# How to interpret a significant effect present in a subset data but absent in the full data

My model has 3 predictors:

1. Group (A vs. B)
2. Condition (baseline vs. treatment)
3. Memory (a continuous variable)

The model gives an interaction between Condition and Group.

I then tested the simple effect of Condition within each level of Group, by subsetting the data by Group and build models on the subset data. The model for Group A shows an interaction between Condition and Memory.

My question is how I should interpret the interaction between Condition and Memory, given that in the full model there is no effect involving Memory, and simple effect doesn't aim to test Memory?

Here is the data data.

Here is the code:

> # read in data
> df <- read.csv(file = "data/df.csv")
>
> # orthogonal contrasts
> contrasts(df$$Group) <- c(-1/2, 1/2) > contrasts(df$$Condition) <- c(-1/2, 1/2)
>
> # build model
> mod <- lmer(score ~ Condition * Group * Memory + (1|SubjID), data = df)
> Anova(mod, type = "III")
Analysis of Deviance Table (Type III Wald chisquare tests)

Response: score
Chisq Df Pr(>Chisq)
(Intercept)            30.5590  1  3.239e-08 ***
Condition               6.1629  1    0.01305 *
Group                  20.5651  1  5.764e-06 ***
Memory                  1.2731  1    0.25918
Condition:Group        25.0994  1  5.445e-07 ***
Condition:Memory        1.9954  1    0.15777
Group:Memory            3.0044  1    0.08304 .
Condition:Group:Memory  2.8056  1    0.09393 .
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>
> # simple effect: subsetting Group A
> df <- df %>% filter(Group == "A") %>% droplevels()
> # orthogonal contrasts
> contrasts(df\$Condition) <- c(-1/2, 1/2)
> # model
> mod <- lmer(score ~ Condition * Memory + (1|SubjID), data = df)
> Anova(mod, type = "III")
Analysis of Deviance Table (Type III Wald chisquare tests)

Response: score
Chisq Df Pr(>Chisq)
(Intercept)      59.4346  1  1.264e-14 ***
Condition        25.5871  1  4.229e-07 ***
Memory            4.6007  1    0.03196 *
Condition:Memory  4.1592  1    0.04141 *
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


The global effects are not significant, but when you drop the Group variable (by choosing only A), the effect is apparent in this group. I would expect that the group B does not have these significant "simple" effects (or as the opposite effect) as to balance the results to be non significant.
These results is somewhat hidden from the marginal (close to significant) effects Condition:Memory and Condition:Group:Memory, which suggest that a phenomenon might occur, but too weakly to be perceived in the complete model.
If the effect Condition:Memory is relevant, you can interpret it and pointing out that controlling for Group lead to a non significant "global" result.