interaction, so performance was the same in all conditions

-only when means are exactly = can we make a sure conclusion

-column effect — a1 = a2

-row effect — b1 = b2

-interaction — (a1b1 + a2b2) ÷ 2 = (a1b1 + a2b2) ÷ 2

(ii) column main effect — look for…

-a difference between the column marginal means

-angle of lines relative to the X-axis

-lines are parallel to each other

-if the column marginals for a1 - a2 ≠ 0, it is possible that the main

effect is signiﬁcant

-*the size of the difference needed for statistical signiﬁcance

depends on the data*

(iii) row main effect — look for…

-a difference between the row marginal means

-distance between the 2 lines on the graph

-lines are parallel to each other & to the X-axis

-if the row marginals for b1 - b2 ≠ 0, it is possible that the main

effect is signiﬁcant

(iv) interaction — look for…

-a difference between the mean values of diagonals

-the lines of the graph are at an angle to each other

-lines are not parallel to each other or the axis

-if [(a1b1 + a2b2) ÷ 2 - (a1b1 + a2b2) ÷ 2] ≠ 0, then it is possible that

the interaction is signiﬁcant

(v) 2 main effect & no interaction — when…

-a1 - a2 ≠ 0, there may be signiﬁcant column main effect

-b1 - b2 ≠ 0, there may be signiﬁcant row main effect

-the mean difference between the diagonals = 0, then the

interaction is not statistically signiﬁcant

(vi) column main effect & interaction — when…

-a1 - a2 ≠ 0, there may be signiﬁcant column main effect

-b1 - b2 = 0, there is no signiﬁcant row main effect

-if the mean difference between the diagonals ≠ 0, there may be

an interaction

(vii) row main effect & interaction — when…

-b1 - b2 ≠ 0, there may be signiﬁcant row main effect

-a1 - a2 = 0, there is no signiﬁcant column main effect

-if the mean difference between the diagonals ≠ 0, there may be

an interaction

(viii) 2 main effects & interaction — when…

-b1 - b2 ≠ 0, there may be signiﬁcant row main effect

-a1 - a2 ≠ 0, there may be signiﬁcant column main effect

-if the mean difference between the diagonals ≠ 0, there may be

an interaction

•interpretation — interactions vs. main effects:

-main effects average values across the individual cell means → may

obscure information & mislead interpretation

-in some situations, you may have a signiﬁcant interaction, but it may not

be very meaningful

-when you have no interaction between factors → the value for F(obs) for

the interaction was not signiﬁcant

•the change in values across trials is therefore consistent & people are

scoring ~same across all levels of your factor

•you can therefore generalize the effect of one factor on the other

•no interaction → effects are additive

•we have independence among the factors

•the differences between diagonals = 0

-if the variables can relate to each other without interacting

-when you have a signiﬁcant interaction → the value for F(obs) for the

interaction was signiﬁcant

•the difference in preference across trials/levels is not consistent

•participant’s behaviour varies as a function of both factors

•interaction → effects are non-additive or multiplicative

•we have dependence among the factors

•the differences between diagonals ≠ 0

PSYC 300B - Chapter 10: Interpreting Effects in Factorial Designs

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