Biba_and_Boba_Final
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## kurtosis, skewness1 Project 1
1.1 Introduction
Our team is Biba and Boba (Diana Piskareva and Daria Rukosueva). Our team wants to explore: The relationship between trust in state institutions and the amount of time spent on media resources.
We are interested in this topic because a large number of studies are devoted to the relationship between media and political participation. According to the Dimensions results, about 50 articles on this topic were published in 2018. Further research on this issue was on the decline, so research analysis of this aspect now seems necessary and important.
Also we were interested in this one because we see how the amount of time in absolutely different media resources increases from generation to generation, so for example, based on Zenith data, in 2021 Americans spent 252 minutes a day on my mobile Internet, and in 2012 60 minutes, this can be assumed to have happened due to the availability of devices with access to the Internet and a reduction in the cost of the Internet itself.
(https://www.vox.com/recode/2020/1/6/21048116/tech-companies-time-well-spent-mobile-phone-usage-data)
We chose Ukraine because these are the states of the post-Soviet space within which we are located, and therefore it would be interesting to observe the relationships that will appear within this state of the near abroad, since this may be applied (or vice versa not) in relation to Russia.
Our research question: how does the amount of time spent in the media space affect political trust?
1.2 Manipulating the data
Thus, in order to perform the necessary manipulations with the data, we downloaded the date ESS 2012
ESS6 <-
read.spss("/Users/DP/Downloads/ESS6.sav",
use.value.labels = T,
to.data.frame = T)Next, we directly selected the relevant data for our study
ESS6 <- dplyr:: select(ESS6, c("cntry", "tvtot", "tvpol", "polintr", "trstlgl", "trstplc", "trstplt"))
ESSn <- filter(ESS6, cntry=="Ukraine")Next, we came across the fact that some of the data we need is presented in a categorical format, so we converted them to numerical
ESSn = ESSn %>% mutate(trstlgl = case_when(trstlgl=="No trust at all" ~ "0",trstlgl=="1" ~ "1",trstlgl=="2" ~ "2", trstlgl=="3" ~ "3", trstlgl=="4" ~ "4", trstlgl=="5" ~ "5", trstlgl=="6" ~ "6",trstlgl=="7" ~ "7",trstlgl=="8" ~ "8", trstlgl=="9" ~ "9", trstlgl=="Complete trust" ~ "10"))
ESSn = ESSn %>% mutate(polintr = case_when(polintr=="Very interested" ~ "4",polintr=="Quite interested" ~ "3",polintr=="Hardly interested" ~ "2", polintr=="Not at all interested" ~ "1"))
ESSn = ESSn %>% mutate(trstplc = case_when(trstplc=="No trust at all" ~ "0",trstplc=="Complete trust" ~ "10",trstplc=="1" ~ "1",trstplc=="2" ~ "2", trstplc=="3" ~ "3", trstplc=="4" ~ "4", trstplc=="5" ~ "5", trstplc=="6" ~ "6",trstplc=="7" ~ "7",trstplc=="8" ~ "8", trstplc=="9" ~ "9"))
ESSn = ESSn %>% mutate(trstplt = case_when(trstplt=="No trust at all" ~ "0",trstplt=="Complete trust" ~ "10",trstplt=="1" ~ "1",trstplt=="2" ~ "2", trstplt=="3" ~ "3", trstplt=="4" ~ "4", trstplt=="5" ~ "5", trstplt=="6" ~ "6",trstplt=="7" ~ "7",trstplt=="8" ~ "8", trstplt=="9" ~ "9"))ESSn$trstlgl <- as.numeric(as.character(ESSn$trstlgl))
ESSn$polintr <- as.numeric(as.character(ESSn$polintr))
ESSn$trstplc <- as.numeric(as.character(ESSn$trstplc))
ESSn$trstplt <- as.numeric(as.character(ESSn$trstplt))The following table describes the categories of the variables we have selected
Variable = c("tvpol","tvtot","polintr","trstlgl","trstplc","trstplt")
Meaning = c("TV watching, news/politics/current, affairs on average weekday", "TV watching, total time on average weekday", "How interested in politics", "Trust in the legal system", "Trust in policy", "Trust in politicans")
Type = c("Ordinal", "Ordinal","Numeric","Numeric","Numeric","Numeric")
df <- data.frame(Variable, Meaning, Type, stringsAsFactors = FALSE)
df %>% kbl() %>% kable_minimal()| Variable | Meaning | Type |
|---|---|---|
| tvpol | TV watching, news/politics/current, affairs on average weekday | Ordinal |
| tvtot | TV watching, total time on average weekday | Ordinal |
| polintr | How interested in politics | Numeric |
| trstlgl | Trust in the legal system | Numeric |
| trstplc | Trust in policy | Numeric |
| trstplt | Trust in politicans | Numeric |
1.3 Data measurements
Next, we calculate the mean, mode and median indicators for our variables
Mode <- function(x) {
ux <- unique(x)
ux[which.max(tabulate(match(x, ux)))]
}
ESSn$polintr = as.numeric(as.character(ESSn$polintr))
polintr <- c(mean(ESSn$polintr, na.rm = TRUE), Mode(ESSn$polintr), median(ESSn$polintr, na.rm = TRUE))
names(polintr) <- c("mean", "mode", "median")
ESSn$trstlgl = as.numeric(as.character(ESSn$trstlgl))
trstlgl <- c(mean(ESSn$trstlgl, na.rm = TRUE), Mode(ESSn$trstlgl), median(ESSn$trstlgl, na.rm = TRUE))
names(trstlgl) <- c("mean", "mode", "median")
ESSn$trstplc = as.numeric(as.character(ESSn$trstplc))
trstplc <- c(mean(ESSn$trstplc, na.rm = TRUE), Mode(ESSn$trstplc), median(ESSn$trstplc, na.rm = TRUE))
names(trstplc) <- c("mean", "mode", "median")
ESSn$trstplt = as.numeric(as.character(ESSn$trstplt))
trstplt <- c(mean(ESSn$trstplt, na.rm = TRUE), Mode(ESSn$trstplt), median(ESSn$trstplt, na.rm = TRUE))
names(trstplt) <- c("mean", "mode", "median")
measure = data.frame(polintr, trstlgl, trstplc, trstplt, stringsAsFactors = FALSE)
kable(measure) %>%
kable_styling(bootstrap_options=c("bordered", "responsive","striped"), full_width = FALSE)| polintr | trstlgl | trstplc | trstplt | |
|---|---|---|---|---|
| mean | 2.161049 | 1.866176 | 2.045823 | 1.722329 |
| mode | 2.000000 | 0.000000 | 0.000000 | 0.000000 |
| median | 2.000000 | 1.000000 | 1.000000 | 1.000000 |
1.4 Visualisation
Next, we want to find out how much time people spend consuming content in general, how many people consume content for more than a few hours a day and how many people in general practically do not watch TV, do not read newspapers, etc.
ggplot(ESSn, aes(x = tvtot)) +
geom_bar(color = "white", fill = "white") +
coord_flip() +
scale_x_discrete(limits = rev(levels(ESSn$tvtot))) +
theme(panel.background = element_rect(fill = "pink", colour = "white"))
As we can see on this histogram, the largest indicator is from 1.5 hours
to 2, the next largest is more than three hours, and what is even more
significant for us is the fact that the number of people who said that
they do not consume this kind of content at all is extremely small in
relation to other indicators
Next, we want to consider whether these indicators differ in the context of not just media content consumption, but content directly related to politics and news
ggplot(ESSn, aes(x = tvpol)) +
geom_bar(color = "white", fill = "white") +
coord_flip() +
scale_x_discrete(limits = rev(levels(ESSn$tvpol))) +
theme(panel.background = element_rect(fill = "pink", colour = "white"))
And in this case, we see that political content is consumed much less
than TV viewing in general. The largest indicator in this case will be
less than 0.5 hours, which again is strikingly different from the
consumption of content in general, the smallest indicator will be from 2
hours to 2.5
Our next step is the question of how much people in this state as a whole are interested in politics
ggplot(ESSn, aes(x = polintr)) +
geom_histogram(binwidth = 1, colour = "pink", fill = "white") +
theme(panel.background = element_rect(fill = "pink", colour = "black"))
According to these data, the majority of people are barely interested in politics, while the smallest group will be people who are actively interested in politics At this stage, we can see a certain correlation between the fact that people do not consume a large amount of political content and, in general, when asked about interest in political processes, they say more about a small interest
Our next aspect is trust in the legal system
ESSn %>%
ggplot() +
geom_bar(aes(y = trstlgl), fill="pink") +
labs (x="Amount of people", y="Trust in the legal system") 
In this case, we see that trust in the legal system is almost completely
absent, the greatest indicator is a sneaky distrust of the legal
system
further, in more detail, we also want to consider the relationship of trust in the legal system with viewing political content
box_plot <- ggplot(ESSn, aes(x = trstlgl, y = tvpol))
box_plot +
geom_boxplot(fill="pink")
In this case, we can see that the average indicators of trust in
political systems for almost all groups will be similar, at a not very
high level, the only critical exceptions here will be people who do not
consume this content at all, their average value is zero, as well as
people who consume from 1 to 1.5 hours of political content, their the
average value is much higher than the others and their response range is
also much wider. While all other groups have approximately the same
range of responses regardless of the number of hours viewed. The only
small exception in this case for gas can be a group consuming from 2 to
2.5 hours, while those who consume only 0.5 more already have much more
standard indicators
Also in this context, it would be logical to consider whether there are serious differences in the range between trust in politicians and trust in police
ggplot(ESSn, aes(x=trstplc, y=trstplt))+
geom_point(color="pink", position = "jitter")+
labs( x = "Trust in the police", y = "Trust in the politicans")
Here we see that there is a correlation between a lack of trust in
politicians and a lack of trust in the police, it is quite obvious that
most people, not trusting politicians, also adhere to a position of
distrust in relation to other state institutions
ggplot(ESSn, aes(fill=tvpol, y=tvtot, x=polintr)) +
geom_bar(position='stack', stat='identity') +
theme_wsj()
And the last graph we reviewed brings us back to the issue of viewing
ordinary content and political content, here we see that almost all
groups consuming TV content are characterized by a small amount of
consumed political content. In this case, it is important to note and
pay attention that people consume it for less than an hour or up to an
hour, but the number of people who answered that they do not watch it is
quite small
In this case, returning to our research question, we can say that the amount of content conducted does not critically affect the credibility of politics, the only exception here will be only people who do not consume political content at all, only in their case we see a correlation between the absence of this content and also the lack of trust in politics. We can assume that trust in political institutions will be more influenced by trust in individual political institutions than viewing political content
2 Project 2
ESS10 <- import("/Users/DP/OneDrive/Рабочий стол/ESS10.sav")
str(df)## 'data.frame': 6 obs. of 3 variables:
## $ Variable: chr "tvpol" "tvtot" "polintr" "trstlgl" ...
## $ Meaning : chr "TV watching, news/politics/current, affairs on average weekday" "TV watching, total time on average weekday" "How interested in politics" "Trust in the legal system" ...
