QUESTION 1: Apply any basic descriptive techniques that you feel are appropriate and explain their meaning. Present and explain the quartiles: Q1 (25th percentile), Q2 (50th percentile), and Q3 (75th percentile). Report the skew and kurtosis values for the Partner and Self variables. Describe your interpretations of these numbers (Be sure you have checked the readings for this week to interpret kurtosis properly).

# Load the necessary library
library(psych)
## Warning: package 'psych' was built under R version 4.2.3
SC <- read.csv("https://blue.butler.edu/~rpadgett/ps310/Data/infidelity.csv")

describe(SC)
##         vars  n  mean    sd median trimmed   mad min max range  skew kurtosis
## Gender*    1 24  1.50  0.51    1.5    1.50  0.74   1   2     1  0.00    -2.08
## Partner    2 24 65.79 14.81   70.5   66.35  8.15  34  93    59 -0.49    -0.69
## Self       3 24 56.67 33.18   54.5   57.05 42.25   9 100    91 -0.04    -1.67
##           se
## Gender* 0.10
## Partner 3.02
## Self    6.77
#Quartiles for Partner and Self
quartiles <- data.frame(Partner=SC$Partner, Self=SC$Self)
apply(quartiles, 2, quantile, probs=c(0.25,0.5,0.75))
##     Partner  Self
## 25%   51.75 27.75
## 50%   70.50 54.50
## 75%   74.25 88.25
#Boxplot
boxplot(quartiles, main="Boxplot of Partner and Self", 
        ylab="Values", names=c("Partner", "Self"))

EXPLANATION OF QUESTION 1

In a descriptive analysis of the data, the Partner variable resulted in a mean score of 65.79 shots at the Partner target with a standard deviation of 14.81 shots (M = 65.79, SD = 14.81). The Self variable resulted in a mean score of 56.67 shots at the Self target with a standard deviation of 33.18 shots (M = 56.67, SD = 33.18). This is interesting because it indicates that participants averaged a greater number of shots when shooting a target of their cheating Partner’s face than their own. However, the stark contrast in standard deviations between the variable indicate a much larger range of shots made at the Self, in which participants made 33.18 shots more and less compared to the mean of 56.67 shots. This finding is also illustrated in the quartiles below.

For the Partner variable: For the Self variable: Q1 = 51.75 Q1 = 27.75 Q2 = 70.50 Q2 = 54.50 Q3 = 74.25 Q3 = 88.25. These quartiles are represented in the boxplot as well.

As illustrated by the numerical values and visual representations of the quartiles, it is evident that the Self variable has a much greater range of shots that hit the target despite a lower average in comparison to the Partner target. Interestingly, the variation in shots fired at the Self target may suggest their own self-blame in contributing to their partner’s cheating. Perhaps those who shot the target higher than average (M = 56.67) felt they were partially to blame for their partner’s cheating because they themselves had been distant, they didn’t feel like a good enough partner, they had their own wandering thoughts, or some other reason to feel responsible for their partner’s infidelity, and they expressed their frustration towards themselves by shooting the Self target a greater number of times. On the other hand, those who shot the target lower than average (M = 56.67) may feel as though their own self/behavior is not to blame for why their partner cheated, but they still expressed their frustration with the situation by shooting the target provided.

According to the statistical output, the skew for the Partner variable was -0.49, and the skew for the Self variable was -0.04. Evidently, both variables are negatively skewed, with the Self variable being only slightly negatively skewed and the Partner variable being more negatively skewed. Additionally, the kurtosis for the Partner variable was -0.69, and the kurtosis for the Self variable was -1.67. This suggests that both Partner and Self variables are platykurtic, though the Self variable is more platykurtic and would produce a flatter distribution compared to the Partner variable. These findings are supported by the stem and leaf plots in Question 3.

QUESTION 2: Add the histograms in your results document and describe the key features of each. Describe the shape of each distribution. Do you see any outliers? How did you decide?

SC <- read.csv("https://blue.butler.edu/~rpadgett/ps310/Data/infidelity.csv")

hist(SC$Partner, main="Partner Target", xlab="Partner")

hist(SC$Self, main="Self Target", xlab="Self")

EXPLANATION OF QUESTION 2

  1. As can be seen in the Partner Target histogram, there is a slight negative skew to the data, with the pique of the data being at the 70-80 shot interval, with a relatively normal climb and considerable drop off thereafter in scores. Based on the frequency of appearance of the values between 30-40 and 90-100 shots being only 1 participant each, this could indicate that the highest and lowest score ranges presented are potential outliers.

  2. Regarding the Self Target histogram, the data forms an odd shape due to the drop-off in scores between 40-80 shots. Based on this distribution, I would describe those 2 participants who scored between 60-80 shots as outliers, because it is both the lowest number of people in that interval, and it is a considerable drop off between the next interval of 80-100 which has 8 participants who scored in that range. By looking at the frequency of occurrence, it would seem to be that in this category people mostly had either relatively low scores (between 0-40, with 4 participants getting about 0-20 and 6 participants getting about 20-40 shots off) or very high scores (8 participants scored about 80-100 shots. Due to this, the graph makes almost a “U” shape, which is nearly the inverse of a histogram displaying normal distribution.

