STATISTICAL METHODS FOR RESEARCH
Programme content
This document gives an overview of the content of each screen in the Supervising Doctoral Studies programme.
Interactive and/or multimedia elements (e.g. activities, videos) are marked bold.
Introduction – Statistics in the context of research
Screen
Unit 1: Getting started
You as a researcher
Pre-programme quiz
What stage are you
currently at?
What will I be able to
do with my research
data by the end of this
course?
Outline of the
programme
Notes
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Defining ‘statistics’
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Unit 2: Statistical investigation
What is a statistical
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investigation?
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Stages 1 to 3 of a
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statistical investigation
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Stage 4: Statistical
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modelling
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Poll activity: Your familiarity with statistical packages
Video interview: Which statistics packages do you use ansd why?
Multiple-choice quiz: Yout current knowledge of statistics
What types of study are there?
What do we mean by ‘statistically valid’?
Click to view activity: Randomisation, replication and blocking/stratification
Video interviews:
o Can you explain your research?
o Can you describe your data collecting methods?
o Approaching randomisation and blocking (stratification)
Download and poll activity: Understanding a model report
The aims of this programme
Click to view activity: Topics covered in each course
Click to view activity: Views on statistics
Click to view activity: Examples of the wuantification of variability
Matching activity: Definitions of ‘statistics’
Royal Statistical Society definition of ‘statistics’
Classification activity: Headlines with/without statistical information
How statistics can help you understand variability in data
Click to view activity: Stages of a statistical investigation
Click to view activity: Questions about estimates, comparisons and
relationships in data
Clickable graphic: What a box plot can tell you
Two parts of a statistical model
Click to view activity: Stages of the statistical modelling process
What do these stages mean in practical terms?
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STATISTICAL METHODS FOR RESEARCH
Thinking statistically – Describing data well
Screen
Unit 1: Describing data well
What is a statistical
investigation?
Summaries for
categorical variables
Summarising
quantitative variables
Reflecting the structure
in the data
The standard deviation
Notes
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Definition of a ‘sample’
Sequencing activity: Steps in the statistical process
Types of data
Click to view activity: Categorical and quantitative variables
One-way tables of frequencies and bar charts
Two-way tables of frequencies and bar charts
Download and reflection activity: Categorical and quantitative variables and
other observations on a dataset
The frequency distribution and histogram
Click to view activity: Location and variability
The quartiles and box plot
Notemaking activity: Summarising the quanitative variable
Reflection activity: Box plots and outliers
Using charts to answer more complex questions
Notemaking activity: Commenting on variability
Statistical measures of variability (dispersion) based on the actual
measurement value
Variance
Standard deviation
Classification activity: Quartiles and standard deviation
Empirical rule for the use of the standard deviation
Animation: Examples of symmetric and skewed distribution
Matching activity: Summary statistics and types of distribution
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STATISTICAL METHODS FOR RESEARCH
Thinking statistically – Making good generalisations
Screen
Notes
Unit 1: Sampling variability and the precision of a sample estimate
What use is all this stuff
 Variability in everyday situations
about variability?
 Click to view activity: What variability means in a practical sense
Sampling – the big idea
 The standard error as a measure of precision of an estimate
 Fundamental concepts in the modelling approach
 Sequencing activity: Stages of modelling
Sampling in practice
 Estimation from a sample
 Animation and notemaking activity: Repeated samples
Sampling distribution
 A conceptual distribution
 Distribution of sample means vs. distribution of raw data
 Standard error and standard deviation
 Click to view activity: Avoiding confusion about the standard error and
standard deviation
 Estimation in practice
 Video: Worked example of how to obtain a summary output using the Instat
statistics package
 Giving a measure of precision
 Missing words activity: Summary
Unit 2: Using standard errors to build confidence intervals
The Normal
 Video interviews:
distribution and
o In what ways do you explore the distributions of your datasets?
confidence intervals
o How do you quantify variability when you present your results?
 Normal distribution
 Click to view activity: A graphical representation of the 70-95-100 rule
 Confidence intervals
 Click to view activity: Confidence intervals
 Other distributions: Sampling from a skewed distribution and a binomial
distribution
 Matching activity: Summary
Calculating a
 Click to view activity: Two ways to interpret a confidence interval
confidence interval
Using software
 Video: Worked example of how to calculate a confidence interval in Instat
 How a confidence interval looks graphically
 Interpretation
 Video: Worked example of how to calculate a confidence interval in Instat
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STATISTICAL METHODS FOR RESEARCH
Which hypothesis test should I use?