## $ Type : chr "Ordinal" "Ordinal" "Numeric" "Numeric" ...View(head(df))2.1 Clean the data
Step 0 - clear the dataset, leave only important things
greece <- filter(ESS10, ESS10$cntry == "GR")Let’s describe relationships between the following pairs of variables:
polintrandvote
I expect to find out if there is a relationship between the level of political interest (polintr) and whether individuals voted during last national elections (vote).
greece_2 <- greece %>% dplyr:: select(polintr, vote)
greece_2 <- na.omit(greece_2)
greece_2## polintr vote
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## 2799 3 3greece_2$polintr <- as.numeric(greece_2$polintr)
greece_2$vote <- as.numeric(greece_2$vote)
greece_2## polintr vote
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## 2799 3 32.2 Chi-squared Test
Part I. Chi-squared Test (2 points) 1) The correct choice of variables. A plot with the two variables involved (0.5 points)
# Convert the variables to factors
greece_2$polintr <- factor(greece_2$polintr)
greece_2$vote <- factor(greece_2$vote)
# Create a table with the counts for each combination of polintr and vote
table_data <- table(greece_2$polintr, greece_2$vote)
# Convert the table to a data frame
table_df <- as.data.frame.matrix(table_data)
# Add row names as a variable
table_df$polintr <- rownames(table_df)
# Reshape the data from wide to long format
table_long <- reshape2::melt(table_df, id.vars = "polintr")
# Create the stacked bar chart
ggplot(table_long, aes(x = polintr, y = value, fill = variable)) +
geom_bar(stat = "identity") +
labs(x = "Political Interest", y = "Count", fill = "Vote")
2) The null hypothesis is spelled out, and you make conclusions as
table(flowers) to how the results relate to it (0.5)
Vote Categories 1 Yes 2 No 3 Not eligible to vote
polintr Category 1 Very interested 2 Quite interested 3
Hardly interested 4 Not at all interested
We are interested in examining the association between political interest (polintr) and voting behavior (vote) among Greek citizens. Specifically, we want to test whether there is a significant difference in the distribution of votes among individuals with different levels of political interest. We can formulate the following null and alternative hypotheses:
Null hypothesis (H0): The distribution of votes is the same across all levels of political interest. Alternative hypothesis (HA): The distribution of votes is different across at least one pair of levels of political interest.
# Perform chi-squared test of independence
chisq_res <- chisq.test(table_data)## Warning in chisq.test(table_data): аппроксимация на основе хи-квадрат может
## быть неправильной# Print the test result
chisq_res##
## Pearson's Chi-squared test
##
## data: table_data
## X-squared = 76.519, df = 6, p-value = 1.867e-14We can reject the null hypothesis (p-value = 1.867e-14 < 0,05) and conclude that there is a significant difference in the distribution of votes across at least one pair of levels of political interest.
CrossTable(table_data, expected=T)## Warning in chisq.test(t, correct = FALSE, ...): аппроксимация на основе
## хи-квадрат может быть неправильной##
##
## Cell Contents
## |-------------------------|
## | N |
## | Expected N |
## | Chi-square contribution |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 2752
##
##
## |
## | 1 | 2 | 3 | Row Total |
## -------------|-----------|-----------|-----------|-----------|
## 1 | 127 | 5 | 1 | 133 |
## | 112.605 | 17.253 | 3.141 | |
## | 1.840 | 8.702 | 1.460 | |
## | 0.955 | 0.038 | 0.008 | 0.048 |
## | 0.055 | 0.014 | 0.015 | |
## | 0.046 | 0.002 | 0.000 | |
## -------------|-----------|-----------|-----------|-----------|
## 2 | 654 | 59 | 4 | 717 |
## | 607.053 | 93.012 | 16.935 | |
## | 3.631 | 12.437 | 9.880 | |
## | 0.912 | 0.082 | 0.006 | 0.261 |
## | 0.281 | 0.165 | 0.062 | |
## | 0.238 | 0.021 | 0.001 | |
## -------------|-----------|-----------|-----------|-----------|
## 3 | 748 | 102 | 23 | 873 |
## | 739.132 | 113.249 | 20.620 | |
## | 0.106 | 1.117 | 0.275 | |
## | 0.857 | 0.117 | 0.026 | 0.317 |
## | 0.321 | 0.286 | 0.354 | |
## | 0.272 | 0.037 | 0.008 | |
## -------------|-----------|-----------|-----------|-----------|
## 4 | 801 | 191 | 37 | 1029 |
## | 871.210 | 133.486 | 24.304 | |
## | 5.658 | 24.781 | 6.632 | |
## | 0.778 | 0.186 | 0.036 | 0.374 |
## | 0.344 | 0.535 | 0.569 | |
## | 0.291 | 0.069 | 0.013 | |
## -------------|-----------|-----------|-----------|-----------|
## Column Total | 2330 | 357 | 65 | 2752 |
## | 0.847 | 0.130 | 0.024 | |
## -------------|-----------|-----------|-----------|-----------|
##
##
## Statistics for All Table Factors
##
##
## Pearson's Chi-squared test
## ------------------------------------------------------------
## Chi^2 = 76.51923 d.f. = 6 p = 1.867254e-14
##
##
## - You have checked all the assumptions of the chi-square test and they are matched. You have run and correctly interpreted the chi-square test, analysing the standardized residuals (1)
The result of the chi-square test is a p-value of 1.867254e-14, which is less than the standard significance level of 0.05. Therefore, we reject the null hypothesis and conclude that there is a significant association between political interest and vote.
In this case, we can see that the cells with the largest standardized residuals are in the fourth second column (vote = 2). Specifically, the observed counts for those cells where political interest = 1 and political interest = 2 we overpredict, while when political interest = 4 we underpredict. Basically, people who are interested in politics do not vote less than we predict, on the other hand people who are not intereste din politics do not vote more often than we predict.
2.3 The t-test
Part II. The t-test (2.5 points) 4) The correct choice of variables, a plot with these variables (0.5)
greece_3 <- greece %>% dplyr:: select(netustm, vote)
greece_3 <- na.omit(greece_3)
greece_3$netustm <- as.numeric(greece_3$netustm)
greece_3$vote <- as.numeric(greece_3$vote)
greece_3## netustm vote
## 1 60 1
## 3 240 1
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## 2798 300 1netustm - internet use in minutes vote - national elections
# Create a vector for each vote category (1, 2, 3)
vote_1 <- subset(greece_3, vote == 1)$netustm
vote_2 <- subset(greece_3, vote == 2)$netustm
vote_3 <- subset(greece_3, vote == 3)$netustm #We will not use itggplot() + labs (title = "Internet use in minutes vs Voting", x="Did people vote on last national elections?", y="") +
geom_boxplot(aes(x='Yes', y=vote_1), fill="tomato1") +
geom_boxplot(aes(x='No', y=vote_2), fill="purple4") +
theme_bw()
5) You have checked the normality assumption for the t-test in 2
different ways (QQ plots / histogram / skew and kurtosis) (0.5)
shapiro.test(vote_1)##
## Shapiro-Wilk normality test
##
## data: vote_1
## W = 0.83022, p-value < 2.2e-16shapiro.test(vote_2)##
## Shapiro-Wilk normality test
##
## data: vote_2
## W = 0.8899, p-value = 7.288e-13var.test(vote_1, vote_2)##
## F test to compare two variances
##
## data: vote_1 and vote_2
## F = 1.0064, num df = 1670, denom df = 261, p-value = 0.9645
## alternative hypothesis: true ratio of variances is not equal to 1
## 95 percent confidence interval:
## 0.8312979 1.2030520
## sample estimates:
## ratio of variances
## 1.006375# QQ plot for vote_1
qqnorm(vote_1)
qqline(vote_1)
# Histogram for vote_1
hist(vote_1)
# QQ plot for vote_2
qqnorm(vote_2)
qqline(vote_2)
# Histogram for vote_2
hist(vote_2)
# Calculate skewness and kurtosis for vote_1
skewness(vote_1)## [1] 1.87265kurtosis(vote_1)## [1] 8.054205# Calculate skewness and kurtosis for vote_2
skewness(vote_2)## [1] 1.2126kurtosis(vote_2)## [1] 4.260232For vote_1, the skewness value is 1.87265 which is greater than zero, indicating a positively skewed distribution. The kurtosis value of 8.054205 indicates that the distribution is highly leptokurtic, meaning it has a sharp peak and heavy tails. These results suggest that the distribution of vote_1 may not be normal.
For vote_2, the skewness value is 1.2126 which is also greater than zero, indicating a positively skewed distribution. The kurtosis value of 4.260232 indicates that the distribution is moderately leptokurtic, meaning it has a relatively sharp peak and moderately heavy tails. These results also suggest that the distribution of vote_2 may not be normal.
Overall, neither vote_1 nor vote_2 appears to have a normal distribution based on their skewness and kurtosis values.
- The null hypothesis is spelled out, and you make conclusions as to how the results relate to it. You have applied the correct t-test formula and interpreted the result correctly. If the result is statistically significant, the effect size is reported (1)
Null hypothesis: There is no significant difference in the mean time spent on the internet between people who voted and those who didn’t vote in the last national elections.
