Age and Intelligence as Predictors of Semantic Relatedness Judgement Speeds in Children and Adolescents: The Role of Semantic Priming, Syllable Complexity and Lexical Ambiguity
Daneka Moroney - Student ID: 589297311
School of Psychology, University of AucklandMay 01, 2026
- Introduction
- Method
- Results
- Discussion
- Reproducibility Appendix
Introduction
This study aimed to investigate whether ambiguous priming and target syllable complexity influence the semantic processing speed of children and adolescents aged 6 to 16 years, and whether intelligence quotient (IQ) scores predict response times above and beyond age. To determine participants’ overall IQ scores, the Wechsler Intelligence Scale for Children (WISC-V) was administered prior to the study. Using a semantic relatedness judgement task, participants were tasked to make decisions on whether presented word pairs ‘go together’ or have a relationship. Age-appropriate language was used to ensure comprehension for the task instructions and stimuli. Through a sequential priming paradigm, each trial began with a fixation point for 500ms, followed by a prime word for 150ms, and then a blank screen for 100ms. A target word was then presented and remained on screen until the participant responded with either a green button for related word pairs (e.g., wave and ocean) or a red button for unrelated word pairs (e.g., wave and hammer). Reaction times were measured from the onset of the target stimulus to the participant’s button press, and therefore used as a measure of semantic processing speeds.
Method
# Seed Used for Simulating Data
set.seed(7311)
# Number of Participants
n <- 180
# Continuous Predictor - Age
age <- rnorm(n, mean = 11, sd = 3)
age <- pmax(age, 6)
age <- pmin(age, 16)
age <- round(age)
# Binary Predictor - Lexical Ambiguity
la_primes <- sample(c("Yes", "No"), n, replace = TRUE)
la_primes <- factor(la_primes)
# Three-Level Predictor - Syllable Number Complexity
syl_num <- sample(c("Monosyllable", "Disyllable", "Trisyllable"), n, replace = TRUE)
syl_num <- factor(syl_num, levels = c("Monosyllable", "Disyllable", "Trisyllable"))
# Additional Predictor - IQ Score
iq_score <- rnorm(n, mean = 100, sd = 15)
iq_score <- pmax(iq_score, 40)
iq_score <- pmin(iq_score, 160)
iq_score_centered <- iq_score - 100
# Continuous Outcome - Mean Reaction Time
mean_reaction_time <- 1000 +
-35 * age +
70 * (la_primes == "Yes") +
40 * (syl_num == "Disyllable") +
80 * (syl_num == "Trisyllable") +
-0.5 * iq_score_centered +
rnorm(n, mean = 0, sd = 100)
mean_reaction_time <- pmax(mean_reaction_time, 550)
# Combining Variables into a Data-set
la_rt_data <- data.frame(
age,
la_primes,
syl_num,
iq_score,
iq_score_centered,
mean_reaction_time
)A sample of 180 participants was simulated in R (version 4.5.3) using set.seed(7311), corresponding to the last four digits of the student ID to ensure full reproducibility. Age was used as a continuous predictor and simulated with a normal distribution (M = 11, SD = 3), rounded to the nearest year. This value was constrained to a plausible range of 6 to 16 years, due to the age administration requirements for the WISC-V. Participants’ WISC-V IQ scores were used as an additional continuous predictor, simulated with a normal distribution and constrained to 40 and 160, consistent with the standardisation of all Wechsler Intelligence Scales (M = 100, SD = 15). IQ scores were mean-centred (by subtracting 100) prior to regression analyses, so that zero represented the average IQ and model intercepts reflect predicted reaction time at average intelligence. Participants’ individual mean reaction times (RT) were used as the continuous outcome measured in milliseconds. The RTs were constrained to a minimum of 550ms to reduce physiologically implausible results.
Participants were randomly assigned to the binary categorical predictor of lexical ambiguity prime condition, presented with either an ambiguous prime condition (all prime words carried multiple meanings) or an unambiguous control condition (all prime words had one clear meaning). Additionally, the number of syllables in a target word was used as a three-level categorical variable and randomly assigned to participants. The syllabic complexity conditions included monosyllabic (one syllable target words), disyllabic (two syllable target words), or trisyllabic (three syllable target words).
