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Chapter 10

PSYC 300B Chapter Notes - Chapter 10: Statistical Hypothesis Testing


Department
Psychology
Course Code
PSYC 300B
Professor
David Medler
Chapter
10

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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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