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# Load the midwest datasetdata("midwest")# Summarizing population statistics by statepopulation_summary <- midwest %>%group_by(state) %>%# Group the data by statesummarise(poptotalmean =mean(poptotal), # Calculate the average total population for each statepoptotalmed =median(poptotal), # Calculate the median total population for each statepopmax =max(poptotal), # Find the maximum total population for each statepopmin =min(poptotal), # Find the minimum total population for each statepopdistinct =n_distinct(poptotal), # Count the number of distinct total population valuespopfirst =first(poptotal), # Get the first total population value for each statepopany =any(poptotal <5000), # Check if any total population values are less than 5000popany2 =any(poptotal >2000000) # Check if any total population values are greater than 2,000,000 ) %>%ungroup() # Remove grouping structure# Display the summarized population dataprint(population_summary)
# Load the tidyverse packagelibrary(tidyverse)# Load the midwest datasetdata("midwest")# Counting counties based on population thresholdspopulation_count_summary <- midwest %>%group_by(state) %>%# Group the data by statesummarise(num5k =sum(poptotal <5000), # Count counties with a total population less than 5000num2mil =sum(poptotal >2000000), # Count counties with a total population greater than 2,000,000numrows =n() # Count the total number of counties in each state ) %>%ungroup() # Remove grouping structure# Display the summarized population countsprint(population_count_summary)
# A tibble: 5 × 4
state num5k num2mil numrows
<chr> <int> <int> <int>
1 IL 1 1 102
2 IN 0 0 92
3 MI 1 1 83
4 OH 0 0 88
5 WI 2 0 72
Problem C
# Counting distinct states per countydistinct_states_count <- midwest %>%group_by(county) %>%# Group by countysummarize(x =n_distinct(state)) %>%# Count distinct states in each countyarrange(desc(x)) %>%# Arrange by count in descending orderungroup() # Remove grouping# Display the results for Part Iprint(distinct_states_count)
# A tibble: 320 × 2
county x
<chr> <int>
1 CRAWFORD 5
2 JACKSON 5
3 MONROE 5
4 ADAMS 4
5 BROWN 4
6 CLARK 4
7 CLINTON 4
8 JEFFERSON 4
9 LAKE 4
10 WASHINGTON 4
# ℹ 310 more rows
# Counting total rows per countytotal_count_per_county <- midwest %>%group_by(county) %>%# Group by countysummarize(x =n()) %>%# Count total rows in each countyungroup() # Remove grouping# Display the results for Part IIprint(total_count_per_county)
# A tibble: 320 × 2
county x
<chr> <int>
1 ADAMS 4
2 ALCONA 1
3 ALEXANDER 1
4 ALGER 1
5 ALLEGAN 1
6 ALLEN 2
7 ALPENA 1
8 ANTRIM 1
9 ARENAC 1
10 ASHLAND 2
# ℹ 310 more rows
# Counting distinct counties in each county (should always be 1)distinct_counties_count <- midwest %>%group_by(county) %>%# Group by countysummarize(x =n_distinct(county)) %>%# Count distinct counties in each countyungroup() # Remove grouping# Display the results for Part IIIprint(distinct_counties_count)
# A tibble: 320 × 2
county x
<chr> <int>
1 ADAMS 1
2 ALCONA 1
3 ALEXANDER 1
4 ALGER 1
5 ALLEGAN 1
6 ALLEN 1
7 ALPENA 1
8 ANTRIM 1
9 ARENAC 1
10 ASHLAND 1
# ℹ 310 more rows
Notes: I am doing this but I still don’t really understand it? Am I doing this right? Am I missing something? IDK HELP!!!! - I am going to finish these questions here as I know what I’m doing in terms of codes etc but not understanding them- so I will go back do some reading and try and understand what this means! feedback would be appreciated!
Good and Bad Questions About the Diamonds Dataset
In this section, I will explore the principles of formulating effective questions by generating one good and one bad question about the diamonds data-set.
Good Question
Question: What is the average price of diamonds for each cut, and how does this vary by clarity?
Why This is a Good Question:
Specific and Focused: It clearly defines the variables of interest (price, cut, and clarity).
Quantitative Analysis: It invites a quantitative analysis that can be explored using summary statistics, making it actionable.
Comparative Aspect: It allows for comparisons between different cuts and clarities, leading to more insightful conclusions.
# Example code to answer the good questiondiamonds_summary <- diamonds %>%group_by(cut, clarity) %>%summarize(average_price =mean(price, na.rm =TRUE)) %>%arrange(cut, clarity)
`summarise()` has grouped output by 'cut'. You can override using the `.groups`
argument.
Vauge and Subjective: Question is too broad and lacks specificity regarding what factors influence prices
Not Quantifiable: Does not provide a clear path for analysis
Lacks Context: Without the scope (size, cut, colour), it can lead to confusion.