Alternative hypothesis: There is a significant difference in the mean time spent on the internet between people who voted and those who didn’t vote in the last national elections.
t.test(vote_1, vote_2, var.equal = TRUE)##
## Two Sample t-test
##
## data: vote_1 and vote_2
## t = -3.2426, df = 1931, p-value = 0.001204
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -47.33311 -11.65582
## sample estimates:
## mean of x mean of y
## 190.8414 220.3359The t-test results show that there is a statistically significant difference between the mean number of minutes spent on the internet by people who voted in the last national elections (vote_1) and those who did not vote (vote_2). The t-statistic value is -3.2426 with a p-value of 0.001204, which is less than the typical threshold of 0.05, indicating strong evidence against the null hypothesis.
The 95% confidence interval for the difference in means is between -47.33311 and -11.65582, which does not include zero, indicating that the difference between the two means is statistically significant. The negative sign of the confidence interval suggests that people who did not vote tend to spend more minutes on the internet compared to those who did vote.
Therefore, we can reject the null hypothesis and conclude that there is a significant difference in the mean number of minutes spent on the internet between people who voted and those who did not vote.
- You have double-checked your results with a non-parametric test (0.5)
wilcox.test(vote_1, vote_2, alternative = "two.sided")##
## Wilcoxon rank sum test with continuity correction
##
## data: vote_1 and vote_2
## W = 183930, p-value = 2.664e-05
## alternative hypothesis: true location shift is not equal to 0The test resulted in a W value of 183930 and a p-value of 2.664e-05. The p-value is less than the significance level of 0.05, indicating that we can reject the null hypothesis of no difference between the two groups. Therefore, we can conclude that there is a significant difference in the internet use in minutes between people who voted on the last national election and those who did not vote.
We can conclude that people who do not vote spend more time in the internet on average then those who do vote.
2.4 ANOVA
Part III. ANOVA (3.5 points) 8) The correct choice of variables, a boxplot with these variables (0.5)
greece_4 <- greece %>% dplyr:: select(polintr, netustm)
greece_4 <- na.omit(greece_4)
greece_4$polintr <- as.factor(greece_4$polintr)
greece_4$netustm <- as.numeric(as.character(greece_4$netustm))
greece_4## polintr netustm
## 1 3 60
## 3 2 240
## 4 3 120
## 5 3 60
## 7 3 120
## 9 3 120
## 11 1 120
## 12 2 480
## 13 3 190
## 14 3 300
## 16 2 360
## 18 4 200
## 19 2 360
## 20 4 240
## 21 4 480
## 22 4 300
## 23 2 75
## 24 3 120
## 25 3 75
## 26 1 420
## 27 3 180
## 32 2 210
## 33 4 300
## 36 4 45
## 37 4 60
## 38 4 60
## 40 4 120
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## 43 3 180
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## 45 2 300
## 48 4 60
## 50 3 240
## 51 1 360
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## 54 2 120
## 55 1 60
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## 566 4 300
## 570 1 360
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## 578 2 30
## 579 4 480
## 580 3 300
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## 585 2 450
## 586 4 90
## 587 2 180
## 589 2 180
## 591 3 330
## 592 3 60
## 593 4 60
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## 596 3 120
## 598 4 120
## 599 2 240
## 601 2 180
## 602 2 240
## 603 3 150
## 608 3 120
## 609 3 180
## 610 1 270
## 611 3 180
## 612 3 180
## 614 3 60
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## 617 4 300
## 618 3 180
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## 621 4 120
## 622 3 60
## 626 3 180
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## 629 3 170
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## 636 2 300
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## 650 2 120
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## 652 4 300
## 653 3 180
## 654 4 600
## 655 4 120
## 656 3 240
## 657 3 60
## 658 3 240
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## 661 4 120
## 662 3 120
## 663 4 420
## 664 3 180
## 666 4 150
## 668 2 60
## 670 2 240
## 671 1 150
## 672 4 180
## 673 4 180
## 676 3 60
## 677 3 60
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## 686 3 60
## 687 3 120
## 688 3 120
## 690 3 210
## 691 4 720
## 692 3 480
## 695 2 240
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## 701 1 600
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## 704 4 120
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## 707 4 300
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## 795 3 210
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## 815 3 300
## 816 3 300
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## 820 4 300
## 821 4 90
## 822 4 330
## 826 3 90
## 827 3 60
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## 831 3 180
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## 834 2 330
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## 837 3 600
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## 844 3 180
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## 847 3 60
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## 852 2 90
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## 907 1 240
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## 916 4 180
## 918 4 90
## 919 4 300
## 920 3 300
## 921 4 180
## 925 2 480
## 928 2 120
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## 930 2 120
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## 935 2 330
## 936 3 240
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## 938 2 180
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## 942 2 120
## 943 3 90
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## 949 1 300
## 951 1 120
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## 974 2 330
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## 984 4 120
## 985 4 120
## 987 4 330
## 988 4 120
## 989 3 90
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## 993 2 120
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## 995 4 60
## 997 4 90
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## 1004 3 60
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## 1125 2 120
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## 1150 3 120
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## 1153 3 60
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## 1156 4 120
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## 1168 2 120
## 1169 2 135
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## 1180 3 240
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## 1250 2 150
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## 1289 4 660
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## 1311 4 240
## 1312 2 30
## 1313 2 270
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## 1336 4 170
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## 2798 1 300polintr - interests in politics 1 - Very interested 2 - Quite interested 3 - Hardly interested 4 - Not at all interested
netustm - internet use in minutes
# Create a vector for each polit. interest category (1, 2, 3,4)
pol_1 <- subset(greece_4, polintr == 1)$netustm
pol_2 <- subset(greece_4, polintr == 2)$netustm
pol_3 <- subset(greece_4, polintr == 3)$netustm
pol_4 <- subset(greece_4, polintr == 4)$netustm ggplot()+
geom_boxplot(data = greece_4, aes(x = polintr, y = netustm), fill="green3", col="purple", alpha = 0.5) +
ylim(c(0,1000)) +
xlab("How interested are people in politics?") +
ylab("Internet use in minutes ") +
ggtitle("Internet use in minutes vs Political interest")## Warning: Removed 1 rows containing non-finite values (`stat_boxplot()`).
- You have checked and correctly interpreted the assumptions (1)
Hypothesis: the mean amount of time spent on the Internet is the same for people with different levels of political interests
library(kableExtra)
library(psych)
describeBy(greece_4$netustm, greece_4$polintr, mat = TRUE) %>% #create dataframe
dplyr:: select(polintr = group1, N=n, Mean=mean, SD=sd, Median=median, Min=min, Max=max,
Skew=skew, Kurtosis=kurtosis, st.error = se) %>%
kable(align=c("lrrrrrrrr"), digits=2, row.names = FALSE,
caption="Political interests") %>%
kable_styling(bootstrap_options=c("bordered", "responsive","striped"), full_width = FALSE)| polintr | N | Mean | SD | Median | Min | Max | Skew | Kurtosis | st.error |
|---|---|---|---|---|---|---|---|---|---|
| 1 | 96 | 211.70 | 117.44 | 180 | 30 | 600 | 1.03 | 0.95 | 11.99 |
| 2 | 502 | 193.35 | 131.56 | 150 | 20 | 1200 | 1.94 | 7.40 | 5.87 |
| 3 | 660 | 181.22 | 127.12 | 150 | 1 | 960 | 1.94 | 5.55 | 4.95 |
| 4 | 761 | 207.33 | 149.58 | 180 | 0 | 900 | 1.53 | 2.34 | 5.42 |
par(mar = c(3,10,0,3))
barplot(table(greece_4$polintr)/nrow(greece_4)*100, horiz = T, xlim = c(0,60), las = 2)
it can be concluded from these data that the samples can be compared
leveneTest(greece_4$netustm ~ greece_4$polintr)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 3 3.3025 0.01956 *
## 2015
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1The variances are not equal, since Pr < 0.05 , so we can reject the null hypothesis of equality of variances
oneway.test(greece_4$netustm ~ greece_4$polintr, var.equal = F) ##
## One-way analysis of means (not assuming equal variances)
##
## data: greece_4$netustm and greece_4$polintr
## F = 4.9501, num df = 3.00, denom df = 432.13, p-value = 0.002174pairwise.t.test(greece_4$netustm, greece_4$polintr,
adjust = "bonferroni")##
## Pairwise comparisons using t tests with pooled SD
##
## data: greece_4$netustm and greece_4$polintr
##
## 1 2 3
## 2 0.457 - -
## 3 0.207 0.402 -
## 4 0.768 0.302 0.002
##
## P value adjustment method: holmplot_grpfrq(greece_4$netustm, greece_4$polintr, type = "box")## Warning: The `fun.y` argument of `stat_summary()` is deprecated as of ggplot2 3.3.0.
## ℹ Please use the `fun` argument instead.
## ℹ The deprecated feature was likely used in the sjPlot package.
## Please report the issue at <]8;;https://github.com/strengejacke/sjPlot/issueshttps://github.com/strengejacke/sjPlot/issues]8;;>.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.## Warning in rq.fit.br(wx, wy, tau = tau, ...): Solution may be nonunique
## Warning in rq.fit.br(wx, wy, tau = tau, ...): Solution may be nonunique
## Warning in rq.fit.br(wx, wy, tau = tau, ...): Solution may be nonunique
## Warning in rq.fit.br(wx, wy, tau = tau, ...): Solution may be nonunique
## Warning in rq.fit.br(wx, wy, tau = tau, ...): Solution may be nonunique
## Warning in rq.fit.br(wx, wy, tau = tau, ...): Solution may be nonunique
## Warning in rq.fit.br(wx, wy, tau = tau, ...): Solution may be nonunique
it can be concluded that those who are Very interested, Quite interesting and Not at all interested spend the most time on the Internet, unlike those who are Hardly interested in politics
3 Project 3
RQ: Are related persons satisfied with the national government, happy and trust the legal system with the ability of the population to influence on politics in Greek government?
