Presenting data

Scientific Research

Have a hypothesis and use scientific methods to draw a conclusion

Variable

Anything that varies

Data

Values that variables receive in measurements

Results

Systematic variation in the data that is related to the hypothesis and research question.

Analysis

The process of revealing or testing patterns in data to produce results.

Three ways of presenting results

Text, table, graphics

Text

A verbal description used to present results, which establishes unambiguous meaning and logical relationship but risk to get lost in details.

Table

A spatially organized representation of precise specifications. communicate larger number of details but meaning/logical relationships aren’t communicated

Graphics

Visualization of data patterns used to highlight main patterns in data and communicate different kinds of information in parallel.

But specific details get lost and visual interpretation may depend on viewer

2 main uses of graphics

1. To assess quality of data (detects faults in your experiment, characterise data distribution and identifying outliers)

2. Visualise results (highlights and explains main results)

What do you need to focus on when making graphics?

dimensionality and format

How to use graphic tools

1. How many variables

2. Types of variation

3. Types of scale

4. Resolution

5. Pattern

Types of variation

independent variation, dependent variation, other variation (noise) not part of testing logic, but interferes with the tested variation and defines reliability of results

How to decrease resolution?

Through aggregation (eg by categorising for nominal data or for quantitative data using mean and standard deviation) to avoid clutter

Freedom rating

more freedom, more versatile so describes more complex relationships but also less organised

Pie chart

low freedom rating

Variable 1 - a a continous, ratio-scaled axis is represented as a circle 

Variable 2 – discrete data is show as wedges 

Evaluation of pie charts

Advantage – Part-whole relationships – relate parts to the whole  

But limited scope – limited to 2 sources of variation (no error bars) and requires ratio-scale and finite data 

Bar chart

has the next higher freedom rating

Variable 1 – discrete, more intuitve with regular steps  

Variable 2 – quantative scale along 

Can add error bars 

Bar chart evaluation

Advantage: grouping – highlight distance from zero/another baseline and highlight differences across groups/conditions and visualise different groups/conditiions 

Disadvantage: useless for continous data along both axes. Risks clutter when many data points 

Line chart

has even higher freedom rating

Variable 1 – continous, at least ordinal scale (otherwise connecting line misleading) 

Variable 2 – continous, at least ordinal scale  

Error bars 

Additional continous variables: grouping of ata by seperate lines identified by visual appearance 

Scatter chart

has highest freedom rating

Variable 1 and 2 – continous X and Y-axis, at least interval scale  

Error bars possible along both axis  

Additional varibales – identify by visual appearance 

Scatter chart evaluation

Advantage: covariation  

Disadvantage: lacks structure, risks clutter

Typically use graphics to..

• See whether it is nominal or skewed distribution

• used to highlight main results for comparison and reference

Proportion

A part, share or number considered in comparative relation to a whole (fraction) = relative frequency

What pattern to use for nominal?

pie chart, but can also ue bar chart

What pattern to use for ordinal?

bar chart

What pattern to use for ratio scale?

scattergram

Continuous data aggregation….

by frequency is useless so we use binning which is transforming continuous data into discrete data by allocating it to intervals (bins)

Histogram

A bar chart using bins to display continuous data

Frequency data

frequency of data per equal interval (frequency/ bin size). Allows estimation of probability density, which is fundamental for statistical testing

Probability density

probability of data per value

cumulation

A collection of objects laid on top of each other

Cumulative sum: sum up progressively

Aggregation by central tendency

By obtaining the mean and standard deviation. Can plot mean and standard deviation in bar chart making it much more simple

Mean and SD can only be sed for…

symmetrical distribution and misrepresents asymmetrical distribution

median and quartiles do not assume symmetry

Boxplot

Does not assume symmetry. Shows outliers and interquartile range (which is the width of the box)

Qualitative IV and Qualitative DV (nominal/ordinal)

Use bar chart as pie charts are difficult to compare

 

Qualitative IV (nominal/ ordinal) and Quantitative DV (interval/ratio , discrete)

Aggregation by central tendency

Aggregation by central tendency

Boxplot provides more information about distributions than a bar chart with mean and standard deviation

Quantitave IV (interval/ratio , discrete) and quantitive DV (interval/ratio continous/discrete)

Use line graph

Quantitative IV (interval/ratio , continous) and quantitative DV (interval/ratio discrete/continous)

line graph

Bivariate distribution

use scattergram