Results
Descriptive Statistics and Visualisations
Participants ranged in ages from 6 to 16 years (M = 10.82, SD = 2.90), with mean WISC-V IQ scores of 98.68 (SD = 14.62). Mean RT across all participants was 711.78ms (SD = 125.54). Priming conditions were unevenly distributed, with the ambiguous prime condition having 105 participants and 75 in the unambiguous condition. Additionally, target word random assignment included 58 participants given monosyllabic target words, 62 had disyllabic targets, and 60 had trisyllabic targets.
Variable Descriptions
| Variable | Role | Type | Description | Values |
|---|---|---|---|---|
| ‘mean_reaction_time’ | Outcome | Continuous | Individual mean reaction time on semantic relatedness tasks in milliseconds | ≥550 ms |
| ‘age’ | Predictor | Continuous | Age of participants in years | 6 - 16 |
| ‘la_primes’ | Predictor | Binary Categorical | Lexical prime ambiguity presented | Yes, No |
| ‘syl_num’ | Predictor | Three-level Categorical | Target words syllable complexity | Monosyllable, Disyllable, Trisyllable |
| ‘iq_score’ | Predictor | Additional Continuous | WISC intelligence quotient score | 40 - 160 |
Descriptive Statistics Tables
# Continuous Variables Descriptive Statistics Table
descript_stat <- data.frame(
Variable = c("Age", "IQ Score", "Individual Mean Reaction Time"),
M = round(c(mean(la_rt_data$age),
mean(la_rt_data$iq_score),
mean(la_rt_data$mean_reaction_time)), 2),
SD = round(c(sd(la_rt_data$age),
sd(la_rt_data$iq_score),
sd(la_rt_data$mean_reaction_time)), 2),
Min = round(c(min(la_rt_data$age),
min(la_rt_data$iq_score),
min(la_rt_data$mean_reaction_time)), 2),
Max = round(c(max(la_rt_data$age),
max(la_rt_data$iq_score),
max(la_rt_data$mean_reaction_time)), 2)
)
kable(descript_stat,
caption = "Table 1 Descriptive Statistics for Continuous Variables",
col.names = c("Variable", "M", "SD", "Min", "Max"))| Variable | M | SD | Min | Max |
|---|---|---|---|---|
| Age | 10.82 | 2.90 | 6.00 | 16.00 |
| IQ Score | 98.68 | 14.62 | 58.12 | 137.01 |
| Individual Mean Reaction Time | 711.78 | 125.54 | 550.00 | 1045.10 |
# Ambiguity Prime Condition Reaction Times and Frequency
la_rt_data %>%
group_by(la_primes) %>%
summarise(
n = n(),
mean = mean(mean_reaction_time),
sd = sd(mean_reaction_time),
min = min(mean_reaction_time),
max = max(mean_reaction_time)
) %>%
kable(caption = "Table 2 Mean Reaction Times by Lexical Ambiguity Prime Condition",
col.names = c("Ambiguous Prime", "n", "M", "SD", "Min", "Max"))| Ambiguous Prime | n | M | SD | Min | Max |
|---|---|---|---|---|---|
| No | 75 | 687.0027 | 126.8442 | 550 | 1045.0951 |
| Yes | 105 | 729.4790 | 122.1476 | 550 | 998.8324 |
# Syllable Amount Condition Reaction Times and Frequency
la_rt_data %>%
group_by(syl_num) %>%
summarise(
n = n(),
mean = mean(mean_reaction_time),
sd = sd(mean_reaction_time),
min = min(mean_reaction_time),
max = max(mean_reaction_time)
) %>%
kable(caption = "Table 3 Mean Reaction Times by Syllable Amount Condition",
col.names = c("Syllable Count", "n", "M", "SD", "Min", "Max"))| Syllable Count | n | M | SD | Min | Max |
|---|---|---|---|---|---|
| Monosyllable | 58 | 683.4132 | 125.1170 | 550 | 998.8324 |
| Disyllable | 62 | 710.5322 | 123.4163 | 550 | 1045.0951 |
| Trisyllable | 60 | 740.4922 | 123.7539 | 550 | 983.4734 |
Visualisations
# Figure 1. Mean Reaction Times by Age
ggplot(la_rt_data, aes(x = age, y = mean_reaction_time)) +
geom_point(alpha = 0.5) +
geom_smooth(method = "lm", se = FALSE) +
labs(
title = "Figure 1. Age and Mean Reaction Time",
x = "Age",
y = "Mean Reaction Time (ms)"
) +
theme_minimal()
# Figure 2. Mean Reaction Times by IQ Scores
ggplot(la_rt_data, aes(x = iq_score, y = mean_reaction_time)) +
geom_point(alpha = 0.5) +
geom_smooth(method = "lm", se = FALSE) +
