stats2

Contingency Table

Displays the distribution frequency of categorical variables

Bar Plot

A graph that represents numeric categorical variables with rectangles

Making a bar plot in R

ggplot(Dataset) + aes(x = Variable1, y = Variable2) + geom_bar()

Making a 2 way contingency table in R

Dataset %>% count(Variable1, Variable2) %>% mutate(prop = n / sum (n)) %>% pivot_wider (names_from = Variable1, values_from = Variable2)

2 way contingency table

Displays frequencies for combinations of two categorical variables. They classify outcomes for one variable in rows and the other in columns

Overall 2 way contingency table

Dividing the observations by the overall total

Conditional, row or column, 2 way contingency table

Dividing the observations by the row or column total

Stacked bar plot

Showing multiple (raw data) values for each category by stacking bars atop each other. Total bar height represents the sum

Dodged bar plot

Compares bars side by side

Standardized stacked bar plot

Like a regular stacked bar plot but with proportions

Unimodal distribution

Probability distribution with a clear peak

Bimodal distribution

Has two clear peaks

Multimodal distribution

Having two or more peaks

Uniform distribution

Every outcome is equally likely to occur

Symmetric distribution

Distribution where the left and right sides mirror each other

Left skewed distribution

Having a tail on the left

Right skewed distribution

Having a tail on the right

Skewness

A measure of asymmetry of a distribution

Histogram

Like a bar graph without gaps between the bars

Density plot

Like a histogram except it uses a smooth curve to represent data distribution

Box plots are best for…?

For comparing data across different groups

Mean

The average sum of all observations in a dataset

Median

The middle observation value (or middle 2 added and divided)

Mode

The most common value in a dataset

Standard deviation

The average variation of the values from the mean

Variance

The expectation of a squared deviation of a random variable from it’s mean

Quartile 1

The 25th percentile, where the lowest 25% lies

Quartile 3

Where 75% of the data lies

IQR(interquartile range)

The 50% of data that lie between Q1 and Q3

What data shows

Raw values (examples: 1, 2, 3, 4, 5)

What numerical data shows

Summary statistics (examples: mean = 5.5, median = 4.5)

What graphical data shows

Shape, spread, and outliers (examples: histogram, box plot, density plot)

What verbal data shows

Conceptual summary (examples: “right skewed with one high outlier, median around 5”)

Mean = median

Roughly symmetric graph

Mean > median

Graph shows a right skew

Mean < median

Graph shows a left skew

Large SD or IQR

Graph shows a wide spread

Graph shows outliers

Isolated points in boxplots or gaps in histograms

IQR = 0 means…?

Means the middle 50% of data are all the same value

Standard deviation equals..?

The square root of sample variance

1.5 IQR method

Method for identifying outliers

1.5 x IQR =

Below -1.5 x IQR - Q1 or above 1.5 x IQR + Q3

Use Mean and SD for…?

For symmetric data

Use Median and IQR for..?

Skewed data

When to use mean and SD

Symmetric data w no outliers, Interval data with equal spacing, heights of students in class, daily high temperatures in June, normally distributed test scores

When to use Median and IQR

For asymmetrical skewed data, if data has one outlier, small sample, ordinal ratings (satisfaction from 1-5 stars), salaries of employees (CEO makes $10m), number of emergency room visits per patient, response times for a computer program (some fast some very slow)

Use a histogram when:

You want to see the shape of distribution, you need frequency of data points for specific intervals, you are analyzing a single numerical dataset with many data points, you need to determine if a process is meeting customer requirements based on its distribution

Use a boxplot when:

Comparing distributions across multiple groups, you want a quick summary of the key statistics components (like mean), if you have a large amount of data and need a way to visualize it without showing every data point, you want to identify potential outliers.