Introduction to Research Methodology - Pre-Master's
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Universiteit Van Amsterdam (UvA)
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Discovering Statistics Using IBM SPSS
An extended summary of the IRM statistics part, including Univariate Stats, Bivariate Stats (Correlations, Crosstabs), t-tests, one- and two-way ANOVA, Regression Analysis, Factor Analysis, Scale Reliability Tests. Basically everything you need to know about the statistics part of the course is in...
4.4 Multivariate Data Analysis - Literature Summary
Summary Applied Data Analyses
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Introduction to Research Methodology - Pre-Master's
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Content preview
IRM Statistics
An extended summary
Lectures, Tutorials and Field’s book
Table of Contents
Table of Contents 1
1. Univariate statistics 4
Levels of measurement 4
Proportion 4
Measures of central tendency 4
Mean (M / x̄ / μ) 4
Median 4
Mode 4
Measures of Dispersion 5
Standard Deviation 5
Sum of Squared Errors (SS) 5
Variance (s2) 5
What’s a parameter? 6
Z-Scores 6
Distribution Types 7
The Standard Normal Distribution: 7
A standard normal distribution 8
Sampling distributions 8
Standard Error of the Mean (SE) 8
Confidence Intervals 9
Computing Confidence Intervals (SOS) 9
Hypothesis Testing 9
Null hypothesis significance testing (NHST) 10
, p-value (probability) 10
Test statistic 11
Test statistic = variance explained by the modelvariance not explained by the
model= effect -signalerror - noise 11
2. Bivariate Statistics 12
Scatterplots 12
Association Types 13
Contingency Tables (Crosstabs) 14
Fielding & Gilbert article; “Categorical Data: Tables” 15
Chi-Square Distribution 15
Measuring Association 17
Nominal Variables 17
Ordinal Variables 19
Elaboration 19
Tutorial Example 20
3.Student’s t-tests 23
a. One-Sample t-test 24
b. Paired-Samples t-test 25
c. Independent t-test 25
4. One-Way ANOVA 27
Group Size - groups must be of approximate equal size 28
F-ratio 29
Effect size 29
Effect location 29
Reporting ANOVA 30
6. Regression 36
STEPS WHEN CONDUCTING REGRESSION ON SPSS: 37
1. SIGNIFICANCE - Evaluate the regression model as a whole 37
2. R2 - Evaluate how well the model fits the data 38
3. Predict Y based on the value of X 38
note; sometimes we can turn ordinal level into interval level (we assume it to be
interval) if we have enough categories
Proportion
% = proportion (f/N) * 100
➔ standardized measure
➔ reflects distribution of observations
➔ not dependent on number of observations
➔ used to compare groups
➔ do not use if observations < 20
Measures of central tendency
1. Mean (M / x̄ / μ)
the arithmetic average, centre of observations – affected by outliers (can only
be used for continuous variables) the point with the l east distance to all
values, affected by outliers
2. Median
middle value after ranking, not affected by outliers (needs minimim ordinal
level)
3. Mode
the most frequent value - can only be counted (only solution for nominal level)
4
, Measures of Dispersion
How far away are units from the mean? the fit of the mean to my data, how
heterogenous is my group of observations.
Standard Deviation
SMALL SD: DATA POINTS ARE CLOSE TO THE MEAN (typically homogenous
groups, smaller error. no error = SD is 0)
LARGE SD: DATA POINTS ARE DISTANT FROM THE MEAN (heterogenous
groups)
Sum of Squared Errors (SS)
the Σ=(x-xbar)2
affected by the n the scores we have, therefore we cannot compare it with other
samples that may have different n
Variance (s2)
sum of squares divided by degrees of freedom (n-1)
also:
● RANGE
the highest value minus the lowest value
● INTERQUARTILE RANGE
the 75% value – 25% value, or put simply, the middle 50% values.
Outliers: values that are too far away from rest of observations. Outliers shouldn't
be tossed away, but it's best to investigate into them to see if something went
wrong.
Inferences: from descriptives to predictives
5
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