Chapter 2 - Displaying Data

Survivorship Bias

Incomplete information due to removing "failures" from analysis -> look at groups that do what you want them to

Familiarity/Recall Bias

We overemphasize information we are familiar with

Gambler's Fallacy

An erroneous belief that probabilities "change"

Ex. even if a coin flips and is heads 10 times in a row, the next flip still has the same chance of being 50% heads or tails

Base Rate Fallacy

Focusing on individual cases to the detriment of the whole

Ex. one person got sick from covid, so someone only focuses on that, even though there is a higher rate of people who did not get sick

Levels of Measurement

Qualitative and Quantitative

Qualitative Levels of Measurement

Nominal and ordinal -> descriptors, categorical, generally described with words

Quantitative Levels of Measurement

Interval, ratio, and ordinal -> numeric things we can do math with, "true numbers"

Nominal Data

-Name -> ex. brown hair, blue eyes

-Can't order in a meaningful way

Ordinal Data

-Ordered/ranked -> doesn't need to be regular or clearly defined, can be numbers

-Can be ordered in some way, ex. women's clothing sizes, grades, and year in college

Interval Data

Measured variable has regular intervals and no true zero -> ex. ruler, temperature

Ratio Data

Has a true zero -> nothing can go below -> ex. mass, age, Kelvin

How can we name or group things?

Nominal or qualitative data

How can we order or rank things?

Ordinal or ranked data

How can we put things on a logically spaced scale?

Interval data (no true zero)

Ratio data (true zero)

SPSS calls both of these "scale"

Can data be demoted or promoted?

Data can almost always be demoted, but it can never be promoted

nominal/qualitiative <- ordinal/ranked <- interval/ratio/quantitative

Frequency Data

How often a thing is observed

Frequency Data Measures

Sample, sample size, datum, frequency/count

Sample

The group of observations

Sample Size

n -> the number of observations

Datum

x -> one data point/occurrence (singular of data)

Frequency/Count

f -> the number of occurrences of same category

Bar Graph Styles

Cluster, stacked bar, pie

Cluster Graph

Subgroups -> a graph with dots not connected by lines in no specific order

Stacked Bar Graph

A bar graph that compares the same categories for different groups and shows category totals

Pie Graph

A graph that highlights segments of a circle to show simple distribution patterns

Rules and Guidelines for Visual Data

-Axes should be labeled with units

-The lower end of the frequency scale should be set to 0, or indicated as broken with crossover lines

-Width of the bars should be regular

-The scales of the X and Y axis should be roughly similar

-Bars should touch for continuous data, and should be separate for categorical

-Y axis generally should increase up; X axis should generally increase right

What are bar and pie graphs good for?

Categories, counts, ordinal data

Binning Data

When it is impossible or impractical to have a category for every value in a data set, we bin (or group) the data into categories (bins), each covering a range of possible data values

Scalar -> Ordinal Data

-Taking individual data and grouping them into ranges

-Can always denote data, but never promote it

Histogram

-Displays frequency data

-Bars touching/contiguous (implies continuous distribution)

-X axis from left to right

-Y axis ascends from bottom to top (should index at 0)

-Bins should be uniform size, ~10 is good