labs(
title = "Figure 2. Intelligence Quotient Scores and Mean Reaction Time",
x = "Intelligence Quotient Scores",
y = "Mean Reaction Time (ms)"
) +
theme_minimal()
# Figure 3: Mean reaction time differences by lexical prime ambiguity
ggplot(la_rt_data, aes(x = la_primes, y = mean_reaction_time))+
geom_boxplot() +
labs(
title = "Figure 3. Lexical Prime Ambiguity and Mean Reaction Time",
x = "Ambiguous Lexical Prime",
y = "Mean Reaction Time (ms)"
) +
theme_minimal()
# Figure 4: Mean reaction time differences by word pair relationship type}
ggplot(la_rt_data, aes(x = syl_num, y = mean_reaction_time))+
geom_boxplot() +
labs(
title = "Figure 4. Type of Word Pair Relationship and Mean Reaction Time",
x = "Word Pair Relationship",
y = "Mean Reaction Time (ms)"
) +
theme_minimal()
Hypothesis Testing
The focal analysis of this study examined whether lexical ambiguity priming significantly predicted mean RT in children and adolescents.
H0: There is no difference in mean RT between participants presented with ambiguous primes and those presented with unambiguous primes.
H1: Participants presented with ambiguous primes show significantly slower RT than those with unambiguous primes.
Independent Samples T-Test
# T-Test
t_test <- t.test(mean_reaction_time ~ la_primes, data = la_rt_data, var.equal = TRUE)
t_test
##
## Two Sample t-test
##
## data: mean_reaction_time by la_primes
## t = -2.2635, df = 178, p-value = 0.02481
## alternative hypothesis: true difference in means between group No and group Yes is not equal to 0
## 95 percent confidence interval:
## -79.507636 -5.444927
## sample estimates:
## mean in group No mean in group Yes
## 687.0027 729.4790
# Cohen's D
cohen.d(mean_reaction_time ~ la_primes, data = la_rt_data)
##
## Cohen's d
##
## d estimate: -0.3422148 (small)
## 95 percent confidence interval:
## lower upper
## -0.64267752 -0.04175208The t-test revealed that participants presented with ambiguously primed words (M = 729.48, SD = 122.15) exhibited significantly slower mean RTs compared to participants given unambiguous prime words (M = 687.00, SD = 126.84), t(178) = -2.26, p = .025, 95% CI [-79.51, -5.45], d = 0.34. While the effect size is small, these results suggest that lexical ambiguity in prime words may increase processing demands for young people.
# T-test results table
tidy(t_test) %>%
select(estimate, estimate1, estimate2, statistic, p.value, conf.low, conf.high) %>%
mutate(across(where(is.numeric), ~ round(., 3))) %>%
mutate(p.value = ifelse(p.value < .001, "< .001", as.character(p.value))) %>%
kable(caption = "Independent Samples t-Test Results",
col.names = c("Mean Difference", "M (Unambiguous)", "M (Ambiguous)",
"t", "p", "95% CI Lower", "95% CI Upper"))| Mean Difference | M (Unambiguous) | M (Ambiguous) | t | p | 95% CI Lower | 95% CI Upper |
|---|---|---|---|---|---|---|
| -42.476 | 687.003 | 729.479 | -2.264 | 0.025 | -79.508 | -5.445 |
# Cohen's d table
d_result <- cohen.d(mean_reaction_time ~ la_primes, data = la_rt_data)
data.frame(
d = round(d_result$estimate, 3),
magnitude = d_result$magnitude,
CI_lower = round(d_result$conf.int[1], 3),
CI_upper = round(d_result$conf.int[2], 3)
) %>%
kable(caption = "Cohen's d Effect Size",
col.names = c("d", "Magnitude", "95% CI Lower", "95% CI Upper"))| d | Magnitude | 95% CI Lower | 95% CI Upper | |
|---|---|---|---|---|
| lower | -0.342 | small | -0.643 | -0.042 |
Regression Equivalent of the T-Test
# Regression Equivalent of T-Test
reg_t_eq <- lm(mean_reaction_time ~ la_primes, data = la_rt_data)
# Summary of Regression Results
summary(reg_t_eq)
##
## Call:
## lm(formula = mean_reaction_time ~ la_primes, data = la_rt_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -179.48 -98.94 -18.40 83.08 358.09
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 687.00 14.33 47.934 <2e-16 ***
