Item #5 Final Term Exam Stat 54
Marvanessa Dinorog
2023-05-25
- A psychologist conducts a study to determine whether or not noise can inhibit learning. Each of 15 subjects is randomly assigned to one of three groups. Each subject is given 20 minutes to memorize a list of 10 nonsense syllables which she is told she will be tested on the following day. The five subjects assigned to Group 1, the no noise condition, study the list of nonsense syllables while they are in a quiet room. The five subjects assigned to Group 2, the moderate noise condition, study the list of nonsense syllables while listening to classical music. The five subjects assigned to Group 3, the extreme noise condition, study the list of nonsense syllables while listening to rock music.
library(tidyverse)Warning: package 'tidyverse' was built under R version 4.2.2── Attaching packages ─────────────────────────────────────── tidyverse 1.3.2 ──
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Attaching package: 'rstatix'
The following object is masked from 'package:stats':
filterlibrary(readxl)
Kruskal_Wallis <- read_excel("D:/MARV BS MATH/4th year, 2nd sem/Nonparametric Statistics/Final Exam/Kruskal-Wallis.xlsx")
Kruskal_Wallis# A tibble: 5 × 4
Subject Condition1 Condition2 Condition3
<dbl> <dbl> <dbl> <dbl>
1 1 8 7 4
2 2 10 8 8
3 3 9 5 7
4 4 10 8 5
5 5 9 5 7F <- Kruskal_Wallis %>%
gather(key = "Condition", value = "score", Condition1, Condition2, Condition3) %>%
convert_as_factor(Subject, Condition)
head(F, 5)# A tibble: 5 × 3
Subject Condition score
<fct> <fct> <dbl>
1 1 Condition1 8
2 2 Condition1 10
3 3 Condition1 9
4 4 Condition1 10
5 5 Condition1 9head(F)# A tibble: 6 × 3
Subject Condition score
<fct> <fct> <dbl>
1 1 Condition1 8
2 2 Condition1 10
3 3 Condition1 9
4 4 Condition1 10
5 5 Condition1 9
6 1 Condition2 7summary(Kruskal_Wallis) Subject Condition1 Condition2 Condition3
Min. :1 Min. : 8.0 Min. :5.0 Min. :4.0
1st Qu.:2 1st Qu.: 9.0 1st Qu.:5.0 1st Qu.:5.0
Median :3 Median : 9.0 Median :7.0 Median :7.0
Mean :3 Mean : 9.2 Mean :6.6 Mean :6.2
3rd Qu.:4 3rd Qu.:10.0 3rd Qu.:8.0 3rd Qu.:7.0
Max. :5 Max. :10.0 Max. :8.0 Max. :8.0 set.seed(12345)
F %>% sample_n_by(Condition, size = 5)# A tibble: 15 × 3
Subject Condition score
<fct> <fct> <dbl>
1 3 Condition1 9
2 4 Condition1 10
3 2 Condition1 10
4 5 Condition1 9
5 1 Condition1 8
6 2 Condition2 8
7 1 Condition2 7
8 3 Condition2 5
9 5 Condition2 5
10 4 Condition2 8
11 2 Condition3 8
12 5 Condition3 7
13 3 Condition3 7
14 4 Condition3 5
15 1 Condition3 4F1 <- F %>%
reorder_levels(Condition, order = c("C1", "C2", "C3"))summary statistics
Compute summary statistics by groups:
F %>%
group_by(Condition) %>%
get_summary_stats(score, type = "common")# A tibble: 3 × 11
Condition variable n min max median iqr mean sd se ci
<fct> <fct> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 Condition1 score 5 8 10 9 1 9.2 0.837 0.374 1.04
2 Condition2 score 5 5 8 7 3 6.6 1.52 0.678 1.88
3 Condition3 score 5 4 8 7 2 6.2 1.64 0.735 2.04Visualization
ggboxplot(F, x = "Condition", y = "score")
Computation
res.kruskal <- F %>% kruskal_test(score ~ Condition)
res.kruskal# A tibble: 1 × 6
.y. n statistic df p method
* <chr> <int> <dbl> <int> <dbl> <chr>
1 score 15 8.75 2 0.0126 Kruskal-WallisEffect size
F %>% kruskal_effsize(score ~ Condition)# A tibble: 1 × 5
.y. n effsize method magnitude
* <chr> <int> <dbl> <chr> <ord>
1 score 15 0.562 eta2[H] large A large effect size is detected, eta2[H] = 0.562284
# Pairwise comparisons
pwc <- F %>%
dunn_test(score ~ Condition, p.adjust.method = "bonferroni")
pwc# A tibble: 3 × 9
.y. group1 group2 n1 n2 statistic p p.adj p.adj.signif
* <chr> <chr> <chr> <int> <int> <dbl> <dbl> <dbl> <chr>
1 score Condition1 Condition2 5 5 -2.34 0.0193 0.0578 ns
2 score Condition1 Condition3 5 5 -2.74 0.00621 0.0186 *
3 score Condition2 Condition3 5 5 -0.396 0.692 1 ns Only Condition1 and Condition3 are statistically significant with p-value 0.01863958.
Pairwise comparisons using Wilcoxon’s test:
pwc2 <- F %>%
wilcox_test(score ~ Condition, p.adjust.method = "bonferroni")
pwc2# A tibble: 3 × 9
.y. group1 group2 n1 n2 statistic p p.adj p.adj.signif
* <chr> <chr> <chr> <int> <int> <dbl> <dbl> <dbl> <chr>
1 score Condition1 Condition2 5 5 24 0.019 0.057 ns
2 score Condition1 Condition3 5 5 24.5 0.015 0.045 *
3 score Condition2 Condition3 5 5 15 0.664 1 ns The pairwise comparison shows that, Condition1 and Condition3 are significantly different (Wilcoxon’s test, p = 0.045).
Interpretation
There was a statistically significant differences between inhibiting learning depending on the noise present during the memorizing as assessed using the Kruskal-Wallis test (p = 0.013). Pairwise Wilcoxon test between groups showed that only the difference between Condition1 and Condition3 group was significant (Wilcoxon’s test, p = 0.045)
# Visualization: box plots with p-values
pwc <- pwc %>% add_xy_position(x = "Condition")
ggboxplot(F, x = "Condition", y = "score") +
stat_pvalue_manual(pwc, hide.ns = TRUE) +
labs(
subtitle = get_test_label(res.kruskal, detailed = TRUE),
caption = get_pwc_label(pwc)
)