df <- import("/Users/DP/OneDrive/Рабочий стол/ESS10.sav")3.1 Manipulation the data
in order to make it easier to work with data, we will create a separate dataset with Greek data
attributes(df$cntry)## $label
## [1] "Country"
##
## $format.spss
## [1] "A2"
##
## $labels
## Albania Austria Belgium Bulgaria
## "AL" "AT" "BE" "BG"
## Switzerland Cyprus Czechia Germany
## "CH" "CY" "CZ" "DE"
## Denmark Estonia Spain Finland
## "DK" "EE" "ES" "FI"
## France United Kingdom Georgia Greece
## "FR" "GB" "GE" "GR"
## Croatia Hungary Ireland Iceland
## "HR" "HU" "IE" "IS"
## Israel Italy Lithuania Luxembourg
## "IL" "IT" "LT" "LU"
## Latvia Montenegro North Macedonia Netherlands
## "LV" "ME" "MK" "NL"
## Norway Poland Portugal Romania
## "NO" "PL" "PT" "RO"
## Serbia Russian Federation Sweden Slovenia
## "RS" "RU" "SE" "SI"
## Slovakia Turkey Ukraine Kosovo
## "SK" "TR" "UA" "XK"greece <- filter(df, cntry=="GR")
dim(greece)## [1] 2799 586Let’s choose 3 continuous and 1 categorical variables
continuous
happy - How happy are you. C1 Taking all things together, how happy would you say you are?
stfgov - How satisfied with the national government
trstlgl - Trust in the legal system B6-12a Using this card, please tell me on a score of 0-10 how much you personally trust each of the institutions I read out. 0 means you do not trust an institution at all, and 10 means you have complete trust. Firstly… …the legal system?
categorical psppipla - Political system allows people to have influence on politics. And how much would you say that the political system in [country] allows people like you to have an influence on politics?
greece <- select(greece, c("stfgov", "happy", "trstlgl", "psppipla"))
skim(greece)| Name | greece |
| Number of rows | 2799 |
| Number of columns | 4 |
| _______________________ | |
| Column type frequency: | |
| numeric | 4 |
| ________________________ | |
| Group variables | None |
Variable type: numeric
| skim_variable | n_missing | complete_rate | mean | sd | p0 | p25 | p50 | p75 | p100 | hist |
|---|---|---|---|---|---|---|---|---|---|---|
| stfgov | 21 | 0.99 | 4.12 | 2.27 | 0 | 2 | 4 | 6 | 10 | ▇▇▇▅▁ |
| happy | 5 | 1.00 | 6.58 | 1.54 | 0 | 6 | 7 | 8 | 10 | ▁▁▅▇▁ |
| trstlgl | 13 | 1.00 | 6.43 | 2.26 | 0 | 5 | 7 | 8 | 10 | ▂▃▆▇▅ |
| psppipla | 78 | 0.97 | 1.90 | 0.96 | 1 | 1 | 2 | 3 | 5 | ▇▅▅▁▁ |
summary(greece) ## stfgov happy trstlgl psppipla
## Min. : 0.000 Min. : 0.000 Min. : 0.00 Min. :1.000
## 1st Qu.: 2.000 1st Qu.: 6.000 1st Qu.: 5.00 1st Qu.:1.000
## Median : 4.000 Median : 7.000 Median : 7.00 Median :2.000
## Mean : 4.116 Mean : 6.579 Mean : 6.43 Mean :1.897
## 3rd Qu.: 6.000 3rd Qu.: 8.000 3rd Qu.: 8.00 3rd Qu.:3.000
## Max. :10.000 Max. :10.000 Max. :10.00 Max. :5.000
## NA's :21 NA's :5 NA's :13 NA's :78using the summary function, we saw that the missing values are encoded correctly and are reflected as NA, so we can remove them from the dataset so that they do not distort the results.
greece <- greece[complete.cases(greece),]
summary(greece)## stfgov happy trstlgl psppipla
## Min. : 0.000 Min. : 0.000 Min. : 0.000 Min. :1.0
## 1st Qu.: 2.000 1st Qu.: 6.000 1st Qu.: 5.000 1st Qu.:1.0
## Median : 4.000 Median : 7.000 Median : 7.000 Median :2.0
## Mean : 4.105 Mean : 6.593 Mean : 6.426 Mean :1.9
## 3rd Qu.: 6.000 3rd Qu.: 8.000 3rd Qu.: 8.000 3rd Qu.:3.0
## Max. :10.000 Max. :10.000 Max. :10.000 Max. :5.03.2 descriptive statistics
We get general information about variables using the describe function
greece %>%
dplyr::select(-4) %>%
describe() ## vars n mean sd median trimmed mad min max range skew kurtosis
## stfgov 1 2685 4.11 2.28 4 4.08 2.97 0 10 10 0.10 -0.75
## happy 2 2685 6.59 1.53 7 6.70 1.48 0 10 10 -0.73 0.96
## trstlgl 3 2685 6.43 2.26 7 6.65 1.48 0 10 10 -0.72 -0.13
## se
## stfgov 0.04
## happy 0.03
## trstlgl 0.04greece %>%
dplyr::select(-4) %>%
sjmisc::descr(show = c('n', "mean","sd", "md", "range")) %>%
rename("variable" = "var",
"Number of obs." = "n",
"Mean" = "mean",
"SD" = "sd",
"Median" = "md",
"Range" = "range") ##
## ## Basic descriptive statistics
##
## variable Number of obs. Mean SD Median Range
## stfgov 2685 4.105400 2.278420 4 10 (0-10)
## happy 2685 6.593296 1.527917 7 10 (0-10)
## trstlgl 2685 6.426071 2.259652 7 10 (0-10)greece %>%
pivot_longer(c(stfgov, happy, trstlgl),
names_to = 'Var', values_to = 'Score') %>%
ggplot(aes(y=Score)) +
geom_boxplot() +
ggtitle("Distribution of scores") +
xlab("Variable") +
ylab("Score") +
theme_bw()+
theme(legend.position="none") +
facet_wrap(~Var)
In boxplot we see several outliers in the values of happy and trust
greece %>%
pivot_longer(c(stfgov, happy, trstlgl),
names_to = 'Var', values_to = 'Score') %>%
ggplot(aes(x=Score, fill=Var)) +
geom_histogram(aes(y=..density.., fill = Var), bins = 10) +
geom_density(alpha = .5, color="blue")+
ggtitle("Distribution of scores") +
xlab("Variable") +
ylab("Score") +
theme_bw()+
theme(legend.position="none") +
facet_wrap(~Var)## Warning: The dot-dot notation (`..density..`) was deprecated in ggplot2 3.4.0.
## ℹ Please use `after_stat(density)` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.
As it can be seen from the histograms, satisfaction with government,
happy close to normal distribution. As for the trust in the legal system
the histogram is not normally distributed.
categorical Let’s look at the categorical variable
table(greece$psppipla)##
## 1 2 3 4 5
## 1205 710 614 146 10Category 5 (`A great deal’) contains only 5 observations. This may affect the evaluation of the coefficients. Therefore, let’s combine categories 4 and 5
greece$psppipla <- car::recode(greece$psppipla, "1 = 1;
2 = 2;
3 = 3;
4 = 4;
5 = 4")greece %>%
group_by(psppipla) %>%
count()## # A tibble: 4 × 2
## # Groups: psppipla [4]
## psppipla n
## <dbl> <int>
## 1 1 1205
## 2 2 710
## 3 3 614
## 4 4 156greece$psppipla = factor(greece$psppipla) greece %>%
ggplot(aes(x = psppipla)) +
geom_bar(fill = "lightblue", color = "blue") +
xlab("Category") +
ylab("Frequency") +
theme_bw() 
scatter plot
par(mfrow = c(1, 3))greece %>%
ggplot(aes(x=stfgov, y=happy)) +
geom_point(size=2) +
geom_smooth(method=lm)## `geom_smooth()` using formula = 'y ~ x'
greece %>%
ggplot(aes(x=stfgov, y=trstlgl)) +
geom_point(size=2) +
geom_smooth(method=lm)## `geom_smooth()` using formula = 'y ~ x'
greece %>%
ggplot(aes(x=trstlgl, y=happy)) +
geom_point(size=2) +
geom_smooth(method=lm)## `geom_smooth()` using formula = 'y ~ x'
there is a positive correlation between happy and satisfaction with
government there is a positive correlation between trust in the legal
system and satisfaction with government there is a positive correlation
between happy and trust in the legal system
3.3 Correlations
chart.Correlation(greece[,c('stfgov', 'happy', 'trstlgl')],
histogram = TRUE) # by default Pearson## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
chart.Correlation(greece[,c('stfgov', 'happy', 'trstlgl')],
histogram = TRUE,
method = "spearman") # Spearman's method## Warning in cor.test.default(as.numeric(x), as.numeric(y), method = method):
## Есть совпадающие значения: не могу высчитать точное p-значение
## Warning in cor.test.default(as.numeric(x), as.numeric(y), method = method):
## argument 1 does not name a graphical parameter## Warning in cor.test.default(as.numeric(x), as.numeric(y), method = method):
## Есть совпадающие значения: не могу высчитать точное p-значение## Warning in par(usr): argument 1 does not name a graphical parameter## Warning in cor.test.default(as.numeric(x), as.numeric(y), method = method):
## Есть совпадающие значения: не могу высчитать точное p-значение## Warning in par(usr): argument 1 does not name a graphical parameter
chart.Correlation(greece[,c('stfgov', 'happy', 'trstlgl')],
histogram = TRUE,
method = "kendall") # Kendall's method## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
heatmap
heatmaply_cor(
cor(greece[,c('stfgov', 'happy', 'trstlgl')], method = "spearman"),
Colv=NA, Rowv=NA)матрица корреляций
cor.test(greece$happy, greece$stfgov)##
## Pearson's product-moment correlation
##
## data: greece$happy and greece$stfgov
## t = 12.302, df = 2683, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.1949530 0.2665744
## sample estimates:
## cor
## 0.2310767cor.test(greece$happy, greece$stfgov,method="spearman")## Warning in cor.test.default(greece$happy, greece$stfgov, method = "spearman"):
## Есть совпадающие значения: не могу высчитать точное p-значение##
## Spearman's rank correlation rho
##
## data: greece$happy and greece$stfgov
## S = 2550059838, p-value < 2.2e-16
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
## rho
## 0.2095602cor_matrix <- cor(greece[,c('stfgov', 'happy', 'trstlgl')], method = "spearman")
stargazer(cor_matrix, title="Correlation Matrix", type = "latex")##
## % Table created by stargazer v.5.2.3 by Marek Hlavac, Social Policy Institute. E-mail: marek.hlavac at gmail.com
## % Date and time: Пт, июн 09, 2023 - 16:16:10
## \begin{table}[!htbp] \centering
## \caption{Correlation Matrix}
## \label{}
## \begin{tabular}{@{\extracolsep{5pt}} cccc}
## \\[-1.8ex]\hline
## \hline \\[-1.8ex]
## & stfgov & happy & trstlgl \\
## \hline \\[-1.8ex]
## stfgov & $1$ & $0.210$ & $0.313$ \\
## happy & $0.210$ & $1$ & $0.324$ \\
## trstlgl & $0.313$ & $0.324$ & $1$ \\
## \hline \\[-1.8ex]
## \end{tabular}
## \end{table}sjPlot::tab_corr(greece[,c('stfgov', 'happy', 'trstlgl')],
corr.method = "spearman") | stfgov | happy | trstlgl | |
