Studies must be critically reviewed:
Association does not mean causation!
Does the effect remain when additional variables are included? For this question we use a multiple regression.
Simple linear regression: involved 1 outcome, and 1 predictor.
Multiple linear regression: involves 1 outcome, and multiple predictors.
The relevance of a predictor is determined by:
A multiple regression model is also called an additive lineair model.
There are 4 types of variables:
We distinguish these in:
Nominal & ordinal = categorical or qualitative
Interval & Ratio = continuous, quantitive, numerical
For MLR we use continuous outcome and continuous predictors. But categorical predictors can be included as dummy variables. Then you’d have to assign numbers to the categorical variables. Dummy variables only have values 0 and 1.
If you have categorical predictors with more than 2 levels, you will need always 1 variable less than the amount of predictors to create a dummy variable.
Hierarchical MLR: using two or more models. If the first one is accounted for, it the second model better, etc.? You use multiple hypotheses for hierarchical MLR.
Multiple correlation coefficient: correlation between y observed and y predicted.
The R2 of the sample, is not a good indicator of the R2 of the population. The more predictors, the more biased it is. If you correct the R2 for this, you call it the adjusted R2. This variable you use when talking about the population.
With the R2 chance you can see if the added predictors improve the prediction. Then after the output, you decide whether you want to continue with the first or second model.
B-coëfficient: tells you what the unique contribution of that variable is, given that all the others are also in the model.
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Lecture 1: Multiple Linear regression (ARMS, Utrecht University)Studies must be critically reviewed:
Association does not mean causation!
Does the effect remain when additional variables are included? For this question we use a multiple regression.
Simple linear regression: involved 1 outcome, and 1 predictor.
Multiple linear regression: involves 1 outcome, and multiple predictors.
The relevance of a predictor is determined by:
A multiple regression model is also called an additive lineair model.
There are 4 types of variables:
We distinguish these in:
Nominal & ordinal = categorical or qualitative
Interval & Ratio = continuous, quantitive, numerical
For MLR we use continuous outcome and continuous predictors. But categorical predictors can be included as dummy variables. Then you’d have to assign numbers to the categorical variables. Dummy variables only have values 0 and 1.
If you have categorical predictors with more than 2 levels, you will need always 1 variable less than the amount of predictors to create a dummy variable.
Hierarchical MLR: using two or more models. If the first one is accounted for, it the second model better, etc.? You use multiple hypotheses for hierarchical MLR.
Multiple correlation coefficient: correlation between y observed and y predicted.
The R2 of the sample, is not a good indicator of the R2 of the population. The more predictors, the more biased it is. If you correct the R2 for this, you call it the adjusted R2. This variable you use when talking about the population.
With the R2 chance you can see if the added predictors improve the prediction. Then after the output, you decide whether you want to continue with the first or second model.
B-coëfficient: tells you what the unique contribution of that variable is, given that all the others are also in the model.
Questions? Let me know in the contribution section!
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Lecture 2: Moderation & Mediation (ARMS, Utrecht University)Moderation: the effect of predictor X1 on outcome Y is different for different levels of a second predictor X2. For example when X2 is gender: the effect of X1 on Y is different for males and females.
The conceptual model for this example is:
The statistical model for this example is:
If you use 10 models in your analysis, you have an inflated type 1 error. This is because the error ‘kind of’ adds up (not literally) with every model you use.
When you’ve established a significant interaction effect, further investigation is needed. This can be done through a simple slope analysis: are the slopes of the relation of one predictor with the outcome different for different levels of the other predictor?
Reading a plot of a simple slope: high means one SD above the average, low means one SD below the average.
How to test for interactions?
1. Through SPSS: analyse > regression > linear. Add 3 predictors:
- X1, X2 and X1X2
--> Important! Center the predictors before computing the products. This avoids multicollinearity.
2. Use PROCESS. Choose model number 1 for moderation. Use options for centering and for getting syntax that gives you the ‘mean 1 SD plots’.
Mediation: the effect of the independent variable on a dependent variable is explained by a third intermediate variable.
Complete mediation: the effect is fully explained by a third intermediate variable.
Partial mediation: the effect is partly explained by a third intermediate variable
This is the model for mediation:
Old methods for mediation (statistical methods):
1. Is there a significant effect of X on Y?
2. is there a significant effect of X on M?
3. is there a significant effect of M on Y, controlled for X?
Then you see if 1 and 2&3 differ. If yes, M has an effect. Criticism: it is just eyeballing to see if c has become smaller.
Current best practice: bootstrapping. This method you can use when you don’t know the sampling distribution. We use the output to understand how we interpret the bootstrap values:
.....read more
Seminar 1: Bootstrapping (ARMS, Utrecht University)You use bootstrapping to get rid of troublesome situations, for example distributions that are not in agreement with the assumptions causing:
One assumption, is that the residuals should be normally distributed. There are 5 ways of how you can address this problem:
1. Ignore the problem, claim that the MLE (maximum likelihood estimation) is robust. This is defensible if the distribution is not extreme and N is large.
