Chapter 2

Uniform

Same frequency in all categories (ex. Skittles)

Inferential statistics

set of technique that uses the laws of chance and probability to help researchers understand the meaning of their data and inferences they can make from those data.

Inferential statistics example

Using data from a small sample to make predictions about a larger population

Descriptive statistics

organizes the properties of a dataset without any inferential analysis. Two main ways are graphs and numbers.

X-axis

Horizontal axis running along the bottom of the graph

What does the x-axis identify?

The variable you are meaasuring

Y-axis

Vertical axis on the left side of the graph

What does the Y-axis identify?

How the values are presented, such as percent or frequency

What information do we visualize in graphs?

Display a key statistical value for a given variable and visualize all responses for a variable

Relative frequency or relative percent

Frequency of the response divided by the total number of participants

Frequency table

Presents frequency data for participant responses for categorical data

Column in a frequency table

Vertical elements (number of people who chose that option)

Rows in a frequency table

Horizontal elements for response options or categories (first row typically contains labels to identify variables)

How do you normally display categorical data?

Bar graph

How do you visualize data with quantiative/continuous data?

Averages

How do you visualize averages with categorical data?

Counting responses

Bar graphs

Bars represent the relationship between different values

Raw data

Unaltered by any statistical technique

When are bar graphs most useful?

Displaying data from two different categorical values (ex. yes/no questions)

Horizontal bar graphs

Mainly for aesthetic reasons or to improve readbility

Stacked bar graph

Subcategories of the item being measured

Histograms

Similar to a bar graph, but instead it illustrates continuous variables

Line graphs

Visualize the data changes in one variable over time. Sometimes they show how multiple variables change over time

What is one problem with line graphs?

They can exaggerate findings

When are line graphs most useful?

Comparing two trends over time

Scatterplots

Includes multiple dots with each dot illustrating two continuous variable scores for each participant or case

How are scatterplots helpful in identifying?

If a linear relationship exists between the two variables measured

Pie charts

Displays categorical data ad shows the proportion/percent of observations in each category

When are pie charts most useful?

When you have relatively few categories and when people can only choose one option

Advantages of a pie chart

Focuses on proportions as a whole
Don’t have to pick an order for our categories on X-axis

Disadvanatges of a pie chart

Can be hard to make precise comparisons between categories
Can get messy with too many categories

Violin plots

creates a graph of a continuous data distribution that looks vaguely like a stringed musical instrument.

What does violin plots demonstrate?

Frequency

Wider areas of a violin plot

Higher frequency of data responses

Thinner areas of violin plots

Lower frequency of responses

Density plots

Violin plots cut in half and presented horizontally

Advantages of a density plot

Compare multiple groups at once
Shows overlap and variability
The peak is the most common/average

Jitter plots

Visualizes individual participant scores on a single quantitative variable

What does each dot represent on a jitter plot

One participant’s response

Key features on a jitter plot

Aces (one variable measured on either x-axis or y-axis)
Clustering (dense clusters of dots indicate popular responses)

Advanatges of a jitter plot instead of a density plot?

Can see how many data points
Better when the variable is not continuous

Truncated Y-axis

one that is shortened by cutting off one or both ends of it. It doesn’t show the full range of all possible data values for the variable measured on the Y-axis.

When is a truncated Y-axis appropriate?

When a small data change is a big deal

Words to describe continuous data

Normal distribution, skewed distribution, outliers, ode, unimodal, bimodal

Normal distribution

Normal/bell curve. Most of the data clustered around the average

What do the upper and lower tails of a normal distribution curve represent?

Rare but not impossible cases

Skewed distribution

data pile up at one end of the distribution and taper off at the other end.

Outliers

Extreme relative to other data points for the same variable

Positively skewed

Right skewed

Negatively skewed

Left skewed

Mode

most frequent response for a given variable

Unimodal

One mode, or peak

Bimodal

Two most frequency responses