|---|---|---|---|
| stfgov | 0.210*** | 0.313*** | |
| happy | 0.210*** | 0.324*** | |
| trstlgl | 0.313*** | 0.324*** | |
| Computed correlation used spearman-method with listwise-deletion. | |||
cor.test(greece$happy, greece$stfgov)##
## Pearson's product-moment correlation
##
## data: greece$happy and greece$stfgov
## t = 12.302, df = 2683, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.1949530 0.2665744
## sample estimates:
## cor
## 0.2310767cor.test(greece$happy, greece$stfgov,method="kendall")##
## Kendall's rank correlation tau
##
## data: greece$happy and greece$stfgov
## z = 11.315, p-value < 2.2e-16
## alternative hypothesis: true tau is not equal to 0
## sample estimates:
## tau
## 0.1679942cor_matrix <- cor(greece[,c('stfgov', 'happy', 'trstlgl')], method = "kendall")
stargazer(cor_matrix, title="Correlation Matrix", type = "latex")##
## % Table created by stargazer v.5.2.3 by Marek Hlavac, Social Policy Institute. E-mail: marek.hlavac at gmail.com
## % Date and time: Пт, июн 09, 2023 - 16:16:11
## \begin{table}[!htbp] \centering
## \caption{Correlation Matrix}
## \label{}
## \begin{tabular}{@{\extracolsep{5pt}} cccc}
## \\[-1.8ex]\hline
## \hline \\[-1.8ex]
## & stfgov & happy & trstlgl \\
## \hline \\[-1.8ex]
## stfgov & $1$ & $0.168$ & $0.238$ \\
## happy & $0.168$ & $1$ & $0.256$ \\
## trstlgl & $0.238$ & $0.256$ & $1$ \\
## \hline \\[-1.8ex]
## \end{tabular}
## \end{table}sjPlot::tab_corr(greece[,c('stfgov', 'happy', 'trstlgl')],
corr.method = "kendall")| stfgov | happy | trstlgl | |
|---|---|---|---|
| stfgov | 0.168*** | 0.238*** | |
| happy | 0.168*** | 0.256*** | |
| trstlgl | 0.238*** | 0.256*** | |
| Computed correlation used kendall-method with listwise-deletion. | |||
cor.test(greece$happy, greece$stfgov)##
## Pearson's product-moment correlation
##
## data: greece$happy and greece$stfgov
## t = 12.302, df = 2683, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.1949530 0.2665744
## sample estimates:
## cor
## 0.2310767cor.test(greece$happy, greece$stfgov,method="spearman")## Warning in cor.test.default(greece$happy, greece$stfgov, method = "spearman"):
## Есть совпадающие значения: не могу высчитать точное p-значение##
## Spearman's rank correlation rho
##
## data: greece$happy and greece$stfgov
## S = 2550059838, p-value < 2.2e-16
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
## rho
## 0.2095602cor_matrix <- cor(greece[,c('stfgov', 'happy', 'trstlgl')], method = "spearman")
stargazer(cor_matrix, title="Correlation Matrix", type = "latex")##
## % Table created by stargazer v.5.2.3 by Marek Hlavac, Social Policy Institute. E-mail: marek.hlavac at gmail.com
## % Date and time: Пт, июн 09, 2023 - 16:16:13
## \begin{table}[!htbp] \centering
## \caption{Correlation Matrix}
## \label{}
## \begin{tabular}{@{\extracolsep{5pt}} cccc}
## \\[-1.8ex]\hline
## \hline \\[-1.8ex]
## & stfgov & happy & trstlgl \\
## \hline \\[-1.8ex]
## stfgov & $1$ & $0.210$ & $0.313$ \\
## happy & $0.210$ & $1$ & $0.324$ \\
## trstlgl & $0.313$ & $0.324$ & $1$ \\
## \hline \\[-1.8ex]
## \end{tabular}
## \end{table}sjPlot::tab_corr(greece[,c('stfgov', 'happy', 'trstlgl')],
corr.method = "spearman")| stfgov | happy | trstlgl | |
|---|---|---|---|
| stfgov | 0.210*** | 0.313*** | |
| happy | 0.210*** | 0.324*** | |
| trstlgl | 0.313*** | 0.324*** | |
| Computed correlation used spearman-method with listwise-deletion. | |||
rcorr(as.matrix(greece[,c('stfgov', 'happy', 'trstlgl')]), type = "spearman")## stfgov happy trstlgl
## stfgov 1.00 0.21 0.31
## happy 0.21 1.00 0.32
## trstlgl 0.31 0.32 1.00
##
## n= 2685
##
##
## P
## stfgov happy trstlgl
## stfgov 0 0
## happy 0 0
## trstlgl 0 0cor_mat <- greece[,-4] %>%
rstatix::cor_mat()
cor_mat %>%
rstatix::cor_get_pval()## # A tibble: 3 × 4
## rowname stfgov happy trstlgl
## <chr> <dbl> <dbl> <dbl>
## 1 stfgov 0 7.09e-34 1.03e-68
## 2 happy 7.09e-34 0 2.03e-63
## 3 trstlgl 1.03e-68 2.03e-63 0cor_mat %>%
rstatix::cor_gather()## # A tibble: 9 × 4
## var1 var2 cor p
## <chr> <chr> <dbl> <dbl>
## 1 stfgov stfgov 1 0
## 2 happy stfgov 0.23 7.09e-34
## 3 trstlgl stfgov 0.33 1.03e-68
## 4 stfgov happy 0.23 7.09e-34
## 5 happy happy 1 0
## 6 trstlgl happy 0.32 2.03e-63
## 7 stfgov trstlgl 0.33 1.03e-68
## 8 happy trstlgl 0.32 2.03e-63
## 9 trstlgl trstlgl 1 0greece[,-4] %>%
apa.cor.table(filename = "cor_matrix_Greece.doc")##
##
## Means, standard deviations, and correlations with confidence intervals
##
##
## Variable M SD 1 2
## 1. stfgov 4.11 2.28
##
## 2. happy 6.59 1.53 .23**
## [.19, .27]
##
## 3. trstlgl 6.43 2.26 .33** .32**
## [.29, .36] [.28, .35]
##
##
## Note. M and SD are used to represent mean and standard deviation, respectively.
## Values in square brackets indicate the 95% confidence interval.
## The confidence interval is a plausible range of population correlations
## that could have caused the sample correlation (Cumming, 2014).
## * indicates p < .05. ** indicates p < .01.
## greece[,-4] %>%
sjPlot::sjp.corr()## Warning: 'sjp.corr' is deprecated. Please use 'correlation::correlation()' and
## its related plot()-method.## Computing correlation using pearson-method with listwise-deletion...## Warning: Removed 6 rows containing missing values (`geom_text()`).
From what we can see, all the relationship between our variables are
quite moderate and have positive direction. The highest correlation
coefficient is between trstlgl and stfgov. The presented values confirm
the situation on the scatterplots. It is also worth noting that there is
a very high level of significance (p <0.001)
a boxplot for the categorical predictor and the outcome
greece %>%
ggplot(aes(x = factor (psppipla),
y = happy,
fill = factor (psppipla))) +
geom_boxplot() +
ggtitle("Distribution of happy level") +
xlab("Category") +
ylab("Happy level") +
theme_bw()+
theme(legend.position="none") 
Regardless of the level of psppipla, we observe the same distribution of
the level of happiness of citizens
3.4 Linear regression
model1 = lm(happy ~ stfgov, data = greece)
sjPlot::tab_model(model1)| happy | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | 5.96 | 5.84 – 6.07 | <0.001 |
| stfgov | 0.15 | 0.13 – 0.18 | <0.001 |
| Observations | 2685 | ||
| R2 / R2 adjusted | 0.053 / 0.053 | ||
we standardize - so we can compare the coefficients with each other, and interpret them as the size of the effect
greece <- greece %>%
mutate(Zhappy = scale(happy)[,1],
Zstfgov = scale(stfgov)[,1],
Ztrstlgl = scale(trstlgl)[,1])model1_std = lm(Zhappy ~ Zstfgov, data = greece)
sjPlot::tab_model(model1_std)| Zhappy | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | 0.00 | -0.04 – 0.04 | 1.000 |
| Zstfgov | 0.23 | 0.19 – 0.27 | <0.001 |
| Observations | 2685 | ||
| R2 / R2 adjusted | 0.053 / 0.053 | ||
# let's add a categorical variable
model2 = lm(happy ~ stfgov + psppipla, data = greece)
sjPlot::tab_model(model2)| happy | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | 5.99 | 5.86 – 6.11 | <0.001 |
| stfgov | 0.15 | 0.13 – 0.18 | <0.001 |
| psppipla [2] | -0.05 | -0.19 – 0.09 | 0.497 |
| psppipla [3] | -0.09 | -0.24 – 0.05 | 0.206 |
| psppipla [4] | 0.18 | -0.07 – 0.43 | 0.161 |
| Observations | 2685 | ||
| R2 / R2 adjusted | 0.055 / 0.054 | ||
# with standardized coefficients
model2_std = lm(Zhappy ~ Zstfgov + psppipla, data = greece)
sjPlot::tab_model(model2_std)| Zhappy | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | 0.02 | -0.04 – 0.07 | 0.582 |
| Zstfgov | 0.23 | 0.19 – 0.27 | <0.001 |
| psppipla [2] | -0.03 | -0.12 – 0.06 | 0.497 |
| psppipla [3] | -0.06 | -0.16 – 0.03 | 0.206 |
| psppipla [4] | 0.12 | -0.05 – 0.28 | 0.161 |
| Observations | 2685 | ||
| R2 / R2 adjusted | 0.055 / 0.054 | ||
# comparison of models
anova(model1_std, model2_std)## Analysis of Variance Table
##
## Model 1: Zhappy ~ Zstfgov
## Model 2: Zhappy ~ Zstfgov + psppipla
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 2683 2540.7
## 2 2680 2536.2 3 4.4841 1.5794 0.19233.5 Conclusion:
Model 1 is statistically significantly better suited to the data than model 2 (p>0.05)
summary(model1)##
## Call:
## lm(formula = happy ~ stfgov, data = greece)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.7319 -0.8869 0.1131 0.9582 4.0429
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.95712 0.05914 100.7 <2e-16 ***
## stfgov 0.15496 0.01260 12.3 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.487 on 2683 degrees of freedom
## Multiple R-squared: 0.0534, Adjusted R-squared: 0.05304
## F-statistic: 151.3 on 1 and 2683 DF, p-value: < 2.2e-16For a model with non-standardized coefficients
p-value: < 2.2-16 <0.05, maybe makes sense Adjusted R-squared: 0.053, i.e. this indicator is 5.3% of the expected variable (happy) with my independent time (stfgov) Coefficients 0.15 and p-value:< 0.001, with each increase in atf gov per unit, the happiness level increases by 0.15. intersept = 5.96 - this refers to the predicted value of happy when stfgov is 0. The regression equation looks like this: happy = 5.96 + 0.15*stfgov
Linear regression model with 2 continuous predictors Now we add another predictor to our model.