## la_primesYes 42.48 18.77 2.264 0.0248 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 124.1 on 178 degrees of freedom
## Multiple R-squared: 0.02798, Adjusted R-squared: 0.02252
## F-statistic: 5.124 on 1 and 178 DF, p-value: 0.02481
# Regression Confidence Intervals
confint(reg_t_eq)
## 2.5 % 97.5 %
## (Intercept) 658.719519 715.28585
## la_primesYes 5.444927 79.50764A simple linear regression model using lexical ambiguity prime conditions as a dummy coded binary predictor (0 = unambiguous, 1 = ambiguous) confirmed the t-test results. The intercept (β₀ = 687.00) represents the mean RTs for the unambiguous reference group, consistent with the group mean reported above. The positive coefficient (β₁ = 42.48, SE = 18.77, t = 2.26, p = .025, 95% CI [5.44, 79.51]) represents the estimated difference in mean RTs between conditions, with the model accounting for approximately 2.3% of RT variance (R² = .027). Both analyses were conceptually linked because they represent the same underlying model, but expressed differently; the regression coefficient is mathematically equivalent to the difference between group means reported in the t-test.
# Coefficients Table
tidy(reg_t_eq, conf.int = TRUE) %>%
mutate(across(where(is.numeric), ~ round(., 3))) %>%
mutate(p.value = ifelse(p.value < .001, "< .001", as.character(p.value))) %>%
kable(caption = "Equivalent Simple Linear Regression: Ambiguity Prime Predicting Reaction Time")| term | estimate | std.error | statistic | p.value | conf.low | conf.high |
|---|---|---|---|---|---|---|
| (Intercept) | 687.003 | 14.332 | 47.934 | < .001 | 658.720 | 715.286 |
| la_primesYes | 42.476 | 18.765 | 2.264 | 0.025 | 5.445 | 79.508 |
# Model Fit Table
glance(reg_t_eq) %>%
select(r.squared, adj.r.squared, sigma, statistic, p.value) %>%
mutate(across(where(is.numeric), ~ round(., 3))) %>%
mutate(p.value = ifelse(p.value < .001, "< .001", as.character(p.value))) %>%
kable(caption = "Model Fit Statistics")| r.squared | adj.r.squared | sigma | statistic | p.value |
|---|---|---|---|---|
| 0.028 | 0.023 | 124.122 | 5.124 | 0.025 |
Simple Regression
# Simple Regression
reg_simp <- lm(mean_reaction_time ~ age, data = la_rt_data)
# Summary of Regression Results
summary(reg_simp)
##
## Call:
## lm(formula = mean_reaction_time ~ age, data = la_rt_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -230.359 -64.553 -9.474 60.700 257.381
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1029.616 26.750 38.49 <2e-16 ***
## age -29.384 2.389 -12.30 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 92.57 on 178 degrees of freedom
## Multiple R-squared: 0.4594, Adjusted R-squared: 0.4563
## F-statistic: 151.2 on 1 and 178 DF, p-value: < 2.2e-16
# Regression Confidence Intervals
confint(reg_simp)
## 2.5 % 97.5 %
## (Intercept) 976.8274 1082.40421
## age -34.0990 -24.66869A simple linear regression model was used to understand how age predicted RT, indicating that adolescents had faster RTs than younger children (β = -29.38, SE = 2.39, t = -12.30, p < .001, 95% CI [-34.10, -24.67]). The large negative slope reflects the large negative relationship between the age coefficient and RT, with RT decreasing by 29ms for every year age increased. This result suggests that older children processed semantic relationships significantly faster than younger children. The narrow 95% CI indicates the true population slope is closely estimated. Furthermore, while age accounted for approximately 46% of the variance (adjusted R² = .456), there was a residual error of approximately 93ms. This error suggests a large individual variability in mean RTs unexplained by age alone, highlighting the need for a multiple regression analysis.
