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Summary ARMS for Psychology (UU): Midterm Grasple, Lectures, Seminars and Workgroups (grade 8.0) CA$16.68   Add to cart
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Summary ARMS for Psychology (UU): Midterm Grasple, Lectures, Seminars and Workgroups (grade 8.0)

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  • Course
  • ARMS
  • Institution
  • Universiteit Utrecht (UU)

This document summarizes all test material for the midterm exam of ARMS. Some parts of the Grasple lessons are written in Dutch, but overall in English. With this summary i got an 8 for the exam.

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Document information

  • February 20, 2024
  • 58
  • 2023/2024
  • Summary

Subjects

  • arms
  • statistics
  • psychology
  • grasple
  • lecture
  • seminar
  • workgroup
  • regression
  • fair
  • analysis
  • mediation

Written for

  • Universiteit Utrecht (UU)
  • Psychologie
  • ARMS
All documents for this subject (12)

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Inhoud
Lecture 1 Multiple Linear Regression (MLR) ........................................................................................... 3
Lecture 2 Analysis of Variance (ANOVA) .................................................................................................. 8
Lecture 3 Analysis of Covariance (ANCOVA) .......................................................................................... 11
Lecture 4 Repeated Measures ANOVA (RMA) ....................................................................................... 13
Lecture 5 Mediation analysis ................................................................................................................. 16
Rehearsal of everything ......................................................................................................................... 18
All assumptions ................................................................................................................................. 19
Seminar 1 Preregistration and Open Science ........................................................................................ 21
Seminar 2 Open Data Analyses.............................................................................................................. 24
Seminar 3 Software choices & Informative hypotheses........................................................................ 25
Seminar 4 Solutions to assumptions violations including bootstrap .................................................... 27
Grasple lessons ...................................................................................................................................... 29
Refresh part 1 ........................................................................................................................................ 29
Refresh part 2 ........................................................................................................................................ 30
Refresh part 3 ........................................................................................................................................ 31
Week 1 Bayes and MLR ......................................................................................................................... 33
The Bayesian approach...................................................................................................................... 33
Assumptions 1 ................................................................................................................................... 34
Assumptions 2 ................................................................................................................................... 35
Multiple Linear Regression, including hierarchical MLR.................................................................... 37
Creating dummy variables ................................................................................................................. 38
Multiple regression with dummy variables (interpretation) ............................................................. 39
Week 2 Factorial ANOVA Factorial ANOVA: visually assessing main and interaction effects ................ 40
ANOVA assumptions .......................................................................................................................... 41
Factorial ANOVA ................................................................................................................................ 41
About multiple testing and error rates .............................................................................................. 41
Follow-up testing (frequentist) .......................................................................................................... 42
Informative hypotheses (Bayes) ........................................................................................................ 44
Week 3 ANCOVA .................................................................................................................................... 45
Averages and corrected averages ...................................................................................................... 45
ANCOVA (frequentist) ........................................................................................................................ 48
FAIR .................................................................................................................................................... 49
ANCOVA as regression ....................................................................................................................... 49
ANCOVA (Bayesian) ........................................................................................................................... 50

, Supporting the null hypothesis ......................................................................................................... 50
Week 4 Repeated measures ANOVA ..................................................................................................... 51
Within factors and between factors .................................................................................................. 51
The sphericity assumption ................................................................................................................ 51
Mixed design RMA (repeated measures ANOVA) ............................................................................. 52
Week 5 Mediation analysis.................................................................................................................... 53
Moderation vs. mediation ................................................................................................................. 53
Bootstrapping .................................................................................................................................... 54
Mediation analysis............................................................................................................................. 54
Workgroup 1 .......................................................................................................................................... 56
Workgroup 2 .......................................................................................................................................... 56
Workgroup 3 .......................................................................................................................................... 57
Workgroup 4 .......................................................................................................................................... 58
Workgroup 5 .......................................................................................................................................... 58

,Lecture 1 Multiple Linear Regression (MLR)
Frequentist framework = tests how well the data fits the null hypothesis (NHST)
- P-values
- Confidence intervals (=if we were to repeat this experiment many times and calculate
a CI each time, 95% of the intervals will include the true parameter value, and 5%
won’t)
- Effect sizes
- Power analysis

Bayesian framework = probability of the hypothesis given the data, taking prior information
into account
- Bayes factor (BFs)
- Priors (expectation beforehand)
- Posteriors (=prior and data)
- Credible intervals (=there is 95% probability that the true values is in the interval)

Empirical research = uses collected data to learn from, information is captured in a likelihood
function. →frequentist
X-axis: values for population mean
→for example height: 140 and 230 cm height for an adult are less likely than 165 cm for an
adult.
Y-axis: probability of the observed data for each value of population mean (µ)

Bayesian approach = prior knowledge is updated with information in the data and together
provides the posterior distribution for µ
- Advantage = accumulating knowledge (today’s posterior is tomorrow’s prior)
- Disadvantage = results depend on choice of prior

The posterior distribution of the parameters of interest provides all desired estimates:
- Posterior mean or mode
- Posterior SD (comparable to frequentist standard error)
- Posterior 95% credible interval (providing the bounds of the part of the posterior in
which 95% of the posterior mass is)

Results depend on things not observed and on the sampling plan (how you test).

Bayesian probability = probability that hypothesis Hj is supported by the data.
→Pr(Hj|data)

Frequentist probability = probability of observing same or more extreme data given that the
null hypothesis is true (p-values).
→Pr(data|H0)

PMP = Posterior Model Probability; the (Bayesian) probability of the hypothesis after
observing the data
→are also relative probabilities

, →PMPs are updates of prior probabilities for hypotheses with the BF

Bayesian probability of a hypothesis being true depends on two criteria:
- The prior = how sensible it is, based on prior knowledge
- The data = how well it fits the new evidence

Bayesian testing is comparative: hypotheses are tested against one another
Bayes Factor (BF) = 10 → support for H1 is 10 times stronger than for H0
Bayes Factor (BF) = 1 → support for H1 is as strong as support for H0

Both frameworks use probability theory, but:
- Frequentist: probability is the relative frequency of events
→more formal
- Bayesian: probability is the degree of belief
→more intuitive
→this leads to debate (=same word is used for different things)
→and leads to differences in the correct interpretation of statistical results (like confidence
and credible interval)

Multiple linear regression (MLR)
‘normal’ linear regression:
^Y = B0 + B1 x X
^Y = intercept + slobe x X-value
→so we use X to predict Y

Residual = distance from the line = e

Multiple linear regression = with more predictors (Y = observed, Y^ = predicted)
Y = B0 + B1 x X + B2 x X + e
Y = intercept + slobe 1 x X-value + slobe 2 x X-value + residual




→Life satisfaction decreases by age, but increases by years of education

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