2. Use normalizing transformation
3. Use robust estimators (MLR)
4. Bootstrapping
5. Bayesian estimation
What does bootstrapping do? It approximates the sampling distribution by re-sampling (with replacement) from the original sample, each size of n. This results in alternative SE estimates, 95% Cis, and p-values.
We do this because most of what we know about the ‘true’ probability distribution (the population) comes from the data. So we use the data as a proxy for the population. We draw multiple samples from this proxy, as if we sample from the population. Then we compute the statistic of interest on each of the sampled datasets and calculate the results.
The resampling size is always as big as the original sample size. This is because otherwise there would be an inaccurate standard error, since SE is also based on sample size.
The one assumption for bootstrapping is that your sample needs to be representative for the population. This is a visualization of taking bootstrap samples:
The mean of the bootstrap distrubution does not have to equal the mean of the sampling distribution (and this is not a problem). The spreak/variance does equal the mean, and if the sample is representative, so does the shape/skewness.
Does bootstrapping help in the following cases?
a. Regression, when the assumptions are met --> no additional value to do bootstrapping.
b. Regression, with heteroscedasticity --> yes, for a better/unbiased estimate of SE.
c. Regressioin, with very small sample size --> no, because a very small sample is often not representative for the population. If it is representative: yes.
d. Regression, with non linearity --> no, does not fix or even indicate this.
e. Regression, with multicollinearity --> no, does not fix or even indicate this.
Bootstrapping the indirect effect: in every bootstrap you estimate the indirect effect to get a SE and CI. This goes as follows:
1. Repeatedly sample from dataset with replacement
2. Estimate indirect effect ab in every sub-sample: X --> M --> Y
3. Make a histogram of all values of ab
4. Look at the middle 95% --> 95% CI
5. Optional: determine the bias corrected and accelerated interval
Checking for significance: if the 0 is included in your confidence interval: do not reject H0. If it is not,
.....read more Lecture 3: ANOVA & ANCOVA (ARMS, Utrecht University)ANOVA: comparing groups on a continuous variable. The analysis separates between group variation and within group variation.
But what if there are more factors that influence the outcome y? You need to control for them. You use an ANCOVA to do this. Example: you want to research whether there is a difference in cognitive abilities between babies of teen moms and adult moms. But, not only age, but also IQ influences the cognitive abilities. You need to control for IQ when conducting this experiment.
In an ANCOVA, you always need a categorical predictor (factor): we want to compare groups so there must be a variable creating groups.
The covariate is always continuous.
Homogeneity is an assumption for ANCOVA. Checking homogeneity:
1. When you draw a line through the clouds of the scatter plot, the lines of the two groups must be parallel. If not, there is no homogeneity of regression slopes.
2. You can also check homogeneity by looking at the significance of the interaction effect. If the effect is significant: there is no homogeneity. If the effect is not significant the assumption is met.
Do both 1&2!
There is another assumption (but researchers don’t all agree on how to interpret this) that states that there should be independence of the covariate and the factor:
AN(C)OVA test statistic: F = MSgroup/MSresidual
Adding a covariate will change the F-test if:
So: inclusion of a covariate can be useful when groups differ on the covariate, but also when they do not! But, to be useful, the covariate must be related to Y.
In a regression model, you have R2 for the explained variance. In AN(C)OVA we have a similar measure, called eta-squared. But SPSS provides the partial eta-squared. This is still the amount of variance explained, but it’s not divided by the total variation but by the sum of the variance of this effect and the residuals. So it answers: how much variance is explained compared to the part that’s not explained (since there are more effects in one model).
The AN(C)OVA tells you whether
.....read more Lecture 4: Factorial ANOVA & MANOVA (ARMS, Utrecht University)A 2x3 ANOVA means there were two factors, one with two and one with three levels.
In this case you test three hypotheses:
Definition interaction effect: the effect of one factor is different for different levels of another factor. For example: the effect of the treatment is different for men and women.
If you found a significant interaction effect, it does not tell you the story of interest (which subgroups score higher/lower than others). Follow-up tests are needed, these are called Simple (Main) Effects. Here you look at the effect of one factor within one level of the other factor (for example only for women).
In the interaction plot you can quickly see whether there is an interaction or not: if the lines are parallel, there is no interaction. But disadvantage: you don’t know the confidence intervals from the plot only.
In a 2x3 ANOVA there are 2+3=5 simple main effects you could test.
In SPSS, you can only run a simple main effect test through the syntax.
Effect sizes for all effects (main and interaction) for factorial ANOVA are: partial eta-squared.
In factorial ANOVA, you can use contrast testing as alternative to post-hoc pairwise comparisons. This only tests pre-specified hypotheses. No alpha corrections are needed --> more power. Disadvantage: it’s unlikelier you expose unexpected results that may be interesting for future research.
With MANOVA, you can compare two or more groups on multiple dependent variables simultaneously with one test.
The advantes of a MANOVA are important to understand and know. These advantages are:
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Seminar 2: Open Science (ARMS, Utrecht University)*These notes do not include the introduction to R*
HARKing: changing or creating the hypothesis after seeing the results.
P-hacking: researchers collect or select data or statistical analyses until nonsignificant results become significant.