# Coefficients Table
tidy(reg_simp, conf.int = TRUE) %>%
mutate(across(where(is.numeric), ~ round(., 3))) %>%
mutate(p.value = ifelse(p.value < .001, "< .001", as.character(p.value))) %>%
kable(caption = "Simple Linear Regression: Age Predicting Reaction Time")| term | estimate | std.error | statistic | p.value | conf.low | conf.high |
|---|---|---|---|---|---|---|
| (Intercept) | 1029.616 | 26.750 | 38.490 | < .001 | 976.827 | 1082.404 |
| age | -29.384 | 2.389 | -12.298 | < .001 | -34.099 | -24.669 |
# Model Fit Table
glance(reg_simp) %>%
select(r.squared, adj.r.squared, sigma, statistic, p.value) %>%
mutate(across(where(is.numeric), ~ round(., 3))) %>%
mutate(p.value = ifelse(p.value < .001, "< .001", as.character(p.value))) %>%
kable(caption = "Model Fit Statistics") | r.squared | adj.r.squared | sigma | statistic | p.value |
|---|---|---|---|---|
| 0.459 | 0.456 | 92.57 | 151.233 | < .001 |
Multiple Regression
# Multiple Regression
reg_multi <- lm(mean_reaction_time ~ age + la_primes + iq_score_centered, data = la_rt_data)
# Summary of Regression Results
summary(reg_multi)
##
## Call:
## lm(formula = mean_reaction_time ~ age + la_primes + iq_score_centered,
## data = la_rt_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -201.818 -59.512 -7.536 61.313 233.439
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1004.6714 26.3632 38.109 < 2e-16 ***
## age -29.9493 2.2951 -13.049 < 2e-16 ***
## la_primesYes 51.9571 13.5718 3.828 0.000179 ***
## iq_score_centered -0.5708 0.4578 -1.247 0.214118
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 88.7 on 176 degrees of freedom
## Multiple R-squared: 0.5092, Adjusted R-squared: 0.5008
## F-statistic: 60.87 on 3 and 176 DF, p-value: < 2.2e-16
# Regression Confidence Intervals
confint(reg_multi)
## 2.5 % 97.5 %
## (Intercept) 952.642616 1056.7000971
## age -34.478790 -25.4198275
## la_primesYes 25.172636 78.7416040
## iq_score_centered -1.474368 0.3327059A multiple regression analysis found age, ambiguous primes and centred IQ scores, significantly predicted RTs (F(3,176) = 60.87, p < .001). This analysis allows for interpretation of coefficients’ unique contribution to RT by controlling for other predictors. Holding the priming condition and IQ scores constant, age (β = -29.95, SE = 2.29, t = -13.05, p <.001, 95% CI [-34.48, -25.42]) was a significant predictor of RT. Similarly, holding age and IQ scores constant, ambiguous priming (β = 51.96, SE = 13.57, t = 3.83, p < .001, 95% CI [25.17, 78.74]) significantly predicted RT. In contrast, centred IQ scores did not significantly predict RTs when holding age and the priming condition constant (β = -0.57, SE = 0.46, t = -1.25, p = .214, 95% CI [-1.47, 0.33]). These results suggest participants’ age decreased RT by 30ms per year, but increased by 52ms when faced with lexical ambiguity.
