Lecture 2 - Data Summary and Visualization

How do measures of central tendency fall?

In normal distribution, mean = median = mode

In skewed/multimodal distribution, mean, median, and mode differ

• when distributions are highly skewed → median is a better measure

• when distributions are multimodal, this indicates the presence of multiple groups

• we can use modes to describe the ‘center’ or non-numeric data

Standard deviation features

• when sd is low, points are clustered to the mean

• when there’s high variability, the points are more spread out

• observations that are a lot higher oor lower than the mean are going to be common in a distribution with high variability

Good vs bad graph features

Good

1. clean

2. informative AND

3. easy to understand

Bad

1. confusing

2. misleading BAD

3. OR meaningless

Pie Charts

to show proportions of different categorical and mutually-exclusive options

• Proportions need to add up to 1 (percentages need to add up to 100%)

Good or bad graph?

Good graph! It’s possible to describe the graph

Good or bad graph?

Bad graph! the percentages need to add up to 100%

Bar plots

to compare values associated with separate (usually categorical) variables

• These can be any sort of numeric variable that we are looking for differences across groups, such as means, counts/frequencies, medians, or percentages

  • In some cases, either a bar plot or pie chart can be used (i.e. if we can calculate percentages that sum to 100)

• Can be vertical or horizontal

• Can quickly become overwhelming if too many categories

Error bars

show uncertainty (or confidence) in the average

• Wider bar = more variation/uncertainty

• Narrower bar = less uncertainty (or more confidence)

• *Imagine a distribution on the side of the bar

Good or bad graph?

Bad graph! Too much and redundant info, could use a line plot.

Good or bad graph?

Bad graph! Too much and redundant info

Line graphs

only appropriate when x values are linear

• Frequently used for time-series data → 

• Can involve 2 y-axes (with caution)

• Can have error bars/bands

Scatterplots

shows every data point; can help show relationships between variables while looking at all the data

• They can easily be overwhelming when there’s lots of data

Histograms

bar plots specifically that plot frequency (i.e. the number of times a certain value occurs in the data)

• The x-axis has a variable, and y-axis is always frequency

• Plot shapes are readability can depend extensively on bin widths

Guide for Choosing a graph

1. Are we looking at percentages of different categories on a single variable that sum to 100? (one variable)

   1. Pie chart

2. Are we looking at a numeric variable by groups of different categories? (two variables)

   1. Bar graph

3. Are we looking at a numeric variable over a series of time? (two variables)

   1. Line graph

4. Are we looking at the relationship between two different numeric variables? (two variables)

   1. Scatterplot

5. Are we looking at the distribution of a numeric variable? (one variable)

   1. Histogram

When is it okay to truncate axes?

• it’s okay to truncate axes to the reasonable range for a measure

  • Ex: 95 is a good temp, 99.5 and above indicates fever → when values are so close, it makes sense to truncate to get a sense what the real meaningful difference is

  • it’s okay when you want to show change over time

Basic elements of color for representation

• Magnitude (low to high; 0-50) = light to dark shade of same color (ex: light red to dark red)

• Divergent/bidirectional (negative to positive; -15 to 15) = dark shade of color 1 to dark shade of color 2 (ex: dark blue to white to dark red)

• Categorical = different colors

• Consider audience and accessibility (ex: colorblind population)

Aspect ratio

ratio of width to height

• Widening the x-axis (see x-axis numbers on left panel) makes the slope look steeper, implying a greater increase, and affects our interpretation

How to make a good plot

• Logical representation

• Labeled axes

• No redundancy

• All plot elements are clearly visible

• Clean presentation

  • Sufficiently large font

  • Avoid clutter

  • No unnecessary color 

• Include a title

• Include a legend (if necessary)