# Let's add another continuous variable to the model
model3 = lm(happy ~ stfgov + trstlgl, data = greece)
sjPlot::tab_model(model3)| happy | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | 5.03 | 4.86 – 5.20 | <0.001 |
| stfgov | 0.10 | 0.07 – 0.12 | <0.001 |
| trstlgl | 0.18 | 0.16 – 0.21 | <0.001 |
| Observations | 2685 | ||
| R2 / R2 adjusted | 0.118 / 0.117 | ||
model3_std = lm(Zhappy ~ Zstfgov + Ztrstlgl, data = greece)
sjPlot::tab_model(model3_std)| Zhappy | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | 0.00 | -0.04 – 0.04 | 1.000 |
| Zstfgov | 0.14 | 0.10 – 0.18 | <0.001 |
| Ztrstlgl | 0.27 | 0.23 – 0.31 | <0.001 |
| Observations | 2685 | ||
| R2 / R2 adjusted | 0.118 / 0.117 | ||
# model comparison
anova(model1_std, model3_std)## Analysis of Variance Table
##
## Model 1: Zhappy ~ Zstfgov
## Model 2: Zhappy ~ Zstfgov + Ztrstlgl
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 2683 2540.7
## 2 2682 2367.0 1 173.68 196.8 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Conclusion: Model 3 is statistically significantly better suited to the data than model 1 (p<0.05)
summary(model3_std)##
## Call:
## lm(formula = Zhappy ~ Zstfgov + Ztrstlgl, data = greece)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.3653 -0.5186 0.0344 0.6186 3.2524
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.498e-15 1.813e-02 0.000 1
## Zstfgov 1.425e-01 1.920e-02 7.422 1.54e-13 ***
## Ztrstlgl 2.694e-01 1.920e-02 14.028 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9394 on 2682 degrees of freedom
## Multiple R-squared: 0.1181, Adjusted R-squared: 0.1174
## F-statistic: 179.6 on 2 and 2682 DF, p-value: < 2.2e-16For a model with standardized coefficients
p-value: < 2.2-16 <0.05, maybe makes sense Adjusted R-squared: 0.1174, i.e. this indicator is 11.74% of the expected variable the model is quite high-quality (happy) with mine, independent, unchangeable (stfgov & trstlgl) Correlation coefficients 0.14 and 0.27 and p-value:< 0.001, correlation coefficient = 0.00. The regression equation outputs: Z happy = 0.14Zstfgov + 0.27Ztrstlgl
summary(model3)##
## Call:
## lm(formula = happy ~ stfgov + trstlgl, data = greece)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.6697 -0.7923 0.0526 0.9452 4.9695
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.03054 0.08731 57.620 < 2e-16 ***
## stfgov 0.09557 0.01288 7.422 1.54e-13 ***
## trstlgl 0.18213 0.01298 14.028 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.435 on 2682 degrees of freedom
## Multiple R-squared: 0.1181, Adjusted R-squared: 0.1174
## F-statistic: 179.6 on 2 and 2682 DF, p-value: < 2.2e-16For a model with non-standardized coefficients
p-value: < 2.2-16 <0.05, maybe makes sense Adjusted R-squared: 0.1174, i.e.this means that the model is not quite good quality R-squared: 11,8% of dependent variable deviation can be explained by the model Coefficients of independent variables are 0.10 and 0.18 and p-value:< 0.001, intercept = 5.0 - this refers to the predicted value of happy when stfgov and trstlgl indicators are equal to 0.
The regression equation looks like this: happy = 5.03 + 0.10stfgov + 0.18trstlgl
With each increase in stfgov by one, happy rises by 0.10. With each increase in trstlgl by one, happy rises by 0.18
3.6 check the assumptions of linear regression
Checking Linear Regression Assumptions Linear regression makes several assumptions about the data, such as :
- Linearity of the data
- Normality of residuals
- Homogeneity of residuals variance
- Independence of residuals error terms
- multicolleniarity
autoplot(model3_std)
let’s check in a little more detail, the assumptions of linear regression are fulfilled 1) normality of the remainder distribution
res <- resid(model3_std)
hist(res, breaks = 20, col = 'lightblue', freq = FALSE)
lines(density(res), col = 'red', lwd = 2)
shapiro.test(res) # the leftovers are NOT distributed normally##
## Shapiro-Wilk normality test
##
## data: res
## W = 0.98214, p-value < 2.2e-16#QQ-plot
par(mfrow = c(1, 1))
qqnorm(res)
qqline(res)
car::qqPlot(model3_std)
## 1402 1484
## 1346 1424#The histogram, test and qqplot graphs DO NOT show the normal distribution of residuals# homoscedasticity
plot(fitted(model3_std), res)
abline(0,0)
ggplot(data = model3_std, aes(x = .fitted, y = .stdresid)) +
geom_point() +
geom_hline(yintercept = 0)
bptest(model3_std) # The Broich — Pagan or Breusch — Pagan test##
## studentized Breusch-Pagan test
##
## data: model3_std
## BP = 112.38, df = 2, p-value < 2.2e-16# we can say that homoscedasticity does NOT hold# let's check multicollinearity
car::vif(model3_std)## Zstfgov Ztrstlgl
## 1.12121 1.12121# there is NO multicollinearityLinearity assumption: at the Residuals vs.Fitted plot a horizontal line, without distinct patterns can be seen, which is surely a good thing. (Our data is linear) The histogram, test and qqplot graphs DO NOT show the normal distribution of residuals Scale-Location & Residuals vs. Leverage plot DO NOT show us a horizontal line with equally, though in a funny way, spread points. This corresponds with NO homoscedasticity of our data.
4 Project 4
4.1 Introduction
In this project, we want to consider the impact of such a variable as the number of hours spent on the Internet on the indicator of the level of happiness, on satisfaction with the government and trust in the legal system. There is a significant amount of research on these topics. Some of those that we have considered: The study “Internet Use and Happiness: A Longitudinal Analysis” by Richard H. Hall suggests that students who spent the most hours on the Internet showed fewer scores on the scale of happiness than students who spent fewer hours on the Internet. Another study conducted by American researchers “E-Citizenship: Trust in Government, Political Efficiency, and Political Participation in the Internet Era” by Sari Sharoni shows that the relationship between these two factors is present, but it is impossible to say about the presence of direct correlation. Thus, we can emphasize that the number of hours spent on the Internet has a significant impact on different areas of a person’s life. Thus, our research question is: Which of these indicators (trust in the legal system, level of happiness, satisfaction with national government) does the number of hours spent on the Internet have the greatest impact?