# Coefficients Table
tidy(reg_multi, conf.int = TRUE) %>%
mutate(across(where(is.numeric), ~ round(., 3))) %>%
mutate(p.value = ifelse(p.value < .001, "< .001", as.character(p.value))) %>%
kable(caption = "Multiple Linear Regression: Age, Lexical Ambiguity and IQ Predicting Reaction Time")| term | estimate | std.error | statistic | p.value | conf.low | conf.high |
|---|---|---|---|---|---|---|
| (Intercept) | 1004.671 | 26.363 | 38.109 | < .001 | 952.643 | 1056.700 |
| age | -29.949 | 2.295 | -13.049 | < .001 | -34.479 | -25.420 |
| la_primesYes | 51.957 | 13.572 | 3.828 | < .001 | 25.173 | 78.742 |
| iq_score_centered | -0.571 | 0.458 | -1.247 | 0.214 | -1.474 | 0.333 |
# Model Fit Table
glance(reg_multi) %>%
select(r.squared, adj.r.squared, sigma, statistic, p.value) %>%
mutate(across(where(is.numeric), ~ round(., 3))) %>%
mutate(p.value = ifelse(p.value < .001, "< .001", as.character(p.value))) %>%
kable(caption = "Model Fit Statistics")| r.squared | adj.r.squared | sigma | statistic | p.value |
|---|---|---|---|---|
| 0.509 | 0.501 | 88.697 | 60.87 | < .001 |
One-Way ANOVA
# One-Way ANOVA
anova_oneway <- aov(mean_reaction_time ~ syl_num, data = la_rt_data)
# Summary of ANOVA Results
summary(anova_oneway)
## Df Sum Sq Mean Sq F value Pr(>F)
## syl_num 2 96231 48116 3.125 0.0464 *
## Residuals 177 2725007 15396
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# Tukey HSD
TukeyHSD(anova_oneway)
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = mean_reaction_time ~ syl_num, data = la_rt_data)
##
## $syl_num
## diff lwr upr p adj
## Disyllable-Monosyllable 27.11897 -26.454715 80.69266 0.4568507
## Trisyllable-Monosyllable 57.07905 3.075522 111.08259 0.0355628
## Trisyllable-Disyllable 29.96008 -23.150279 83.07044 0.3786340A one-way ANOVA revealed a statistically significant effect of syllable complexity on RT (F(2,177) = 3.13, p < .05), indicating that at least one syllable group differed significantly from the others. The F-statistic indicates between-group RT variance was approximately 3 times larger than the within-group variance. This result indicates that changes in syllable complexity account for variations in semantic processing speeds. A post hoc comparison suggested that the trisyllabic RTs (M = 740.49, SD = 123.75) were significantly slower than monosyllables by 57ms (M = 683.41, SD = 125.12, p < .05), but nonsignificantly slower by 30ms than disyllables (M = 710.53, SD = 123.42, p = .378). Additionally, disyllabic word RTs were not significantly slower (27ms) than monosyllabic (p = .457). This post hoc comparison suggests that moving from a one-syllable word to a three-syllable word placed increased processing demands on participants.
# ANOVA omnibus result
tidy(anova_oneway) %>%
mutate(across(where(is.numeric), ~ round(., 3))) %>%
mutate(p.value = ifelse(p.value < .001, "< .001", as.character(p.value))) %>%
kable(caption = "One-Way ANOVA: Syllabic Complexity Predicting Reaction Time")| term | df | sumsq | meansq | statistic | p.value |
|---|---|---|---|---|---|
| syl_num | 2 | 96231.32 | 48115.66 | 3.125 | 0.046 |
| Residuals | 177 | 2725006.82 | 15395.52 | NA | NA |
# Tukey post hoc comparisons
tidy(TukeyHSD(anova_oneway)) %>%
mutate(across(where(is.numeric), ~ round(., 3))) %>%
mutate(adj.p.value = ifelse(adj.p.value < .001, "< .001", as.character(adj.p.value))) %>%
kable(caption = "Tukey Post Hoc Comparisons")| term | contrast | null.value | estimate | conf.low | conf.high | adj.p.value |
|---|---|---|---|---|---|---|
| syl_num | Disyllable-Monosyllable | 0 | 27.119 | -26.455 | 80.693 | 0.457 |
| syl_num | Trisyllable-Monosyllable | 0 | 57.079 | 3.076 | 111.083 | 0.036 |
| syl_num | Trisyllable-Disyllable | 0 | 29.960 | -23.150 | 83.070 | 0.379 |
Regression Equivalent of One-Way ANOVA
# Regression Equivalent of the One-Way ANOVA
reg_oneway_eq <- lm(mean_reaction_time ~ syl_num, data = la_rt_data)
# Summary of Regression Results
summary(reg_oneway_eq)
##
## Call:
## lm(formula = mean_reaction_time ~ syl_num, data = la_rt_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -190.49 -99.19 -17.24 77.32 334.56
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 683.41 16.29 41.947 <2e-16 ***
## syl_numDisyllable 27.12 22.67 1.196 0.2331
## syl_numTrisyllable 57.08 22.85 2.498 0.0134 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 124.1 on 177 degrees of freedom
## Multiple R-squared: 0.03411, Adjusted R-squared: 0.0232
## F-statistic: 3.125 on 2 and 177 DF, p-value: 0.04636A simple linear regression model using syllable complexity as a dummy-coded predictor produced identical results to the one-way ANOVA. The model’s intercept (β₀ = 683.41) represents the mean RT for the monosyllabic condition group, which served as the reference condition. The disyllabic coefficient (β₁ = 27.12, SE = 22.67, t = 1.19, p = .401) indicated a small non-significant increase in mean RT relative to the monosyllabic group. In contrast, the trisyllabic coefficient (β₂ = 57.08, SE = 22.85, t = 2.49, p = .013) showed a statistically significant increase in mean RTs compared to monosyllabic conditions. This model is mathematically identical to the ANOVA and post hoc results, accounting for 2.3% of RT variance (adjusted R² = .023).
