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...
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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