QUESTION 3: Produce stem & leaf plots of the Partner and Self variables. Set the scale as to maximize the usefulness of the graphs. Tell me in words how to interpret the two stem and leaf plots.

SC <- read.csv("https://blue.butler.edu/~rpadgett/ps310/Data/infidelity.csv")

stem(SC$Partner, scale = 2)
## 
##   The decimal point is 1 digit(s) to the right of the |
## 
##   3 | 4
##   4 | 138
##   5 | 112
##   6 | 459
##   7 | 00112344566
##   8 | 24
##   9 | 3
stem(SC$Self, scale = 2)
## 
##   The decimal point is 1 digit(s) to the right of the |
## 
##    0 | 9
##    1 | 014
##    2 | 678
##    3 | 334
##    4 | 6
##    5 | 18
##    6 | 9
##    7 | 
##    8 | 02389
##    9 | 577
##   10 | 00

EXPLANATION OF QUESTION 3

The stem-and-leaf plot for the Partner condition shows that most participants achieved scores ranging from 34-93 shots on target. The distribution appears negatively skewed, with the concentration of scores in the 70’s. The Self condition shows platykurtic distribution of shooting scores, with most participants hitting between 9 and 100 shots on target, and a concentration of scores in the 80s causing a slightly negatively skew. These findings suggest that participants may have different emotional responses and behaviors when targeting their partner’s image compared to their own image.

QUESTION 4: Produce a single boxplot displaying both the Partner and Self variables and paste that boxplot into your results document. Identify all the parts of the boxplots for the data. What does it tell you that the median is not in the center of the box for one of the variables? What do you learn from this box plot in general?

SC <- read.csv("https://blue.butler.edu/~rpadgett/ps310/Data/infidelity.csv")

#Boxplot
boxplot(SC$Partner, SC$Self, names=c("Partner", "Self"), 
        main="Boxplot for Partner and Self", col="lightblue")

#Numerical summary for Partner and Self
summary_partner <- fivenum(SC$Partner)
summary_self <- fivenum(SC$Self)

print(summary_partner)
## [1] 34.0 51.5 70.5 74.5 93.0
print(summary_self)
## [1]   9.0  27.5  54.5  88.5 100.0

EXPLANATION OF QUESTION 4

PARTNER SELF Min: 34 Min: 9 Q1: 51.5 Q1: 27.5 Q2: 70.5 Q2: 54.5 Q3: 74.5 Q3: 88.5 Max: 93 Max: 100

Partner → The boxplot parts would be marked with the above values Self → The boxplot parts would be marked similarly

Median Position - For Partner, the median (70.5) is closer to Q3 (74.5) than to Q1 (51.5), which means that it’s most likely skewed to the left. This would mean that many participants hit their partner’s target more consistently than the median would suggest. It might indicate a tendency for participants to focus more on their partner’s target, possibly as a means of venting their frustrations. - For Self, the median (54.5) is more centered between Q1 (27.5) and Q3 (88.5), but still a slight right skew is possible.

Boxplot Takeaways - The narrower IQR in the Partner data shows that the middle 50% of the scores (number of hits) are more consistently grouped around the median compared to the Self data. This could suggest that participants had more consistent performance when shooting at their partner’s target than at their own face. - The wider spread in Self data suggests that the participants performences were more varied when shooting at their own face. This could be due to mixed emotions or hesitations affecting their focus and aim. - The difference in spread and skewness between the two datasets could reflect the emotional turmoil and conflict faced by individuals in this situation. The skewness in the Partner data might be an indicator of a general tendency among participants to aim more consistently at their partner’s target as a form of release or confrontation.

QUESTION 5: Now redo the boxplot you did above (on the Self and Partner variables) only this time divided it by gender so that all 4 boxplots are on the same graph. To do this you will need to create 4 new variables and then boxplot those variables. Add some colors, names, and labels to make it look nice. Describe what the boxplot reveals about gender differences in response to infidelity. Let the data “speak to you.” Include a copy of this plot in your results document.

SC <- read.csv("https://blue.butler.edu/~rpadgett/ps310/Data/infidelity.csv")

Partner_Male <- SC$Partner[SC$Gender=="Male"]
Self_Male <- SC$Self[SC$Gender=="Male"]
Partner_Female <- SC$Partner[SC$Gender=="Female"]
Self_Female <- SC$Self[SC$Gender=="Female"]
boxplot (Partner_Male,Self_Male,Partner_Female,Self_Female,
         names = c("Partner Male","Self Male","Partner Female","Self Female"),
         main= "Partner and Self by Gender", col="lightblue")

EXPLANATION OF QUESTION 5

  1. Self compared - By breaking the “Self” identifier into male/female, you can see what exactly was skewing the data in the histogram to have most of the participants either scoring very low or very high. It appears that more male participants scored lower when shooting at a picture of themselves, with a notable positive skew depicted by the top whisker on the Self Male box indicating that, while some male participants scored in that 40-60 interval, most scored around 0-30 shots, with a median score falling between 20-30 shots. For the Self Female box you can see where the large number of participants scoring high came from in the histogram from earlier. Most of the female participants when shooting at a picture of themselves shot between 80-100 shots, with a negative skew depicted by the bottom whisker. Even when looking at the whiskers depicting the skew, there is no overlap in the number of shots fired by male vs. female participants at their own face, with range for males being between (what looks to be) about 5-55* shots (on the highest end of participants) and the range for females being between a little under 60-100 shots (*on the lowest end of participants).

