R Notebook
library(tidyverse)
library(plotly)
library(ggplot2)
library(ggfortify)
library(ggpubr)
library(sciplot)
library(lsr)
library(knitr) **Abstract**This survey analysis was performed with scales obtained from the Becks Cognitive Insight Scale (Beck, Bauruch, Balter, Steer, & Warman, 2004) and The Centrality of Religiosity Scale (Huber & Huber, 2012) to see if there is a relationship between the participants Insight and Religiosity. This survey collected 45 participants. Additionally, the study looked at the relationship between Age and Gender with Insight and Religiosity scores. In addition to a plot that shows the approximate scores of each participant a linear regression was performed. In addition the the regression analysis a One-Way ANOVA were performed to examine the similar concept. A One-Way ANOVA were then Performed followed by an ANCOVA and MANOVA. There were no significance in any of the analysis performed. This could be due to the small sample size and poor diversity among the population.
**Methods**A bar graph were used to represent the overall scores of each participant. A regression analysis were then performed to analyze the relationship between the Religiosity (R Totals) and Insight (I Totals) scores. A One-Way ANOVA was then performed to also assess the relationship between Religiosity and Insight Scores. This was then followed by a Three-Way ANOVA to assess the relationship between the Religiosity scores, Age, and Gender to the Insight scores. Lastly, A MANOVA analysis were performed to combine the Religiosity and Insight scores to compare the relationship with the Age and Gender variables.
**Results**summary(FaithandInsight) Subnum Gender Age I1 I2
Length:45 Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
Class :character 1st Qu.:2.000 1st Qu.:1.000 1st Qu.:2.000 1st Qu.:2.000
Mode :character Median :2.000 Median :1.000 Median :2.000 Median :2.000
Mean :1.778 Mean :2.267 Mean :2.556 Mean :2.333
3rd Qu.:2.000 3rd Qu.:4.000 3rd Qu.:3.000 3rd Qu.:3.000
Max. :3.000 Max. :5.000 Max. :4.000 Max. :4.000
I3 I4 I5 I6 I7
Min. :1.000 Min. :1.000 Min. :1.0 Min. :1.000 Min. :1.000
1st Qu.:1.000 1st Qu.:2.000 1st Qu.:1.0 1st Qu.:2.000 1st Qu.:1.000
Median :2.000 Median :2.000 Median :2.0 Median :2.000 Median :2.000
Mean :1.711 Mean :2.356 Mean :1.8 Mean :2.244 Mean :2.067
3rd Qu.:2.000 3rd Qu.:3.000 3rd Qu.:2.0 3rd Qu.:3.000 3rd Qu.:3.000
Max. :4.000 Max. :4.000 Max. :3.0 Max. :4.000 Max. :4.000
I8 I9 I10 I11 I12
Min. :2.000 Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
1st Qu.:2.000 1st Qu.:2.000 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:2.000
Median :3.000 Median :3.000 Median :2.000 Median :2.000 Median :3.000
Mean :3.178 Mean :2.889 Mean :1.622 Mean :2.022 Mean :2.444
3rd Qu.:4.000 3rd Qu.:3.000 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:3.000
Max. :4.000 Max. :4.000 Max. :3.000 Max. :4.000 Max. :4.000
I13 I14 I15 ITotal 18
Min. :1.0 Min. :2.000 Min. :1.000 Min. :29.00 Min. :1.000
1st Qu.:2.0 1st Qu.:3.000 1st Qu.:3.000 1st Qu.:34.00 1st Qu.:2.000
Median :3.0 Median :4.000 Median :3.000 Median :37.00 Median :2.000
Mean :2.4 Mean :3.444 Mean :3.556 Mean :36.51 Mean :2.822
3rd Qu.:3.0 3rd Qu.:4.000 3rd Qu.:5.000 3rd Qu.:40.00 3rd Qu.:5.000
Max. :4.0 Max. :4.000 Max. :6.000 Max. :44.00 Max. :6.000
19 20 21 22 23
Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000
Median :2.000 Median :3.000 Median :1.000 Median :2.000 Median :1.000
Mean :2.333 Mean :3.444 Mean :2.067 Mean :2.267 Mean :1.667
3rd Qu.:3.000 3rd Qu.:6.000 3rd Qu.:3.000 3rd Qu.:3.000 3rd Qu.:2.000
Max. :6.000 Max. :6.000 Max. :6.000 Max. :7.000 Max. :5.000
24 25 26 RTotal Total
Min. :1.000 Min. :1.000 Min. :1.000 Min. : 9.00 Min. :40.00
1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:15.00 1st Qu.:50.00
Median :2.000 Median :1.000 Median :2.000 Median :21.00 Median :59.00
Mean :2.667 Mean :1.778 Mean :2.956 Mean :21.98 Mean :58.49
3rd Qu.:3.000 3rd Qu.:2.000 3rd Qu.:4.000 3rd Qu.:28.00 3rd Qu.:64.00
Max. :7.000 Max. :7.000 Max. :6.000 Max. :40.00 Max. :81.00 This is a summary of the data by column and questions.
