IRM Statistics - An Extended Summary (Lectures, Tutorials & Books)

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

5. Factorial ANOVA 30
Philosophy behind two-way ANOVA: 30
Finding the interaction effect visually 31
Effect Size 31
Reporting a two-way ANOVA 31



2

, Factorial ANOVA Example 32

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

7. Factor Analysis 42




3

, 1. Univariate statistics
Levels of measurement
● Nominal (also binary)
● Ordinal
● Interval
● Ratio (nothing below 0)
● Categorical ​vs​ Continuous

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 (s​2​)
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




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