Lecture 1: General Linear Model Flashcards
What are the assumptions of a t-test?
- continuous DV
- SE only valid if variance is not different between groups (homoscedasticity)
- subjects must be independent, otherwise SE formula not valid (cannot be tested, thinking exercise)
- look up t-statistic under $H_0$ but only if DV is normally distributed in both groups
Why is there a translational problem between basic and applied research?
- communication and shared language → communication issues between scientists in basic & applied
- replicability of findings → replication problems with many psychological findings - stability is crucial in the translational process
- establishing Causality → establishing causality is difficult since much of research is focusing on correlations
- unclear external validity → often mentioned that non-clinical samples is not beneficial
- fat-handedness problem → fat-handedness of psychological treatments - treatments often affect multiple processes, they do not operate in isolation
How does the t-distribution change shape based on the df values?
The more df the narrower it becomes, the less df the wider it becomes
What is b0?
The intercept and the expected/ average score on the DV when the IV is 0 o
Error
The difference between the observed and the expected score
What are the assumptions for the GLM?
- DV continuous
- variance of residuals equal at all levels of x (homoscedasticity)
- data is independent
- residuals normally distributed
What are the assumptions for the factorial ANOVA?
- DV continuous
- variances of DV equal in all groups
- data of all subjects is independent of each other
- DV is normally distributed in each group
What is b1?
The score on the dependent variable when the independent variable increases by 1 or the difference in averages of the different groups in the IV
How does the GLM work?
It creates a line that best fits with the observed data, results found to be the same as for the linear regression as the the t-test
What does the t-test test?
Whether the differences in averages across the groups is significant. Formula is= (y group 1- y group2)/ se
Standard error
√(sd²1/N1)+ (sd²2/N2)
What needs to be interpreted for a t-test?
- Look at the means to see the direction
- Check equal variances
- Look at the F values and p values to see significance
How would this be interpreted?
Self-esteem at posttest differed significantly between running and sitting
Self-esteem at posttest on average higher for running than for sitting
What is y(i)?
The observed score for the dependent variable
What needs to be interpreted for a linear regression?
The unstandardized b coefficients and the value and p value
How could we report regression analysis (does not need to be APA on the exam)?
- Intervention predicts self-esteem at posttest, F(1, 38) =
4.22, p = .047. - On average, self-esteem at posttest is higher for the running group than for the sitting group (b1), t(38) = 2.06, p =
.047.
What is the GLM with two independent variables?
y(i) = b0 + b1x(i) + b2z(i) + b3x(i)z(i) + error(i)
What is the interpretation of an interaction effect?
The effect of {intervention} differs between people across different groups
What needs to be interpreted for a factorial ANOVA?
Any significant main effects and the interaction effect
How can you interpret a plot for factorial ANOVA?
Average between groups= in difference between the mid point of the average lines
Interaction effect= the difference between the average lines at the starting point and end point
What is the sum of squares?
Deciphers how well the model fits the data, uses N-k-1
What is the total sum of squares?
The sum of squared differences between the observed and predicted values using the baseline model
What is the model sum of squares?
SST- SSR
What is R^2?
SSM/SST-> proportion of improvement with the predictive model compared to the baseline model
How can influential cases be detected?
→ calculating the adjusted predicted value for a case (excluding a case and seeing if the predicted value is equally well predicted by both models)
→ calculating Cook’s distance (values larger than 1 are potentially problematic)
What do B values explain?
how much the outcome changes if the predictor changes by one standard deviation
What is the rationale for the t-test?
- Standard error used to gauge variability, difference between means in the observed sample compared to the difference expected
- The larger the difference compared to the standard error, the more likely that the means are different
How to check for normality assumption?
P-P plots (probability-probability plots), which plot the cumulative probability of a variable against the cumulative probability of a distribution, can be used. Ideally, this is a straight diagonal line.
How to check for homoscedasticity?
Through a plot which has standardized residuals on the x axis and standardized predicted values on the y axis-> if there is a funnel shape the assumption has not been met. Or through Levene’s test, if significant the assumption has not been met.
How can violation of independence affect the conclusions drawn?
If the data are dependent (within groups), the test is far too liberal (results that are significant too quickly). In that case, you may conclude that the treatment group
scores are significantly better than the control group, whereas in reality this is not the case.
What are clinical examples of t-test violations?
- Continuity: when the outcome variable is nominal (e.g., recovered or not).
- Equal variances (homoscedasticity): when in one group all people have about the same degree of complaints, while in the other group the spread is much
greater. - Independence of data: when groups of clients have been treated by the same therapist (= nested data).
- Normality of data: within the treatment group, half of the subjects improved while the other half did not. The distribution is then bimodal.
Explain all aspects of the general linear model
y(i) = b0 + b1*x(i) + error(i), where:
y(i) = DV at posttest for subject i,
x(i) = IV where subject i belongs to (0=waiting list, 1=intervention)
b0 = intercept: average DV scores at posttest in the x=0 condition
b1 = difference in average DV scores at posttest between different IV groups
error(i) = difference between observed and expected score for DV scores at posttest for subject i.
What is b3?
difference in average DV score between IV1 groups and between IV2 groups
