3.1 Primary analysis
3.1.1 Frequency analysis
## Frequency Statistics:
## ───────────
## N %
## ───────────
## 0 264 49.2
## 1 273 50.8
## ───────────
## Total N = 537## Frequency Statistics:
## ────────────
## N %
## ────────────
## 11 136 25.3
## 12 134 25.0
## 14 139 25.9
## 15 128 23.8
## ────────────
## Total N = 5373.1.2 ICC and RWG
##
## ------ Sample Size Information ------
##
## Level 1: N = 537 observations ("Manipulation")
## Level 2: K = 154 groups ("B.ID")
##
## n (group sizes)
## Min. 1.000
## Median 4.000
## Mean 3.487
## Max. 4.000
##
## ------ ICC(1), ICC(2), and rWG ------
##
## ICC variable: "Manipulation"
##
## ICC(1) = 0.000 (non-independence of data)
## ICC(2) = 0.000 (reliability of group means)
##
## rWG variable: "Manipulation"
##
## rWG (within-group agreement for single-item measures)
## ────────────────────────────────────────────────────
## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## ────────────────────────────────────────────────────
## rWG 0.000 0.000 0.000 0.028 0.000 1.000 12.000
## ────────────────────────────────────────────────────##
## ------ Sample Size Information ------
##
## Level 1: N = 493 observations ("WP.CreativeProcessEngagementV")
## Level 2: K = 146 groups ("B.ID")
##
## n (group sizes)
## Min. 1.000
## Median 4.000
## Mean 3.377
## Max. 4.000
##
## ------ ICC(1), ICC(2), and rWG ------
##
## ICC variable: "WP.CreativeProcessEngagementV"
##
## ICC(1) = 0.784 (non-independence of data)
## ICC(2) = 0.915 (reliability of group means)
##
## rWG variable: "WP.CreativeProcessEngagementV"
##
## rWG (within-group agreement for single-item measures)
## ────────────────────────────────────────────────────
## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## ────────────────────────────────────────────────────
## rWG 0.000 0.893 0.965 0.893 0.992 1.000 10.000
## ────────────────────────────────────────────────────3.1.3 Manipulation check
3.1.3.1 MLM
Manipulation.MLM= lmer(WA.GraceV~Manipulation + (1|B.ID), na.action = na.exclude, data = data.M, control=lmerControl(optimizer="bobyqa"))
