Chapter 2: Visualizing Data

2 Branches of statistics

Descriptive and Inferential

Descriptive

Characterize attributes of samples and/ or populations

Inferential

Generalize from a sample to an unknown population

Data visualization

Used to interpret and gain insight into data

• They enhance both the processing, understanding, and engagement with the data

Frequency tables

• Organize data to communicate how many observations exist at each category on the scale of measurement

Simple frequency

Number of responses for a given response

Relative frequency

The number of responses represented as a proportion (or percent) of the total sample

Cumulative frequency

The number of responses at each value and all lower ranked values

Grouped frequency distribution

• group scores into intervals that include a range of scores

• Assign frequencies to these intervals

• All intervals should be same width

Categorical frequency distribution

If we have categorical variable we arrange categories into a meaningful order and record frequecies

Nominal (simple + relative)

Ordinal (simple, relative + cumulative)

Normal Distributions

• Bell-shaped

• One peak in the middle (unimodal)

• Symmetrical on each side

• Reflects many natural variables

Bimodal Distributions

• Two clear peaks

• Symmetrical on each side

• Often indicates two distinct subgroups (weights/height of men vs women; math exam scores for math vs non-math majors

Positively-skewed distributions

• Also called right-skewed distributions

• Few scores at the extreme positive end of the distribution

• Most scores on the low end, with few extreme high scores

• Often occurs for more negatively - valenced variables

• Ex: Clinical depression, hospital visits, accidents

Negatively-skewed

• Also called left-skewed distributions

• Few scores at the extreme negative end of the distribution

• Most scores on the high end, with few extreme low scores

• Often occurs for more postiviely-valenced variables

• Ex: Life satisfaction, relationship commitment, retirement age, etc

Histograms

Are useful for showing the distribution of sample-makes it easy to compare to both to an ideal distribution and other distributions

Bar graphs

Useful for comparing across groups and/or samples

Scatterplots

Allow u to see raw data to help identify patterns, measurements issues, outliers, etc

Line graph

Useful for showing changes across time

Can show multiple lines to compare across groups

ChartJunk

Refers to visual features that are unnecessary or distracting for understanding the information in a graph

X-axis

Horizontal axis running along the bottom of the graph

Y axis

The vertical axis on the left side of the graph

Origin

Where the X-value and the Y-value are zero at the origin (two axes intersect)

Relative frequency or relative percent

The frequency of a response divided by the total number of participants

columns

Vertical elements in a table

Violin plot

Summarizes continuous data in a violin shape, with the width corresponding to the number of participants with a given score. The violin is wider at portions that have greater frequencies of response

Density plot

smooth, curved graph that shows how often different values appear in a dataset.