Class notes

Lecture notes (6-9) Statistical Methods (semester 2)

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Course
Statistical Methods (PSGY1004)

Institution
The University Of Nottingham (UON)

Lecture notes (6-9) for Research Methods in 2nd semester. All essential notes from lectures for upcoming exams. Made in Notion with a sleek, readable design (complete with contents, images, tables and summaries).

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Uploaded on May 22, 2024
Number of pages 31
Written in 2023/2024
Type Class notes
Professor(s) Dr stephanie mcdonald, dr megan barnard
Contains All classes

statistics
research methods
psychology statistics
data
data visualisation
graphs
non parametric
inferential statistics
resampling
bayesian

Institution
The University of Nottingham (UON)
Education Unknown
Course
Statistical Methods (PSGY1004)

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1. Class notes - Lecture notes (1-5) statistical methods (semester 2)
2. Class notes - Lecture notes (6-9) statistical methods (semester 2)
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Research Methods 6-10
L6: Data Visualisation
Plotting data
Anscombe’s Quartet
Datasaurus Dozen
How do we interpret graphs?
How to best plot data?
Different ways to plot the same data
Summary
L7: Non-parametric Tests
Non-parametric tests
Interval scales and skews
Mann-Whitney U test
SPSS
Wilcoxon related-samples test
SPSS
Kruskal-Wallis H test
SPSS
Kruskal-Wallis: testing differences
Friedman test
SPSS
Friedman test: testing differences
L8: Resampling
What is resampling?
Motivation
Why use resampling techniques?
Why are resampling approached not more popular?
Outline
Resampling for hypothesis testing
Permutation Tests
Between-subjects randomisation tests
Process
Generalisation
Within-subjects randomisation test
Process
Number of participants
Bootstrap Resamples
Calculating SEM
Calculating a confidence interval

Research Methods 6-10 1

, A one-sample test
Bootstrapping with a model fit
Bootstrap advantages
Other approaches
Issues and concerns
Summary
L9: Bayesian
Bayes Theorem
Posteriors, likelihood and priors
The impact of priors
Bayesian inferential tests
Null hypothesis significance testing
Bayes Factors
Evidence for H0?
Frequentists
Credible intervals
Comparison

L6: Data Visualisation

Plotting data

☁️ Visual explanation compliments statistics and is essential to
understanding data

Anscombe’s Quartet
Anscombe (1973)

Represents that you can have the same summary statistics with different
unerlying data

Anscombe suggested 4 datasets where in all cases:

mean(x) = 9.000; sd(x) = 3.317

mean(y) = 7.500; sd(y) = 2.031

corr(x,y) = 0.816

Research Methods 6-10 2

, The effectiveness of this quartet comes from the fact that four clearly
different and visually distinct datasets are producing the same statistical
properties

Datasaurus Dozen
Matejka & Fitzmaurice, 2017

Represents datasets which are identical over a range of statistical
properties, yet produce dissimilar graphics.

Research Methods 6-10 3

, While the data exhibits normal-seeming statistics, plotting the data reveals
a picture of a dinosaur.

Slightly changing the statistics leads to a variety of different shapes

How do we interpret graphs?
1. Are the measurements clear?

2. Can comparisons between categories be made?

Examples

How to best plot data?
There are many kinds which are each suitable for different situations

Research Methods 6-10 4

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