Module 2 R Notebook

This document reports the results of the following three statistical tests for the personality.csv dataset:

• An independent samples t-test comparing agreeableness scores between older and younger adults.
• A one-way ANOVA comparing extraversion scores between different levels of education.
• A Pearson correlation between extraversion and agreeableness.

---

Independent Samples T-Test

Agreeableness scores between older and younger adults were compared using an independent-samples t-test. The results of this test are shown below:

    Welch Two Sample t-test

data:  agreeableness by age_group
t = 6.7399, df = 454.99, p-value = 4.814e-11
alternative hypothesis: true difference in means between group Old and group Young is not equal to 0
95 percent confidence interval:
  7.822644 14.262048
sample estimates:
  mean in group Old mean in group Young 
           128.4976            117.4553 

An independent samples t-test found that the difference in mean agreeableness between older and younger adults was significant (t(454.99) = 6.74, p < .001, d = 0.63).

---

One-Way ANOVA

Extraversion scores between participants from different educational backgrounds were compared using a one-way ANOVA. The results of this test are shown below:

             Df Sum Sq Mean Sq F value   Pr(>F)    
education     3   9519    3173    7.49 6.67e-05 ***
Residuals   453 191908     424                     
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

  Tukey multiple comparisons of means
    95% family-wise confidence level

Fit: aov(formula = extraversion ~ education, data = personality)

$education
                                                         diff         lwr       upr     p adj
Completed Undergraduate-Completed Masters or Higher -3.184994 -12.6498421  6.279853 0.8215266
Secondary School-Completed Masters or Higher        -9.574468 -20.2563356  1.107399 0.0969546
Some University-Completed Masters or Higher          3.843783  -4.5611497 12.248715 0.6402834
Secondary School-Completed Undergraduate            -6.389474 -15.5448328  2.765885 0.2748473
Some University-Completed Undergraduate              7.028777   0.6757309 13.381824 0.0233889
Some University-Secondary School                    13.418251   5.3634294 21.473072 0.0001252

A one-way ANOVA found significant differences in mean extraversion between participants from different educational backgrounds (F(3, 453) = 7.49, p < .001, \(\eta\)² = 0.05). Tukey post-hoc tests showed that participants who had completed some university reported higher extraversion scores than those who had completed undergraduate (p = .023) or secondary school (p < .001). All other post-hoc comparisons were non-significant.

---

Pearson Correlation

The relationship between extraversion and agreeableness scores was assessed with a Pearson correlation. The results of this test are shown below:

    Pearson's product-moment correlation

data:  extraversion and agreeableness
t = 3.3117, df = 455, p-value = 0.001001
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 0.06256912 0.24174096
sample estimates:
      cor 
0.1534157 

There was a significant correlation between extraversion and agreeableness (r(455) = .15, p < .001).