Mixed design ANOVA

The data set

Subject	Angle	Latency	Group
1	0	450	Young
1	4	510	Young
1	8	630	Young
2	0	390	Young
2	4	480	Young
2	8	540	Young
3	0	570	Young
3	4	630	Young
3	8	660	Young
4	0	450	Young
4	4	660	Young
4	8	720	Young
5	0	510	Young
5	4	660	Young
5	8	630	Young
6	0	360	Young
6	4	450	Young
6	8	450	Young
7	0	510	Young
7	4	600	Young
7	8	720	Young
8	0	510	Young
8	4	660	Young
8	8	780	Young
9	0	510	Young
9	4	660	Young
9	8	660	Young
10	0	510	Young
10	4	540	Young
10	8	660	Young
11	0	420	Old
11	4	570	Old
11	8	690	Old
12	0	600	Old
12	4	720	Old
12	8	810	Old
13	0	450	Old
13	4	540	Old
13	8	690	Old
14	0	630	Old
14	4	660	Old
14	8	780	Old
15	0	420	Old
15	4	570	Old
15	8	780	Old
16	0	600	Old
16	4	780	Old
16	8	870	Old
17	0	630	Old
17	4	690	Old
17	8	870	Old
18	0	480	Old
18	4	570	Old
18	8	720	Old
19	0	690	Old
19	4	750	Old
19	8	900	Old
20	0	510	Old
20	4	690	Old
20	8	810	Old

Data plot

Perform ANOVA tests

kable(
  get_anova_table(
          anova_test(data = data, 
                     dv = Latency, 
                     wid = Subject, 
                     within = Angle, 
                     between = Group,
                     effect.size = "pes", 
                     detailed = TRUE)))

Effect	DFn	DFd	SSn	SSd	F	p	p<.05	pes
(Intercept)	1	18	22767360	327900	1249.809	0.000	*	0.986
Group	1	18	132540	327900	7.276	0.015	*	0.288
Angle	2	36	435090	54420	143.911	0.000	*	0.889
Group:Angle	2	36	21090	54420	6.976	0.003	*	0.279

Simple Effects Young

kable(
  get_anova_table(
    anova_test(data = young, 
                     dv = Latency, 
                     wid = Subject, 
                     within = Angle, 
                     effect.size = "pes", 
                     detailed = TRUE)))

Effect	DFn	DFd	SSn	SSd	F	p	p<.05	pes
(Intercept)	1	9	9712830	146070	598.449	0e+00	*	0.985
Angle	2	18	144960	32040	40.719	2e-07	*	0.819

Comparisons of Cell Means Young

kable(
  young %>% 
  pairwise_t_test(Latency ~ Angle,
                  paired = TRUE,
                  p.adjust.method = "none"))

.y.	group1	group2	n1	n2	statistic	df	p	p.adj	p.adj.signif
Latency	0	4	10	10	-6.194225	9	1.60e-04	1.60e-04	***
Latency	0	8	10	10	-8.158801	9	1.89e-05	1.89e-05	****
Latency	4	8	10	10	-3.253957	9	1.00e-02	1.00e-02	**

Simple Effects Old

kable(
  get_anova_table(
    anova_test(data = old, 
                     dv = Latency, 
                     wid = Subject, 
                     within = Angle, 
                     effect.size = "pes", 
                     detailed = TRUE)))

Effect	DFn	DFd	SSn	SSd	F	p	p<.05	pes
(Intercept)	1	9	13187070	181830	652.718	0	*	0.986
Angle	2	18	311220	22380	125.155	0	*	0.933

Comparisons of Cell Means Old

kable(
  old %>% 
    pairwise_t_test(Latency ~ Angle,
                  paired = TRUE,
                  p.adjust.method = "none"))

.y.	group1	group2	n1	n2	statistic	df	p	p.adj	p.adj.signif
Latency	0	4	10	10	-6.621705	9	9.68e-05	9.68e-05	****
Latency	0	8	10	10	-13.897825	9	2.00e-07	2.00e-07	****
Latency	4	8	10	10	-11.500000	9	1.10e-06	1.10e-06	****

Simple Effects Angle0

angle0 <- summary(aov(Latency ~ 1 + Group, data = subset(data, Angle=="0")))
kable(angle0[[1]])

	Df	Sum Sq	Mean Sq	F value	Pr(>F)
Group	1	21780	21780	3.161103	0.0923101
Residuals	18	124020	6890	NA	NA

Simple Effects Angle4

angle4 <- summary(aov(Latency ~ 1 + Group, data = subset(data, Angle=="4")))
kable(angle4[[1]])

	Df	Sum Sq	Mean Sq	F value	Pr(>F)
Group	1	23805	23805	3.350457	0.0837955
Residuals	18	127890	7105	NA	NA

Simple Effects Angle8

angle8 <- summary(aov(Latency ~ 1 + Group, data = subset(data, Angle=="8")))
kable(angle8[[1]])

	Df	Sum Sq	Mean Sq	F value	Pr(>F)
Group	1	108045	108045	14.91304	0.0011428
Residuals	18	130410	7245	NA	NA

Last updated on Oct 8, 2023