Instead of asking why diamonds are expensive, a more effective question might be:
What factors are significantly associated with the price of diamonds? - This question directs the analysis towards specific variables and allows for a more focused investigation.
Week 5: How to Choose the Correct Analysis and Hypothesis
Formative 5
Graphs:
Bar Chart: Bar charts typically represent categorical data, so the test that can be used depend on whether you compare proportions, frequencies or means across categories.
Chi-Square Test
evaluates whether there is a significance associated between two categorical variables. It checks if the distribution of one variable differs based on the levels of another variable.
T-test:
compares the means between two independent groups to determine if the observed differences are statistically significant.
ANOVA:
tests whether the means of the continuous variables differ significantly across multiple categories.
image
Box-plot: The graph looks like it may be comparing the distribution of sepal length across different species. To see if there is any significance, statistical tests can be used:
ANOVA:
can be used when comparing the means of length across two species
ANOVA tests whether there is a significant difference in the means of sepal length between the species. Since the boxplot visualises the spread and central tendency of sepal lengths for each species, ANOVA would formally test if the observed differences in the means (which might be suggested by the boxplot) are statistically significant.
KRUSKAL-WALLIS TEST
non parametric alternative to ANOVA
compares the medians rather than the means, making it appropriate if the distributions are skewered, which the boxplot can help to identify. This test will help to see if there is a significant different in the sepal length distribution across species.
T-Test
when comparing sepal length between only two species (not three or more!)
t-test compares the means of two independent groups. This test assumes that the data is normally distributed and what variances are equal between the two groups.
Mann-Whitney U Test
non parametric
compares the distribution between two independent groups without assuming normality.
image
Line Graph : Represent continuous data/variable over time. When analyzing data visualized in line graphs, various tests can be used depending on the research question.
Linear Regression
Analyses relationships between a continuous dependent variable and one or more independent variables; useful for trend analysis and predictions
ANOVA
Compares means of a continuous variable across different groups; useful for testing differences over time
image
Scatter-plot : Common way to visualize the relationship between two continuous variables.
Pearson Correlation Coefficient
Measures the strength and direction of linear relationship between two continuous variables.
Linear Regression:
Models the relationship between continuous dependent variable and one or more independent variables; provides predictive equation.
Spearman’s Rank Correlation:
non-parametric alternative to Pearson’s; used for assessing monotonic relationships and ordinal data.
image
Formative 5: Re-creating graphs using the iris data-set
Box-Plot
data("iris")# Creating a boxplot of Sepal.Lenght by Speciesboxplot(Sepal.Length ~ Species, data = iris,main ="Boxplot of Sepal Length by Species",xlab ="Species",ylab ="Sepal Length (cm)",col =c("lightblue", "lightgreen", "lightpink"))
Density Plot
library(ggplot2)data("iris")# Create a density plot using ggplot2ggplot(iris, aes(x = Petal.Length, color = Species)) +geom_density(linewidth =1) +labs(title ="Density of Petal Length by Species",x ="Petal Length (cm)",y ="Density") +theme_minimal() +theme(legend.position ="top")
Scatter Plot
library(ggplot2)data(iris)# Create a scatter plot of Petal.Length vs. Petal.Width with a regression lineggplot(iris, aes(x = Petal.Length, y = Petal.Width, color = Species)) +geom_point(size =3) +geom_smooth(method ="lm", se =FALSE, color ="black") +# Add regression linelabs(title ="Scatter Plot of Petal Length vs. Petal Width",x ="Petal Length (cm)",y ="Petal Width (cm)") +theme_minimal() +theme(legend.position ="top")
`geom_smooth()` using formula = 'y ~ x'
Bar Chart-
library(ggplot2)# Create a new variable 'size' in the iris datasetiris$size <-ifelse(iris$Sepal.Length <median(iris$Sepal.Length), "small", "big")# Create a bar chart of species counts categorized by sizeggplot(data = iris, aes(x = Species, fill = size)) +geom_bar(position ="dodge", color ="black", width =0.7) +# Bars with black outline and dodged for separationlabs(title ="Count of Iris Species by Size Based on Sepal Length",x ="Species",y ="Count") +scale_fill_manual(values =c("small"="lightblue", "big"="lightgreen")) +# Custom colors for sizestheme_minimal(base_size =15) +# Minimal theme with larger base font sizetheme(plot.title =element_text(hjust =0.5, size =20, face ="bold"), # Center and style titleaxis.title.x =element_text(size =16, face ="bold"), # X-axis title stylingaxis.title.y =element_text(size =16, face ="bold"), # Y-axis title stylingaxis.text.x =element_text(size =14), # X-axis text sizeaxis.text.y =element_text(size =14) # Y-axis text size ) +geom_text(stat ="count", aes(label =after_stat(count)), position =position_dodge(0.7), vjust =-0.5, size =5, color ="black") # Add count labels above bars