  2. Partner compared - When looking at the partner data split by sex of participants, an interesting difference emerges. As was described by the histogram, there was a negative skew to this marker overall, but that partner is most salient when looking at the female participants shooting at their partner’s image. When you zero in on the Partner Female box, the data is spread across a broader range of values than Partner Male, with shots varying between a little over 40 to about 75 shots for most participants (that is, not taking whiskers into account just yet). When you examine the Partner Male box, the data is squished, with most participants shooting solidly between (what looks to be) the low 60s to mid 70s. Another unique difference between these groupings is the length of the whisker depicting skewness. For the Partner Female box, the top whisker depicts a considerable positive skewness of the data, with the whisker starting at about 70 shots and going up to a little under 100 shots for the highest number of shots fired. The Partner Male box covers less of a breadth of values with its skew, although it does still present one. Their data too is positively skewed, with the top whisker accounting for values between the mid to late 70s for shots scored to the early 80s on the highest end of shots fired. Interestingly, the median value of the Partner male data is where the whisker begins for the female participants data, demonstrating that the male participants overall score was higher for this measure, despite the range of values extending further out for female participants’ data, given the fact that there is less of a skew present in their data. Unlike the histogram, both Partner boxplots indicate a positive skewness versus the negative skewness the histogram displays. My guess as to why this would be the case is that it is because of the gathering of data split between the sexes. As I already described, male participants scored relatively close together scores compared to their female counterparts whose scores of shots were a wider breadth of values.

QUESTION 6: Run a correlation (and test it for significance (cor.test) between Partner and Self. You should also produce a scatterplot of the data putting Self on the x axis and y Partner on the y axis. You should add the regression line to your plot.

SC <- read.csv("https://blue.butler.edu/~rpadgett/ps310/Data/infidelity.csv")

cor(SC$Self, SC$Partner)
## [1] -0.2429221
cor.test(SC$Self, SC$Partner)
## 
##  Pearson's product-moment correlation
## 
## data:  SC$Self and SC$Partner
## t = -1.1746, df = 22, p-value = 0.2527
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.5886360  0.1779086
## sample estimates:
##        cor 
## -0.2429221
fit <- lm(SC$Partner ~ SC$Self)

summary(fit)
## 
## Call:
## lm(formula = SC$Partner ~ SC$Self)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -32.948 -10.553   2.124   9.874  27.353 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 71.93717    6.03051  11.929 4.46e-11 ***
## SC$Self     -0.10845    0.09233  -1.175    0.253    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 14.69 on 22 degrees of freedom
## Multiple R-squared:  0.05901,    Adjusted R-squared:  0.01624 
## F-statistic:  1.38 on 1 and 22 DF,  p-value: 0.2527
anova(fit)
## Analysis of Variance Table
## 
## Response: SC$Partner
##           Df Sum Sq Mean Sq F value Pr(>F)
## SC$Self    1  297.8  297.77  1.3797 0.2527
## Residuals 22 4748.2  215.83
plot(SC$Self, SC$Partner, main="Partner and Self", xlab="Self", ylab="Partner")
abline(reg=lm(SC$Partner~SC$Self), col="red")

EXPLANATION OF QUESTION 6

The correlation between Partner and Self is found to be equivalent to -0.25. This result is not significant because Pearson’s correlation test produced a p-value of p = .253, which is greater than p = .05 and thus cannot be determined as significant (t = -1.17, df = 22, p = 0.253). Supported by the scatterplot below, it is evident that there is a weak negative correlation between Partner and Self.

QUESTION 7: Finally, be sure to draw some “big-picture” conclusions about how males and females respond to learning that their partner was unfaithful to them.

Males have a diverse response when shooting at their partner’s face, with a range of 34-82 shots hitting the target. In the “Self” condition, they shoot at their own face, with a range of 9-51 shots hitting the target. Females, however, exhibit a more consistent response in the “Partner” and “Self” conditions, with shots hitting the target ranging from 41 to 93 and 58 to 100, respectively, compared to males. Gender differences are evident in how individuals respond to learning about their partner’s infidelity. Males have shown wider variation in their responses, while females exhibit more consistent responses. Males express frustration or anger more variably, as seen in their shot accuracy. Females have a more stable emotional expression, as indicated by their consistent shot accuracy. Both males and females respond differently when targeting their partner’s face, suggesting distinct emotional reactions when confronted with their partner’s betrayal versus their own feelings of hurt and anger.