ggplot(FaithandInsight, aes(x = Subnum, y = Total)) +
geom_col() +
geom_rug() +
labs(title = "Overall Participant Scores", x = "Participant") +
stat_smooth(method = "lm", col = 'red')`geom_smooth()` using formula = 'y ~ x'
Figure 1.1 Indicates the total of each participant. The lowest scores were around 40. The highest were around 80.
regression.model <- lm( ITotal~ RTotal, data = FaithandInsight)
summary.lm( regression.model )
Call:
lm(formula = ITotal ~ RTotal, data = FaithandInsight)
Residuals:
Min 1Q Median 3Q Max
-7.6896 -2.6006 0.3994 3.2391 7.3816
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 36.11962 1.46466 24.661 <2e-16 ***
RTotal 0.01781 0.06103 0.292 0.772
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 3.947 on 43 degrees of freedom
Multiple R-squared: 0.001977, Adjusted R-squared: -0.02123
F-statistic: 0.08519 on 1 and 43 DF, p-value: 0.7718The regression F statistic (0.08519) indicates that there is low variability. However the P value (0.7718) indicates there is not any significance of the Religiosity scores(R Total) effecting the Insight scores(I Total).
autoplot(regression.model)
Figure 1.2 These graphs represents the regression model and indicate that the distributions of scores are too spread out to indicate a correlation between the Religiosity scores and the Insight scores.
aov.model <- aov(formula = ITotal ~ RTotal, data = FaithandInsight)
summary(aov.model) Df Sum Sq Mean Sq F value Pr(>F)
RTotal 1 1.3 1.327 0.085 0.772
Residuals 43 669.9 15.579 This One-Way ANOVA and the P value (0.772) indicate there is not any significance of the Religiosity scores (R Total) effecting the Insight scores (I Total).
autoplot(aov.model)
Figure 1.3 These graphs represent the One-Way ANOVA and indicate that the distributions of scores are too spread out to indicate a correlation between the Religiosity scores and the Insight scores.
aov.model2 <- aov(formula = ITotal ~ RTotal + Age + Gender, data = FaithandInsight)
summary.aov(aov.model2) Df Sum Sq Mean Sq F value Pr(>F)
RTotal 1 1.3 1.327 0.085 0.773
Age 1 8.0 7.971 0.508 0.480
Gender 1 18.2 18.210 1.160 0.288
Residuals 41 643.7 15.701 The Three-way ANOVA and the Religiosity (R Total) P value of (.773), Age P value of (.480), and Gender P value of (.288) indicate there is not any significance of the Religiosity, Age, or Gender Variables effecting the Insight scores(I Total).
ggplot(aov.model2, aes(group = Age, x =RTotal, y = ITotal, color = factor(Age, labels = c("18-30",
"31-40", "41-50", "51-60", "60+")))) +
theme(legend.text = element_text(colour="Black", size = 16, face = "bold")) +
theme(legend.background = element_rect(colour = 'Dark Blue', fill = 'Green', size = 3)) +
geom_boxplot() +
labs(color = "Age") +
labs(title= "Scores by Age Groups") Warning: The `size` argument of `element_rect()` is deprecated as of ggplot2 3.4.0.