HLM_summary(Manipulation.MLM)##
## Hierarchical Linear Model (HLM)
## (also known as) Linear Mixed Model (LMM)
## (also known as) Multilevel Linear Model (MLM)
##
## Model Information:
## Formula: WA.GraceV ~ Manipulation + (1 | B.ID)
## Level-1 Observations: N = 524
## Level-2 Groups/Clusters: B.ID, 154
##
## Model Fit:
## AIC = 931.121
## BIC = 948.167
## R_(m)² = 0.00003 (Marginal R²: fixed effects)
## R_(c)² = 0.73123 (Conditional R²: fixed + random effects)
## Omega² = NA (= 1 - proportion of unexplained variance)
##
## ANOVA Table:
## ────────────────────────────────────────────────────────
## Sum Sq Mean Sq NumDF DenDF F p
## ────────────────────────────────────────────────────────
## Manipulation 0.01 0.01 1.00 374.36 0.06 .813
## ────────────────────────────────────────────────────────
##
## Fixed Effects:
## Unstandardized Coefficients (b or γ):
## Outcome Variable: WA.GraceV
## ─────────────────────────────────────────────────────────────────
## b/γ S.E. t df p [95% CI of b/γ]
## ─────────────────────────────────────────────────────────────────
## (Intercept) 3.820 (0.061) 62.23 180.5 <.001 *** [ 3.699, 3.941]
## Manipulation 0.009 (0.037) 0.24 374.4 .813 [-0.064, 0.082]
## ─────────────────────────────────────────────────────────────────
## 'df' is estimated by Satterthwaite approximation.
##
## Standardized Coefficients (β):
## Outcome Variable: WA.GraceV
## ────────────────────────────────────────────────────────────────
## β S.E. t df p [95% CI of β]
## ────────────────────────────────────────────────────────────────
## Manipulation 0.006 (0.024) 0.24 374.4 .813 [-0.041, 0.052]
## ────────────────────────────────────────────────────────────────
##
## Random Effects:
## ──────────────────────────────────────────
## Cluster K Parameter Variance ICC
## ──────────────────────────────────────────
## B.ID 154 (Intercept) 0.46889 0.73122
## Residual 0.17235
## ──────────────────────────────────────────3.1.4 T-test
##
## ====== ANOVA (Within-Subjects Design) ======
##
## Descriptives:
## ─────────────────────────────────
## "Manipulation" Mean S.D. n
## ─────────────────────────────────
## Manipulation0 3.833 (0.715) 125
## Manipulation1 3.853 (0.699) 125
## ─────────────────────────────────
## Total sample size: N = 154
##
## ANOVA Table:
## Dependent variable(s): WA.GraceV
## Between-subjects factor(s): –
## Within-subjects factor(s): Manipulation
## Covariate(s): –
## ──────────────────────────────────────────────────────────────────────────
## MS MSE df1 df2 F p η²p [90% CI of η²p] η²G
## ──────────────────────────────────────────────────────────────────────────
## Manipulation 0.025 0.080 1 124 0.313 .577 .003 [.000, .037] .000
## ──────────────────────────────────────────────────────────────────────────
## MSE = mean square error (the residual variance of the linear model)
## η²p = partial eta-squared = SS / (SS + SSE) = F * df1 / (F * df1 + df2)
## ω²p = partial omega-squared = (F - 1) * df1 / (F * df1 + df2 + 1)
## η²G = generalized eta-squared (see Olejnik & Algina, 2003)
## Cohen’s f² = η²p / (1 - η²p)
##
## Levene’s Test for Homogeneity of Variance:
## No between-subjects factors. No need to do the Levene’s test.
##
## Mauchly’s Test of Sphericity:
## The repeated measures have only two levels. The assumption of sphericity is always met.emmip(Manipulation.T, ~Manipulation, CIs=TRUE, style = "factor", linearg = list(), CIarg = list( col = "grey",size = 20), dotarg = list(size = 2)) +
ggplot2::theme_bw()
3.1.5 Main effect
Main= lmer(WP.CreativeProcessEngagementV~Manipulation + (1|B.ID), na.action = na.exclude, data = data.M, control=lmerControl(optimizer="bobyqa"))
HLM_summary(Main)##
## Hierarchical Linear Model (HLM)
## (also known as) Linear Mixed Model (LMM)
## (also known as) Multilevel Linear Model (MLM)
##
## Model Information:
## Formula: WP.CreativeProcessEngagementV ~ Manipulation + (1 | B.ID)
## Level-1 Observations: N = 493
## Level-2 Groups/Clusters: B.ID, 146
##
## Model Fit:
## AIC = 723.366
## BIC = 740.168
## R_(m)² = 0.00006 (Marginal R²: fixed effects)
## R_(c)² = 0.78386 (Conditional R²: fixed + random effects)
## Omega² = NA (= 1 - proportion of unexplained variance)
##
## ANOVA Table:
## ────────────────────────────────────────────────────────
## Sum Sq Mean Sq NumDF DenDF F p
## ────────────────────────────────────────────────────────
## Manipulation 0.02 0.02 1.00 350.47 0.13 .718
## ────────────────────────────────────────────────────────
##
## Fixed Effects:
## Unstandardized Coefficients (b or γ):
## Outcome Variable: WP.CreativeProcessEngagementV
## ─────────────────────────────────────────────────────────────────
## b/γ S.E. t df p [95% CI of b/γ]
## ─────────────────────────────────────────────────────────────────
## (Intercept) 3.305 (0.059) 56.36 169.1 <.001 *** [ 3.189, 3.421]
## Manipulation 0.011 (0.032) 0.36 350.5 .718 [-0.051, 0.074]
## ─────────────────────────────────────────────────────────────────
## 'df' is estimated by Satterthwaite approximation.
##
## Standardized Coefficients (β):
## Outcome Variable: WP.CreativeProcessEngagementV
## ────────────────────────────────────────────────────────────────
## β S.E. t df p [95% CI of β]
## ────────────────────────────────────────────────────────────────
## Manipulation 0.008 (0.022) 0.36 350.5 .718 [-0.035, 0.051]
## ────────────────────────────────────────────────────────────────
##
## Random Effects:
## ──────────────────────────────────────────
## Cluster K Parameter Variance ICC
## ──────────────────────────────────────────
## B.ID 146 (Intercept) 0.42142 0.78384
## Residual 0.11621
## ──────────────────────────────────────────
