$\backslash$#$\backslash$#$\backslash$#$\backslash$# Based solely on the means, it seems that the participants without paranoia who power$-$posed felt more powerful than all others. Participants with paranoia who did not power$-$pose felt least powerful. Are these differences statistically significant? Let's run the ANOVA!

$```$

$``\{$r$\}$

fANOVA$\_$results $=$ aov$($Feeling$\_$of$\_$Power ~ Pose$*$Paranoia$,$ DATA$\_$A$7)$

summary$($fANOVA$\_$results$)$

$```$

#### Question $3.$ Which effects are statistically significant?

#### Question $4.$ Calculate the standardized effect size for each Factor and the

interaction $($by hand$).\backslash$#$\backslash$#$\backslash$#$\backslash$# Question $5.$ Based on the guidelines for standardized effect sizes $($e$.$g$.,$ small, large$),$ how would you describe each of these three effects?

Factor A:

Factor B:

Interaction: $```$

Tukey multiple comparisons of means

$95\%$ family$-$wise confidence level

Fit: aov$($formula $=$ Feeling$\_$of$\_$Power ~ Pose $*$ Paranoia, data $=$ DATA$\_$A$7)$

$Pose

$```$

$```$

$Paranoia

diff lwr upr p adj

Paranoid$-$Non$\_$Paranoid $-1\mathrm{.}55-1\mathrm{.}757702-1\mathrm{.}3422980$

$$`$Pose:Paranoia$`$

diff lwr lor upr

Power:Non$\_$Paranoid$-$Non$\_$Power:Non$\_$Paranoid $1\mathrm{.}441\mathrm{.}05406081\mathrm{.}8259392$

Non$\_$Power:Paranoid$-$Non$\_$Power:Non$\_$Paranoid $-0\mathrm{.}94-1\mathrm{.}3259392-0\mathrm{.}5540608$

Power:Paranoid$-$Non$\_$Power:Non$\_$Paranoid $\backslash -0\mathrm{.}72-1\mathrm{.}1059392-0\mathrm{.}3340608$

Non$\_$Power:Paranoid$-$Power:Non$\_$Paranoid $-2\mathrm{.}38-2\mathrm{.}7659392-1\mathrm{.}9940608$

Power:Paranoid$-$Power:Non$\_$Par$$noid $-2\mathrm{.}16-2\mathrm{.}5459392-1\mathrm{.}7740608$

Power:Paranoid$-$Non$\_$Power:Paranoid $0\mathrm{.}22-0\mathrm{.}16593920\mathrm{.}6059392$

p adj

Power:Non$\_$Paranoid$-$Non$\_$Power:Non$\_$Paranoid $0\mathrm{.}0000000$

Non$\_$Power:Paranoid$-$Non$\_$Power:Non$\_$Paranoid $0\mathrm{.}0000000$

Power:Paranoid$-$Non$\_$Power:Non$\_$Paranoid $0\mathrm{.}0000160$

Non$\_$Power:Paranoid$-$Power:Non$\_$Paranoid $0\mathrm{.}0000000$

Power:Paranoid$-$Power:Non$\_$Par$$noid $0\mathrm{.}0000000$

Power:Paranoid$-$Non$\_$Power:Paranoid $0\mathrm{.}4533005$

$```\backslash$#$\backslash$#$\backslash$#$\backslash$# Question $6.$ The post$-$hoc test above provides pairwise comparisons for each factor $($i$.$e$.$ the main effects$)$ as well as for the interaction. However, In this case, we should focus solely on the interaction tests, and not on the marginal mean comparison. Why?

$\backslash$#$\backslash$#$\backslash$#$\backslash$# Question $7.$ Are any of the pairwise comparisons NOT statistically significant? Provide the p$-$value.