# Coefficients Table
tidy(reg_oneway_eq, conf.int = TRUE) %>%
mutate(across(where(is.numeric), ~ round(., 3))) %>%
mutate(p.value = ifelse(p.value < .001, "< .001", as.character(p.value))) %>%
kable(caption = " Equivalent Simple Linear Regression: Syllabic Complexity Predicting Reaction Time")| term | estimate | std.error | statistic | p.value | conf.low | conf.high |
|---|---|---|---|---|---|---|
| (Intercept) | 683.413 | 16.292 | 41.947 | < .001 | 651.261 | 715.565 |
| syl_numDisyllable | 27.119 | 22.666 | 1.196 | 0.233 | -17.612 | 71.850 |
| syl_numTrisyllable | 57.079 | 22.848 | 2.498 | 0.013 | 11.989 | 102.169 |
# Model Fit Table
glance(reg_oneway_eq) %>%
select(r.squared, adj.r.squared, sigma, statistic, p.value) %>%
mutate(across(where(is.numeric), ~ round(., 3))) %>%
mutate(p.value = ifelse(p.value < .001, "< .001", as.character(p.value))) %>%
kable(caption = "Model Fit Statistics") | r.squared | adj.r.squared | sigma | statistic | p.value |
|---|---|---|---|---|
| 0.034 | 0.023 | 124.079 | 3.125 | 0.046 |
Recoded Reference Group
# Recoded Copy of Syl_Num
syl_num_recoded <- relevel(la_rt_data$syl_num, ref = "Trisyllable")
# Refit Model with New Reference Group
refit_model <- lm(mean_reaction_time ~ syl_num_recoded, data = la_rt_data)
# Summary of Refit Model Results
summary(refit_model)
##
## Call:
## lm(formula = mean_reaction_time ~ syl_num_recoded, data = la_rt_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -190.49 -99.19 -17.24 77.32 334.56
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 740.49 16.02 46.227 <2e-16 ***
## syl_num_recodedMonosyllable -57.08 22.85 -2.498 0.0134 *
## syl_num_recodedDisyllable -29.96 22.47 -1.333 0.1841
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 124.1 on 177 degrees of freedom
## Multiple R-squared: 0.03411, Adjusted R-squared: 0.0232
## F-statistic: 3.125 on 2 and 177 DF, p-value: 0.04636# Coefficient Table
tidy(refit_model) %>%
mutate(across(where(is.numeric), ~ round(., 3))) %>%
mutate(p.value = ifelse(p.value < .001, "< .001", as.character(p.value))) %>%
kable(caption = "Regression with Trisyllable as Reference Group",
col.names = c("Term", "Estimate", "SE", "t", "p"))| Term | Estimate | SE | t | p |
|---|---|---|---|---|
| (Intercept) | 740.492 | 16.018 | 46.227 | < .001 |
| syl_num_recodedMonosyllable | -57.079 | 22.848 | -2.498 | 0.013 |
| syl_num_recodedDisyllable | -29.960 | 22.470 | -1.333 | 0.184 |
Discussion
The ambiguity effects observed were statistically significant, allowing for rejection of the null hypothesis of no difference in RT between priming conditions. During this data simulation, a conceptual link between analyses became evident; t-tests, simple regressions and one-way ANOVAs are all expressions of the same underlying linear model that estimates mean group differences. This equivalence is enabled by dummy coding, converting categorical predictors into binary variables, allowing for intercepts to represent the reference group mean, and coefficients to represent the deviation of another group from the reference. This results in mathematically identical F-statistics and p-values between the regression equivalents of the ANOVA and t-test, indicating the same underlying model is being represented differently. This relationship is seen when re-coding the ANOVA as the model results remained the same but the intercept and coefficient results changed reflecting the change in reference group or comparison point from monosyllabic to trisyllabic.