Null statistic hypothesis: there is no relationship between the independent variables (trust in the legal system, level of happiness, satisfaction with national government) and the dependent variable (how often people use Internet)
The alternate statistic hypothesis is that there exists a relationship between the independent variables (trust in the legal system, level of happiness, satisfaction with national government) and the dependent variable (how often people use Internet)
df <- import("/Users/DP/OneDrive/Рабочий стол/ESS10.sav")attributes(df$cntry)## $label
## [1] "Country"
##
## $format.spss
## [1] "A2"
##
## $labels
## Albania Austria Belgium Bulgaria
## "AL" "AT" "BE" "BG"
## Switzerland Cyprus Czechia Germany
## "CH" "CY" "CZ" "DE"
## Denmark Estonia Spain Finland
## "DK" "EE" "ES" "FI"
## France United Kingdom Georgia Greece
## "FR" "GB" "GE" "GR"
## Croatia Hungary Ireland Iceland
## "HR" "HU" "IE" "IS"
## Israel Italy Lithuania Luxembourg
## "IL" "IT" "LT" "LU"
## Latvia Montenegro North Macedonia Netherlands
## "LV" "ME" "MK" "NL"
## Norway Poland Portugal Romania
## "NO" "PL" "PT" "RO"
## Serbia Russian Federation Sweden Slovenia
## "RS" "RU" "SE" "SI"
## Slovakia Turkey Ukraine Kosovo
## "SK" "TR" "UA" "XK"gr <- filter(df, cntry=="GR")
dim(gr)## [1] 2799 5864.2 Manipulating the Data
Variables which we use:
Name <- c("stfgov", "happy", "trstlgl", "netusoft" )
Meaning <- c("Satisfaction with government", "How happy are you", "Trust in the legal system", "How often person use the internet")
Type <- c("continuous ", "continuous ", "continuous ", "categorical")
Measurement <- c("0 - 10","0 - 10", "0 - 10", "1 - 5")
greece1 <- data.frame(Name, Meaning, Type, Measurement, stringsAsFactors = FALSE)
kable(greece1) %>%
kable_styling(bootstrap_options=c("bordered", "responsive","striped"), full_width = FALSE)| Name | Meaning | Type | Measurement |
|---|---|---|---|
| stfgov | Satisfaction with government | continuous | 0 - 10 |
| happy | How happy are you | continuous | 0 - 10 |
| trstlgl | Trust in the legal system | continuous | 0 - 10 |
| netusoft | How often person use the internet | categorical | 1 - 5 |
gr <- select(gr, c("stfgov", "happy", "trstlgl", "netusoft"))
skim(gr)| Name | gr |
| Number of rows | 2799 |
| Number of columns | 4 |
| _______________________ | |
| Column type frequency: | |
| numeric | 4 |
| ________________________ | |
| Group variables | None |
Variable type: numeric
| skim_variable | n_missing | complete_rate | mean | sd | p0 | p25 | p50 | p75 | p100 | hist |
|---|---|---|---|---|---|---|---|---|---|---|
| stfgov | 21 | 0.99 | 4.12 | 2.27 | 0 | 2 | 4 | 6 | 10 | ▇▇▇▅▁ |
| happy | 5 | 1.00 | 6.58 | 1.54 | 0 | 6 | 7 | 8 | 10 | ▁▁▅▇▁ |
| trstlgl | 13 | 1.00 | 6.43 | 2.26 | 0 | 5 | 7 | 8 | 10 | ▂▃▆▇▅ |
| netusoft | 5 | 1.00 | 3.97 | 1.56 | 1 | 3 | 5 | 5 | 5 | ▂▁▁▁▇ |
summary(gr)## stfgov happy trstlgl netusoft
## Min. : 0.000 Min. : 0.000 Min. : 0.00 Min. :1.000
## 1st Qu.: 2.000 1st Qu.: 6.000 1st Qu.: 5.00 1st Qu.:3.000
## Median : 4.000 Median : 7.000 Median : 7.00 Median :5.000
## Mean : 4.116 Mean : 6.579 Mean : 6.43 Mean :3.972
## 3rd Qu.: 6.000 3rd Qu.: 8.000 3rd Qu.: 8.00 3rd Qu.:5.000
## Max. :10.000 Max. :10.000 Max. :10.00 Max. :5.000
## NA's :21 NA's :5 NA's :13 NA's :5table(gr$netusoft)##
## 1 2 3 4 5
## 499 100 151 273 1771prop.table(table(gr$netusoft))##
## 1 2 3 4 5
## 0.17859699 0.03579098 0.05404438 0.09770938 0.63385827Consider this variable (netusoft), we see that categories 2 and 3 contain a small amount of data compared to the other categories of this permanent, since 2 is only occasionally using the Internet, and 3 is a few times a week, then they can be combined into one variable 2 - sometimes I use the Internet, it is necessary in order to avoid mistakes during further analysis.
gr$netusoft <- recode(gr$netusoft, "1=1; c(2,3)=2; 4=3; 5=4")
table(gr$netusoft)##
## 1 2 3 4
## 499 251 273 1771prop.table(table(gr$netusoft))##
## 1 2 3 4
## 0.17859699 0.08983536 0.09770938 0.63385827Now we see that categories 2 and 3 make up about 9% of all categories
gr$netusoft <- as.factor(gr$netusoft )
gr$stfgov = as.numeric(as.character(gr$stfgov))
gr$happy = as.numeric(as.character(gr$happy))
gr$trstlgl = as.numeric(as.character(gr$trstlgl))
gr <- drop_na(gr)Here we refine the types of variables and remove missing values from the dataset. Otherwise we cannot compare different models.
4.3 descriptive statistics
We get general information about variables using the describe function
gr %>%
describe() ## vars n mean sd median trimmed mad min max range skew kurtosis
## stfgov 1 2755 4.11 2.27 4 4.10 2.97 0 10 10 0.09 -0.74
## happy 2 2755 6.58 1.53 7 6.69 1.48 0 10 10 -0.71 0.92
## trstlgl 3 2755 6.44 2.25 7 6.66 1.48 0 10 10 -0.73 -0.08
## netusoft* 4 2755 3.19 1.18 4 3.36 0.00 1 4 3 -1.02 -0.68
## se
## stfgov 0.04
## happy 0.03
## trstlgl 0.04
## netusoft* 0.02Everything seems to be fine with these variables, we can move on to the next stage
- let’s reflect the variables in the boxplot
gr %>%
pivot_longer(c(stfgov, happy, trstlgl),
names_to = 'Var', values_to = 'Score') %>%
ggplot(aes(y=Score)) +
geom_boxplot() +
ggtitle("Distribution of scores") +
xlab("Variable") +
ylab("Score") +
theme_bw()+
theme(legend.position="none") +
facet_wrap(~Var)
In boxplot we see several outliers in the values of happy and trust
- let’s look at the normality of the distribution of variables on histograms
gr %>%
pivot_longer(c(stfgov, happy, trstlgl),
names_to = 'Var', values_to = 'Score') %>%
ggplot(aes(x=Score, fill=Var)) +
geom_histogram(aes(y=..density.., fill = Var), bins = 10) +
geom_density(alpha = .5, color="blue")+
ggtitle("Distribution of scores") +
xlab("Variable") +
ylab("Score") +
theme_bw()+
theme(legend.position="none") +
facet_wrap(~Var)
As it can be seen from the histograms, satisfaction with government,
happy close to normal distribution. As for the trust in the legal system
the histogram is not normally distributed.
- Let’s look at how representative the categories of a categorical variable are
gr %>%
ggplot(aes(x = netusoft)) +
geom_bar(fill = "lightpink", color = "lightblue") +
xlab("Category") +
ylab("Frequency") +
theme_bw() 
There is obviously a bias towards category 4 (Every day of Internet
use)
- Look at the scatterplots to see correlations between different variables
gr %>%
ggplot(aes(x=stfgov, y=happy)) +
geom_point(size=2) +
geom_smooth(method=lm)## `geom_smooth()` using formula = 'y ~ x'
gr %>%
ggplot(aes(x=stfgov, y=trstlgl)) +
geom_point(size=2) +
geom_smooth(method=lm)## `geom_smooth()` using formula = 'y ~ x'
gr %>%
ggplot(aes(x=trstlgl, y=happy)) +
geom_point(size=2) +
geom_smooth(method=lm)## `geom_smooth()` using formula = 'y ~ x'
Based on the scatterplot, we see that: - there is a positive correlation
between happy and satisfaction with government - there is a positive
correlation between trust in the legal system and satisfaction with
government - there is a positive correlation between happy and trust in
the legal system
It is also important to look at how our continuous variables relate (using heatmaps):
heatmaply_cor(
cor(gr[,c('stfgov', 'happy', 'trstlgl')], method = "spearman"),
Colv=NA, Rowv=NA)You can see that all variables are positively and moderately correlated. The highest correlation between happy and trust in the legal system (0.3206)
4.4 Linear regression models
Initially, we standardized variables to be able to compare coefficients in models.
gr <- gr %>%
mutate(Zhappy = scale(happy)[,1],
Zstfgov = scale(stfgov)[,1],
Ztrstlgl = scale(trstlgl)[,1])The first model is a model with a single predictor, in which we consider how happy can be predicted using satisfaction with government
model1 = lm(Zhappy ~ Zstfgov, data = gr)
summary(model1)##
## Call:
## lm(formula = Zhappy ~ Zstfgov, data = gr)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.3804 -0.5687 0.0834 0.6347 2.6443
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.410e-16 1.855e-02 0.00 1
## Zstfgov 2.288e-01 1.855e-02 12.34 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9736 on 2753 degrees of freedom
## Multiple R-squared: 0.05237, Adjusted R-squared: 0.05203
## F-statistic: 152.1 on 1 and 2753 DF, p-value: < 2.2e-16sjPlot::tab_model(model1)| Zhappy | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | 0.00 | -0.04 – 0.04 | 1.000 |
| Zstfgov | 0.23 | 0.19 – 0.27 | <0.001 |
| Observations | 2755 | ||
| R2 / R2 adjusted | 0.052 / 0.052 | ||
- P-value for the model is significant (< 2.2e-16)
- P-value for the coefficient of satisfaction with government is significant (<0.001)
- R adjusted squared is 0,052, that means 5% of variation in happy can be explain by this model, which is not very much
- Equation: Zhappy = 0,23*Zstfgov
- With each unit increase in satisfaction with government, the level of happy increases by 0,23
Next, in the second model, we add the trust in legal system variable to understand whether this will affect the fact that we will be able to predict the level of happy better
model2 = lm(Zhappy ~ Zstfgov + Ztrstlgl, data = gr)
summary(model2)##
## Call:
## lm(formula = Zhappy ~ Zstfgov + Ztrstlgl, data = gr)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.3433 -0.5514 0.0364 0.6228 3.2574
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.768e-16 1.790e-02 0.00 1
## Zstfgov 1.410e-01 1.893e-02 7.45 1.24e-13 ***
## Ztrstlgl 2.703e-01 1.893e-02 14.28 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9396 on 2752 degrees of freedom
## Multiple R-squared: 0.1177, Adjusted R-squared: 0.1171
## F-statistic: 183.6 on 2 and 2752 DF, p-value: < 2.2e-16sjPlot::tab_model(model2)| Zhappy | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | 0.00 | -0.04 – 0.04 | 1.000 |
| Zstfgov | 0.14 | 0.10 – 0.18 | <0.001 |
| Ztrstlgl | 0.27 | 0.23 – 0.31 | <0.001 |
| Observations | 2755 | ||
| R2 / R2 adjusted | 0.118 / 0.117 | ||
- P-value for the model is significant (< 2.2e-16)
