ARMS summary (9,25)

repetition

Pearson r-> linear relation

Y= ax+b

A=Slope/B1= y/x

B= intercept/ b0/constante

Residu= expected value of Y and observed value of Y

 Y=^y
 Least square method->

R^2= explained variance, goodness of fit

R= multiple correlation coefficient

Publication bias

Sloppy science-> questionable research practices

The bayesian way

 Bayesian hypothesis testing
 Bayesian factor
 The fit of the hypothesis and the speceficity of the hypothesis

Reliability -> The extent to which a measurement is free from random measurement errors. This
means that the scores are independent of time, place, and environment.

Construct validity: the extent to which u measure the construct u aim to measure

Internal validity: extent to which u can rule out third variables, and claim the relation causal

external validity: the extent to which u can generalize the results to a bigger population

 Random sample
 Randomization

Statistical validity: The extent to which the way of analyzing the results is relevant, suitable
(assumptions) and accurately.

Conditions for causality: temporal precedence, internal validity, covariance

Use unstandardized B for formula (y=ax+b)

Use standardized b to compare the influence on the dependent variable

R2 measures the goodness of fit without adjusting for the number of predictors, while adjusted
�2R2 considers the number of predictors and penalizes models with too many variables that don't
add meaningful information

 Adjusted R^2 is used for population explained variance it takes account in size of sample and
number of predictors

the table with the F test of H0: R^2=0,so if significant-> reject 0 hypothesis

,the coefficients are ‘unique effects’ (takes account of the other factors), different than bivariate
correlations (doesn’t take account of the other factors)




Hoorcollege 1 13 November 2023

1. Frequentist vs Bayesian statistics
 Frequentist framework: test hw well the data fit H0 (NHST)
 P, values; confidence intervals, effect sizes, power analysis
 Data captured in Likelihood function (normal distribution)
 Empirical research uses collected data to learn from
 U= mean
 All relevant information for inference is contained in the lielihood function

Bayesian framework

Estimation:

 Probability of the hypothesis given te data, taking prior information into account
 In to the data we may also have prior information about u
 Prior knowledge is updated with information in the data and together provides the posterior
distribution for u
 Priors-> how u think it’s distrubeted
 The prior influences the posterior


, 




 U can see if the data supports the prior ur answer will be more certain
 Posterior distribution
o Posterior mean/mode (only the same when its on the same piek)
o Posterior standard deviation
o Posterior 95% confidence interval
 Advantage: Accumulating knowledge
 Disadvantage: results depend on choice of prior

Hypothesis testing

 Which hypothesis is more likely
 Bayes conditions on observerd data
 Pr( Hj/data): probability that HJ IS SUPPORTED BY THE DATA
 Frequentist: Pr (data/H0): p-value= probability of observering same or more extreme
data given that the null is true
 Bayesian probability
o Posterior model probability (PMP)
o How sensisble it is, based on prior knowledge
o How well it fits
 Bayesian is comparative: hypotheses are tested againt on antohe
 BF: BF10: P (data/H1/)/ P(data/H0)
 PMP are relative probabilities
 PMPs are updates of prior probabilities with the BF

Definition of probability

 In frequentist: probability is the relative frequency of events (more formal)
 Bayesian: probability is the degree of belief (more intuitive)
 CI (confidence interval, frequentist): 95%of the times of a repeated experiment that CI of the
the data has the true value
 CI (credible interval, Bayesian): there 95% probability that the true value is in the credible
interval