ℹ Please use the `linewidth` argument instead.
This warning is displayed once every 8 hours.
Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
generated.
Figure 1.4 Represents the Three-Way ANOVA and indicates that the highest scoring group of participants were in the 18-30 range and the least in the 31-40 range. Those in the 60+ range scored higher on Insight. Those in the 18-30 were second highest on Insight. There is little variation from the mean.
`geom_smooth()` using formula = 'y ~ x'
Figure 1.5 Represents the Three-Way ANOVA with a focus on Gender and indicates that female participants scored higher on Insight. There is little variation from the mean.
manova.model <- manova(cbind(ITotal, RTotal) ~ Age*Gender, data = FaithandInsight)
summary(manova.model, test = "Wilks") Df Wilks approx F num Df den Df Pr(>F)
Age 1 0.94400 1.1864 2 40 0.3158
Gender 1 0.94253 1.2195 2 40 0.3061
Age:Gender 1 0.94715 1.1159 2 40 0.3376
Residuals 41 This Two-way MANOVA indicates that the variables of Age and Gender fit the model well with little discrimination as indicated by the Wilks test scores being under 1. However the P value for Gender (.3061), and the P value for Age (.3158) indicate there in no significant in any of the variables to Religiosity or Insight.
ggplot(manova.model, aes(x = Age, y = Gender, color = factor(Gender, labels = c("Male",
"Female", "Decline to Answer")))) +
geom_violin() +
scale_x_continuous(labels =c("1" = "18-30", "2" = "31-40", "3" = "41-50", "4" = "51-60", "5" = "60+")) +
labs(color = "Gender") +
labs(title= "Gender Focus") +
stat_smooth(method = "aov", col = "red")Warning: Groups with fewer than two datapoints have been dropped.
ℹ Set `drop = FALSE` to consider such groups for position adjustment purposes.`geom_smooth()` using formula = 'y ~ x'
Figure 1.6 Represents the MANOVA measuring the relationship of Age and Gender to Religiosity and Insight. It appears that females in the 18-31 range scored the highest on Religiosity and Insight. Males from the 41-60 range scored highest for their group.
ggplot(manova.model, aes(x = Age, y = Gender, color = factor(Age, labels = c("18-30", "31-40", "41-50", "51-60", "60+")))) +
geom_violin() +
labs(color = "Age") +
labs(title= "Age Focus") +
stat_smooth(method = "aov", col = "red")`geom_smooth()` using formula = 'y ~ x'
Figure 1.7 Represents the Age perspective of the above MANOVA and indicates that those in the 41-50 range scored the lowest on Religiosity and Insight while those in the 18-30 range scored the highest.
**Discussion**The Overall goal of this study is to see if there is a relationship between ones Insight and how Religious the participants are. In this Regard there was no evidence found to support that hypothesis. With the small sample collected it was discovered that participants in the 18-30 age group scored the highest on Insight and Religiosity. The 41-50 and the group that scored the least on Insight and Religiosity were those in the age group of 31-40. It was also found that females scored higher on both Religiosity and Insight scales. There was no significant correlation found between Age or Gender on Religiosity or Insight. In the future this study could yield better results with a larger sample size and a more diverse distribution among age. In the future switching the primary scale looked at from the Insight scores to the Religiosity scores would be beneficial for a better overall picture.
**Work Cited**
Beck, A. T., Bauruch, E., Balter, J. M., Steer, R. A., & Warman, D. M. (2004). A new instrument for measuring insight: the Beck Cognitive Insight Scale. Elsevier, 319-329. Huber, S., & Huber, O. W. (2012). The Centrality of Religiosity Scale. Religions, 710-724.