Despite these methodological insights, there were several limitations to this simulation study. The absence of a significant IQ effect may reflect the use of an overall intelligence measure, rather than specifically isolating for verbal intelligence or literacy scores. Additionally, no data were gathered regarding specific demographic factors, learning disabilities, or accuracy rates, alongside no distinction between word pair relationship types. These factors may have provided valuable information regarding the developmental differences in processing semantic relationships. Future research should examine the impacts of inhibition and phonological-related learning disabilities on ambiguity resolution in children and adolescents.
Reproducibility Appendix
set.seed(7311)
head(la_rt_data, 10)
## age la_primes syl_num iq_score iq_score_centered mean_reaction_time
## 1 10 No Disyllable 109.76741 9.767411 664.3658
## 2 8 Yes Monosyllable 90.82436 -9.175636 732.2178
## 3 11 Yes Monosyllable 130.80958 30.809579 706.1575
## 4 8 No Trisyllable 94.18601 -5.813987 823.4557
## 5 16 Yes Monosyllable 119.62693 19.626932 550.0000
## 6 6 Yes Monosyllable 118.20543 18.205431 790.6346
## 7 8 Yes Monosyllable 103.75687 3.756874 727.6174
## 8 6 Yes Monosyllable 75.85787 -24.142130 882.9211
## 9 6 No Disyllable 107.99513 7.995127 712.8208
## 10 16 Yes Trisyllable 107.46913 7.469125 662.7193
str(la_rt_data)
## 'data.frame': 180 obs. of 6 variables:
## $ age : num 10 8 11 8 16 6 8 6 6 16 ...
## $ la_primes : Factor w/ 2 levels "No","Yes": 1 2 2 1 2 2 2 2 1 2 ...
## $ syl_num : Factor w/ 3 levels "Monosyllable",..: 2 1 1 3 1 1 1 1 2 3 ...
## $ iq_score : num 109.8 90.8 130.8 94.2 119.6 ...
## $ iq_score_centered : num 9.77 -9.18 30.81 -5.81 19.63 ...
## $ mean_reaction_time: num 664 732 706 823 550 ...
sessionInfo()
## R version 4.5.3 (2026-03-11)
## Platform: aarch64-apple-darwin20
## Running under: macOS Sequoia 15.6.1
##
## Matrix products: default
## BLAS: /Library/Frameworks/R.framework/Versions/4.5-arm64/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.5-arm64/Resources/lib/libRlapack.dylib; LAPACK version 3.12.1
##
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
##
## time zone: Pacific/Auckland
## tzcode source: internal
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] broom_1.0.12 effsize_0.8.1 dplyr_1.2.1 knitr_1.51 ggplot2_4.0.2
##
## loaded via a namespace (and not attached):
## [1] Matrix_1.7-4 gtable_0.3.6 jsonlite_2.0.0 compiler_4.5.3
## [5] tidyselect_1.2.1 stringr_1.6.0 tidyr_1.3.2 jquerylib_0.1.4
## [9] splines_4.5.3 scales_1.4.0 yaml_2.3.12 fastmap_1.2.0
## [13] lattice_0.22-9 R6_2.6.1 labeling_0.4.3 generics_0.1.4
## [17] backports_1.5.1 tibble_3.3.1 bslib_0.10.0 pillar_1.11.1
## [21] RColorBrewer_1.1-3 rlang_1.1.7 stringi_1.8.7 cachem_1.1.0
## [25] xfun_0.57 sass_0.4.10 S7_0.2.1 cli_3.6.5
## [29] withr_3.0.2 magrittr_2.0.5 mgcv_1.9-4 digest_0.6.39
## [33] grid_4.5.3 rstudioapi_0.18.0 nlme_3.1-168 lifecycle_1.0.5
## [37] vctrs_0.7.1 evaluate_1.0.5 glue_1.8.0 farver_2.1.2
## [41] rmarkdown_2.31 purrr_1.2.2 tools_4.5.3 pkgconfig_2.0.3
## [45] htmltools_0.5.9One surprising finding in my simulated study was the uneven distribution of priming conditions. While this might be expected with randomised sampling, the difference between groups was considerably large (n = 30) and may have skewed my overall findings. Additionally, the strength of the age effect on RT variability (adjusted R² = .456) was considerably large but likely reflected the low SD used in the simulation. In the population, individual variability in RT would be much higher, and may have affected the power of my age results.