MSc Quantitative Analysis Lecture Notes.
A complete collection of notes taken for the Univeristy of Stirling HSPS131 class of 2020 for Research Methods.
This comprehensive set of notes explores equations, statsitcal modelling and best fit for any and a whole host of statistical testing. Used for...
HPSP131
Quantitative Analysis
DR ANTHONY LEE – November 2020
UNIVERSITY OF STIRLING
Notes created by Hannah Moore
(MSc Graduate in Psychological Research Methods within Au sm Research)
1
,HPSP131 – Quan ta ve Analysis
Contents
Uncertainty ............................................................................................................................................. 3
Null Hypothesis Significance Tes ng...................................................................................................... 5
Sta s cal Tests ....................................................................................................................................... 6
Chi Squared............................................................................................................................................. 8
t-tests ANOVA ......................................................................................................................................... 9
Non-Parametric Tes ng .......................................................................................................................... 9
Correla ons .......................................................................................................................................... 10
Regression............................................................................................................................................. 12
Modera on ........................................................................................................................................... 14
Media on ............................................................................................................................................. 16
Sta s cal Power ................................................................................................................................... 18
Meta Analysis ....................................................................................................................................... 20
Structural Equa on Modelling (SEM) .................................................................................................. 21
Model Selec on .................................................................................................................................... 23
Mixed Effects Models ........................................................................................................................... 25
2
, HPSP131 – Quan ta ve Analysis
Uncertainty
Generalisability
The outcome of the research design should be applicable to the population, not just the
sample.
The mean
The measure of central tendency - the typical value
The standard deviation
A measure of dispersion how spread out the values are from the mean
The effect size
A numerical value that represents the strength of the effect of one variable on another.
Sampling error
The sample is always different from the population, therefore we cannot always be sure the data we
are getting from the sample actually tells us about the population.
This difference Is known as the sampling error
Sample Estimate = Population estimate + sampling error
Mathematically, the sampling error can be referred to as;
Sampling error = sample estimate - population estimate
The sampling error can be positive or negative
Positive - over estimate
Negative - under estimate
If sample effect size is greater than the population effect size - sampling error is positive
Population effect size r = 0.30
Sample effect size r = 0.40
Sampling error = 0.40-0.30 = 0.10
If sample effect size is less than the population effect size - sampling error is negative
Population effect size r = 0.10
Sample effect size r = 0.05
Sampling error = 0.05-0.10 = -0.05
Because of uncertainty, we must be sure to say that X influenced Y or may influence, as we cannot
prove anything.
For each new sample, the sampling error will always be different by chance. We don’t know what
the sampling error is, but we can estimate how big it is likely to be with the Standard Error
The standard error
A measure of the statistical accuracy of an estimate
The standard deviation of the estimated parameter
The spread of all possible estimated parameter
A small SE means less uncertainty and more accurate inferences.
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