Selective reporting: only reporting significant results, and not reporting the non-significant results.
Publication bias: only articles with significant effects are published.
So the problem is: the literature is not representative for the population.
What can we do to avoid these biases/to make ‘great results’ less important? --> Registered reports: when you use pre-registration it is on forehand clear what you’re going to do and what you’re interested in, in a manner that is verifiable by others. Four central aspects of the Registered Reports Model are:
Methods of pre-registration include:
How does it work? Authors submit the STAGE 1 manuscript, stage 1 peer review takes place and if the reviews are positive, the journal offers in-principle acceptance (IPA) regardless of the study outcome.
The advantages of Registered Reports:
--> For the scientific community:
--> For scientists
Common misconceptions:
1. ‘Pre-registration prevents the exploration of your data/creativity’. This is not the case. It allows for exploratory science, it simply prevents reporting exploratory analyses as confirmatory.
2. ‘Pre-registration does not allow for making changes and I cannot predict what will happen’. This is not correct. It allows for these things, as long as you report your deviation from your pre-registered plan.
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Lecture 5: Repeated Measures Analysis & Mixed Designs (ARMS, Utrecht University)Designs with one or more within factors are called repeated measures designs. An example of a within factor is time. But condition can also be a within factor, as long as each participant goes through every condition.
The advantages of a within subjects design are:
The data of a repeated measure design is dependent (because the same respondents are used). This means you need to use an analysis technique that takes this into account.
The null hypothesis is that there is no difference between the groups. This is the same in an ANOVA, so why not use that? Because we know how the data was collected and we know the data is dependent on each other.
There is an assumption: the assumption of sphericity. This means that the variances of all difference scores are equal. You can test this with Mauchly’s test for sphericity. But do not only rely on non-significance of the Mauchly test, also ‘eyeball’ your descriptive data to see if the variance is roughly the same, or look at epsilon.
If the Mauchly test is significant, the assumption of sphericity is not met. If you look at Epsilon: 1,000 is perfect sphericity.
The ‘lower bound’ is based on your design. If you have 4 timepoints, the lower-bound will be: 1/(4-1)=.333.
What to do when the assumption is violated? SPSS offers solutions in the ‘tests of within-subjects effects’ table.
--> Greenhouse-Geisser: for bigger violations; epsilon is smaller than .75.
--> Huynh-Feldt: for milder violations; epsilon is .75 or higher.
If there is a very big violation, and you don’t trust it. Look at the Wilks’ Lambda significance in the ‘multivariate tests’ table. Here you don’t have to worry about sphericity (this is the MANOVA approach). The rule of thumb is: if the epsilon is closer to lower bound that to 1, you use this method.
The follow up tests:
These contrasts are called polynomial contrasts and are incluced in SPSS.
Designs with at least one between and at least one within factor are formally called mixed designs (but often also repeated measures).
If the within
.....read more Know your Data - ARMS (neuropsychologie) Signal Detection Theory - ARMS (neuropsychology)
What determines whether the patient is diagnosed?
Sensitivity: how far are these curves apart? How good can. the participant discriminate between these two curves?
There is also a criterion:
Everything > the criterion: we say that the signal is present.
Everything < the criterion: the signal is not present.
This can also be presented as:
From the data from an experiment you could tell how many hits, false alarms, misses and correct rejections there were; you make the decision matrix.
To calculate sensitivity, you only need hits and false alarms. You can calculate this in excel using:
Hits: =IF(AND(CEL=1,CEL=1),1,0)
False alarm: =IF(AND(CEL=0,CEL=1),1,0)
Then you calculate the sum of hits and false alarms, and then you can fill in the matrix.
Amount of misses: (Total amount of stimuli-present trials) - hits
Amount of correct rejections: (Total amount of stimuli-non-present trials) - false alarms
From your raw data, your matrix might look like this:
For the decision matrix, you divide everything by the total number:
To calculate sensitivity, we use d’ (d-prime). d’ = how many standard deviations are the mean of the signal and the mean of the noise apart? d’ = 1 stdev, d’ = 2 stdev etc. The smaller the d’, the lower the sensitivity. We calculate this using:
Reasoning: the difference between the means = the difference between the distance to criterium.
To calculate the Z in excel: normsinv(proportion hits or false alarms). So the total formula to calculate d’: normsinv(hits) – normsinv(false alarms). You use the rates for this formula, not the amounts.
You get a negative d’ if the person was worse than 50% chance of getting it right; they can do this purposefully or maybe they didn’t read the instructions well. This person is still sensitive
In summary, the steps for computing d’:
Every person has a criterion. The criterion can change by e.g. change in the instructions to the participant.
There are two measures for criterion: C=criterion, beta=bias.
You calculate criterion using:
If the criterion is 0, the person has no bias to right or left: it’s placed in the middle of the two curves.
Negative criterion: tendency to say ‘yes, there is a target’
Positive criterion: tendency to
.....read more Single Case Studies - ARMS (neuropsychology)
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Nice! Roos Heeringa contributed on 01-04-2021 13:45
Another nice and clear summary, well done Julia!!
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