- R adjusted squared is 0,117, that means 11,7% of variation in happy can be explain by this model, which is not very much, but better than in previous model
- Equation: Zhappy = 0,14Zstfgov + 0,27Ztrstlgl
- With each unit increase in satisfaction with government, the level of happy increases by 0,14
- With each unit increase in trust in legal system, the level of happy increases by 0,27
We also add a categorical variable (Internet use, how often) to the model to understand how it will help predict the level of happy
model3 = lm(Zhappy ~ Zstfgov + Ztrstlgl + netusoft, data = gr)
summary(model3)##
## Call:
## lm(formula = Zhappy ~ Zstfgov + Ztrstlgl + netusoft, data = gr)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.4219 -0.5196 0.0684 0.6250 3.1718
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.32071 0.04192 -7.651 2.73e-14 ***
## Zstfgov 0.15141 0.01863 8.125 6.67e-16 ***
## Ztrstlgl 0.27769 0.01870 14.848 < 2e-16 ***
## netusoft2 0.15063 0.07274 2.071 0.038464 *
## netusoft3 0.24220 0.07023 3.449 0.000572 ***
## netusoft4 0.44615 0.04743 9.406 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9233 on 2749 degrees of freedom
## Multiple R-squared: 0.149, Adjusted R-squared: 0.1475
## F-statistic: 96.27 on 5 and 2749 DF, p-value: < 2.2e-16sjPlot::tab_model(model3)| Zhappy | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | -0.32 | -0.40 – -0.24 | <0.001 |
| Zstfgov | 0.15 | 0.11 – 0.19 | <0.001 |
| Ztrstlgl | 0.28 | 0.24 – 0.31 | <0.001 |
| netusoft [2] | 0.15 | 0.01 – 0.29 | 0.038 |
| netusoft [3] | 0.24 | 0.10 – 0.38 | 0.001 |
| netusoft [4] | 0.45 | 0.35 – 0.54 | <0.001 |
| Observations | 2755 | ||
| R2 / R2 adjusted | 0.149 / 0.147 | ||
- P-value < 2.2e-16, so the model is significant
- All coefficients here are significant (P-value < 0.05)
- R adjusted squared is 0,147, that means 14,7% of variation in happy can be explain by this model, which is not very much, but also better than in previous model
- Equation: Zhappy = -0,32 + 0,15Zstfgov + 0,28Ztrstlgl + 0,15sometimes I use the Internet + 0,24Most days + 0,45*Every day
- With each unit increase in satisfaction with government, the level of happy increases by 0,15
- With each unit increase in trust in legal system, the level of happy increases by 0,28
- If the respondent sometimes uses the Internet, then the level of happy increases by 0,15
- If the respondent uses Internt most days, then the level of happy increases by 0,24
- If the respondent uses Internet every day, then the level of happy increases by 0,45
4.5 Comparing
anova(model1,model2)## Analysis of Variance Table
##
## Model 1: Zhappy ~ Zstfgov
## Model 2: Zhappy ~ Zstfgov + Ztrstlgl
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 2753 2609.8
## 2 2752 2429.7 1 180.04 203.92 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1It is necessary to look at the p-value, for models it is <0.05, after which we consider the RSS value and the model with a lower value is better, that is, the second model is better than the first
anova(model2, model3)## Analysis of Variance Table
##
## Model 1: Zhappy ~ Zstfgov + Ztrstlgl
## Model 2: Zhappy ~ Zstfgov + Ztrstlgl + netusoft
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 2752 2429.7
## 2 2749 2343.6 3 86.1 33.664 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1The third model is better than the second one
4.6 Interaction model:
model4 = lm(Zhappy ~ Zstfgov + Ztrstlgl + netusoft *Ztrstlgl + netusoft , data = gr)
summary(model4)##
## Call:
## lm(formula = Zhappy ~ Zstfgov + Ztrstlgl + netusoft * Ztrstlgl +
## netusoft, data = gr)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.4248 -0.5308 0.0500 0.6139 3.0981
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.31277 0.04273 -7.320 3.24e-13 ***
## Zstfgov 0.14862 0.01863 7.976 2.19e-15 ***
## Ztrstlgl 0.24291 0.04382 5.543 3.26e-08 ***
## netusoft2 0.17956 0.07380 2.433 0.015043 *
## netusoft3 0.23665 0.07064 3.350 0.000819 ***
## netusoft4 0.43750 0.04810 9.095 < 2e-16 ***
## Ztrstlgl:netusoft2 0.21003 0.07162 2.932 0.003390 **
## Ztrstlgl:netusoft3 0.08643 0.07099 1.218 0.223511
## Ztrstlgl:netusoft4 0.01051 0.04885 0.215 0.829618
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9218 on 2746 degrees of freedom
## Multiple R-squared: 0.1528, Adjusted R-squared: 0.1503
## F-statistic: 61.89 on 8 and 2746 DF, p-value: < 2.2e-16sjPlot::tab_model(model4)| Zhappy | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | -0.31 | -0.40 – -0.23 | <0.001 |
| Zstfgov | 0.15 | 0.11 – 0.19 | <0.001 |
| Ztrstlgl | 0.24 | 0.16 – 0.33 | <0.001 |
| netusoft [2] | 0.18 | 0.03 – 0.32 | 0.015 |
| netusoft [3] | 0.24 | 0.10 – 0.38 | 0.001 |
| netusoft [4] | 0.44 | 0.34 – 0.53 | <0.001 |
| Ztrstlgl × netusoft [2] | 0.21 | 0.07 – 0.35 | 0.003 |
| Ztrstlgl × netusoft [3] | 0.09 | -0.05 – 0.23 | 0.224 |
| Ztrstlgl × netusoft [4] | 0.01 | -0.09 – 0.11 | 0.830 |
| Observations | 2755 | ||
| R2 / R2 adjusted | 0.153 / 0.150 | ||
- P-value < 2.2e-16, so the model is significant
- All coefficients here are significant (P-value < 0.05) except interaction between trust in legal system and using Internet most days also trust in legal system and using Internet every day
- R adjusted squared is 0,150, that means 15% of variation in happy can be explain by this model, which is not very much, but also better than in previous model withot interaction
- With each unit increase in satisfaction with government, the level of happy increases by 0,15
- With each unit increase in trust in legal system, the level of happy increases by 0,24
- If the respondent sometimes uses the Internet, then the level of happy increases by 0,18
- If the respondent uses Internt most days, then the level of happy increases by 0,24
- If the respondent uses Internet every day, then the level of happy increases by 0,44
- The interaction between trust to legal systen and using Internet sometimes is 0,21, that increase the trust in legal system in one point, than 0,24 + 0,21*sometimes I use the Internet
- Equation: Zhappy = -0,31 + 0,15Zstfgov + 0,24Ztrstlgl + 0,18sometimes I use the Internet + 0,24Most days + 0,44Every day + 0,21Ztrstlglsometimes I use the Internet + 0,09 ZtrstlglMost days + 0.01Ztrstlgl*Every day
anova(model3, model4)## Analysis of Variance Table
##
## Model 1: Zhappy ~ Zstfgov + Ztrstlgl + netusoft
## Model 2: Zhappy ~ Zstfgov + Ztrstlgl + netusoft * Ztrstlgl + netusoft
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 2749 2343.6
## 2 2746 2333.3 3 10.353 4.0615 0.006856 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1It is necessary to look at the p-value, for models it is <0.05, after which we consider the RSS value and the model with a lower value is better, that is, the second model is better than the first, so model 4 is better
4.7 Interaction Plot
plot_model(model4, type = "int", terms = "netusoft", mdrt.values = "minmax")
marg1 <- ggeffects::ggpredict(model4,terms = c("Ztrstlgl",'netusoft'))
plot(marg1)
Based on this graph, we can conclude that if a respondent is related to sometimes group of using Internet and he or she has high level of trust in legal system then coefficient of happy is higher than in other categories. However if a respondent is related to sometimes group of using Internet and he or she has low level of trust in legal system then coefficient of happy is lower than in other categories.
tab_model(model3, model4)| Zhappy | Zhappy | |||||
|---|---|---|---|---|---|---|
| Predictors | Estimates | CI | p | Estimates | CI | p |
| (Intercept) | -0.32 | -0.40 – -0.24 | <0.001 | -0.31 | -0.40 – -0.23 | <0.001 |
| Zstfgov | 0.15 | 0.11 – 0.19 | <0.001 | 0.15 | 0.11 – 0.19 | <0.001 |
| Ztrstlgl | 0.28 | 0.24 – 0.31 | <0.001 | 0.24 | 0.16 – 0.33 | <0.001 |
| netusoft [2] | 0.15 | 0.01 – 0.29 | 0.038 | 0.18 | 0.03 – 0.32 | 0.015 |
| netusoft [3] | 0.24 | 0.10 – 0.38 | 0.001 | 0.24 | 0.10 – 0.38 | 0.001 |
| netusoft [4] | 0.45 | 0.35 – 0.54 | <0.001 | 0.44 | 0.34 – 0.53 | <0.001 |
| Ztrstlgl × netusoft [2] | 0.21 | 0.07 – 0.35 | 0.003 | |||
| Ztrstlgl × netusoft [3] | 0.09 | -0.05 – 0.23 | 0.224 | |||
| Ztrstlgl × netusoft [4] | 0.01 | -0.09 – 0.11 | 0.830 | |||
| Observations | 2755 | 2755 | ||||
| R2 / R2 adjusted | 0.149 / 0.147 | 0.153 / 0.150 | ||||
4.8 Linear regression assumptions
par(mfrow = c(2, 2))
plot(model4)
Linearity assumption: at the Residuals vs.Fitted plot a horizontal line,
without distinct patterns can be seen, so our data is linear At the Q-Q
plot points follow the straight dashed line, which is a indicator of
normally distributed residuals. Scale-Location plot show us a red
horizontal line with equally. This corresponds with the homoscedasticity
of our data. On Residuals vs Leverage plot we can spot only a couple of
outliers
4.9 Conclusion:
Based on our results, we can conclude that our hypothesis that the relationship between the (написать какие переменные) and (название зависимой переменной) has been confirmed. All three variables that were used in the analysis have a significant impact on a person’s happiness (coefficients are statistically significant) We can also see that the interaction of trust in legal system and frequency of using internet is significant Which again indicates that if a person trusts the government and at the same time uses the Internet uses the Internet every day, then his level of happiness will be higher than that of other categories. Also, if a person does not trust the government and uses the Internet every day, then his level of happiness will be lower than that of all other categories with the same trust in the government.
4.10 Recources
1)Mazzurco, Sari, E-Citizenship: Trust in Government, Political Efficacy, and Political Participation in the Internet Era (July 2012). Electronic Media & Politics, 1 (8): 119-135, Available at SSRN: https://ssrn.com/abstract=3342574
2)Kitazawa, M., Yoshimura, M., Hitokoto, H. et al. Survey of the effects of internet usage on the happiness of Japanese university students. Health Qual Life Outcomes 17, 151 (2019). https://doi.org/10.1186/s12955-019-1227-5