Screen
Notes
Unit 1: Testing the null hypothesis
Accepting versus not
 Cartoon strip: How hypothesis testing works
rejecting the null
 The alternative hypothesis
hypothesis
A decision-making rule
 Where p-values come from
for hypothesis testing:
 How to interpret p-values
The p-value
 Statistical significance
 Video: Using the Minitab statistics package to calculate the p-value and see if it
is small enough to reject the null hypothesis
 Click to view activity: A visual representation of what the p-value quantifies
 Video: Worked example of conducting a one-sample t-test in Minitab
Decision-making: The
 The significance level
5% significance rule
 Erring on the side of caution in favour of the status quo
 Erring on the side of caution against the status quo
 The effect of the sample size and effect size on hypothesis tests
Unit 2: The practice of statistical hypothesis testing
Recap
 Click to view activity: Recap of key learning points about the practice of
statistical hypothesis testing
Comparing two means
 Comparing the means from two samples drawn from separate populations
 Clickable graphic: Table comparing two samples
 Clarity of the conclusions
 Reflection activity: Why are the results much clearer for one comparison than
for the other?
A more general
 ANOVA (ANalysis Of VAriance)
analysis: ANOVA
 Exploratory stage
 Further analysis
 Video: Worked example of how to compare the sample means from multiple
samples using the R statistics package
 What do we mean by practical importance?
Which test do I use?
 Matching activity: Null hypothesis retained vs. null hypothesis rejected
 Matching activity: Research hypotheses and statistical (null) hypotheses
 Video interview:
o What types of hypothesis tests do you carry out on your data?
o What p-value do you consider to be an indicator of statistical
significance?
 Interactive decision tree: Determining which type of hypothesis test you would
use for your data
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STATISTICAL METHODS FOR RESEARCH
Statistical modelling
Screen
Unit 1: Statistical modelling
What is a statistical
model?
The statistical
modelling framework
Linking a one-sample ttest to the null
regression model
Notes
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Straight line regression
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Straight line regression
stage 4: Generalise
your results
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The quadratic
regression model
Statistical models as adequate summaries
Click to view activity: Statistical modelling
Video interview: How are you using statistical models in your research?
Stages of the statistical modelling framework
Click to view activity: Flowchart of the statistical modelling framework
Video: Worked example of how to use SPSS to conduct a t-test, fit the null
regression model and compare the results
Matching activity: How a one-sample t-test relates to the null regression
model
Book activity: Using the statistical modelling framework
How well does the straight line regression model relate the the observed
relationship?
Interpretation of results: Regression coefficients
Intercept of the fitted line
Slope (gradient) of the fitted line
Stage four: Generalise results
Matching activity: Labelling the data in a table
Click to view activity: Straight line regression
Where are we now?
Quadratic model vs. straight line model
Video: Worked example of how you fit the quadratic regression in SPSS
Interpreting the extended model
Conclusion
Click to view activity: Summary of the steps completed
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STATISTICAL METHODS FOR RESEARCH
Analysis of categorical data
Screen
Notes
Unit 1: Analysis of categorical data
Comparing one single group
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of categorical binary data
with a hypothesised target
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Testing for association with
categorical binary data:
Comparing two groups
Confidence interval for a
true difference between
two proportions
Testing for association with
categorical binary data:
Comparing three or more
groups
Testing for a linear
association between a
categorical binary outcome
and an ordered categorical
explanatory variable
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The logic of testing a proportion of ‘successes’ against a hypothesised
target
The z-test
Click to view activity: Testing the proportion of ‘successes’ against a target
value
Confidence interval for a true proportion
Sequencing activity: Steps for testing a sample proportion against a
hypothesised value
The effect of small sample size and extreme results on inference for a
proportion
Reflection activity: The impact of small sample sizes and extreme
observed proportions when calculating confidence intervals
Equivalence of z-test and Pearson chi-squared test
The logic of testing the equality of proportion of ‘successes in two groups
Click to view activity: Alternative ways of expressing contrastintg
hypotheses
Using Minitab to input data, choose two proportions and generate a table
of results
True or false activity: Observations on the comparison of two groups
Confidence interval for a true difference between two proportions
Multiple-choice quiz: Scenario-based question
The logic of testing the equality of proportion of ‘successes’ in three (or
more) groups
Worked example including performing a chi-squared test in Minitab
Reminder about the alternative hypothesis
Classification activity: True or false?
Chi squared test for a linear trend in proportions
Worked example
Matching activity: Tasks required by research hypotheses and suitable
hypothesis tests
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