Weeks Learning Objectives

1. Review the main concepts from introductory statistics.

2. Understand the concept of a function.

3. Be able to discuss what a statistical model is.

4. Understand the link between models and functions.

Topics for today

• What we need to review:
  • Types of data
    • measurement
    • data
    • levels
  • Principles of visualization
    • what makes a good visualization?
  • Hypothesis testing
    • How do we try and know stuff?

IMPORTANT

PLEASE RE-READ THIS SLIDE REGULARLY

1. Data analysis can be tricky

2. You are not expected to know everything after the first time you hear it.

3. Getting stuff wrong is fine

4. Ask lots of questions

Measurement

Data sets

Data types

Levels of measurement

Data types & levels

Data visualization

• We will make extensive use of data visualization
• Don't try to learn everything now.
• Work through the ggplot2 tutorial in your own time
• Spend time thinking about all the plots we show

Data Visualization

• Important in science, business, journalism, etc.

• Two key roles:

  1. Communication
  2. Analysis

• Summary statistics never give the full picture:

Same summary, different data

ggplot: Grammar of Graphics

• Many graphing programs treat data visualization like painting picture:
  • red circle at $x_1,y_1$, blue square at $x_2,y_2$, etc.
• This is inefficient and very easy to make mistakes.

The ggplot way:

• A graph has 3 core elements:

1. A data set
2. A set of mappings between variables in the data set and properties (aesthetics) of the graph
3. Layers of geoms to instantiate those mappings

An example

• A line plot:

ggplot(Orange, aes(x=age, y=circumference, color=Tree)) + 
  geom_line()

An example

ggplot(Orange, aes(x=age, y=circumference, color=Tree)) + 
  geom_line() + 
  geom_point() # Add points

• Notice that the lines and points have matching colors

Refining figures

• Scales
  • Colours
  • Point shapes
  • Legends/guides
  • Etc.
• Themes
  • Axes, grid lines, tick marks and labels
  • Legend position
  • Font sizes
• Annotations: geoms that are not data

What to look for in plots?

• What does the x-axis represent?
• What does the y-axis represent?
• What are the scales of x and y?
• What is the within the plot (e.g. line, dots, bars)?
• What does that represent?

An example

ggplot(Orange, aes(x=age, y=circumference, color=Tree)) + 
  geom_line() + 
  geom_point() # Add points

Hypothesis testing

• Structure of a Hypothesis Test

• Hypothesis: a formal statement of a research question.

• A hypothesis test:
  • Test statistic: A quantity that represents our question (e.g. difference in means)
  • Observed test statistic: The test statistic calculated on from our data
  • Null distribution: A probability distribution for different values of the tests statistic if the data were random.
  • p-value: A probability value associated with our observed test statistic taken from the null.
  • Significance level: A binary threshold for interpreting our $p$-value.

Next tasks

• If you feel you need a refresher on any of the topics;

  • Go to LEARN dapR2 week 1 folder
  • Click on recap material
  • Select the topic you wish to recap and work through
  • Check for the open office hours related to the topic at the end of the week for questions

• This week:

  • Complete your lab
  • Weekly quiz - practice test 1
    • Open Monday 09:00
    • Closes Sunday 17:00