Personalized Questions (Might not be relevant to you all) Flashcards
Do all estimators work on assumptions. Hence? What does robustness of a confidence interval mean?
Estimators
All estimators work on assumptions. Point estimates can be different too, not just interval estimates
Robust
- Coverage of the interval remains unaffected by violation of the statistical assumptions underlying its construction
- Captures the unknown population parameter value in repeated samplings by the same percentage of times as defined by the size of the interval when one or more assumptions are being violated
What do we need to calculate CIs. As level of confidence of the CIs increase, what happens to the precision
Things for CI
Sample Statistic, Standard Eror, Alpha Value
All else equal, as level of confidence increases, it is less precise (Wider area akin to being more confidence the true population parameter will be captured)
What are summary characteristics? What are the 2 common summary characterstics
Statistics and parameters!
- A summary characteristic is some kind of aggregation undertaken on the individual values in one or more variables to produce a single quantity that is
informative about the value- Mean
- Standard Deviation
- Varaince
- Correlation
- Bla bla
What happens to the sampling distribution as (a) Number of repeated sampling increases; (b) As number of samples increases
(a) Number of repeated sampling increases
* Unbiased sampling distirubtion will get increasingly closer to the populaton distribution
(b) As number of samples increases
- Mean of sampling distribution will get increasingly closer to the mean of populaton distribution
- Sampling distribution will become increasingly normal
- Central Limit Theorem
Don’t mix up the two…
What are some effect size. What are effect sizes
Quantitative measure of the strength of a relationship between construct measures.
- Mean
- Mean DIfference
- R2
- Coefficients (Pearson and Regression)
- Odds Ratio
- Cramer’s V
- Anything you can put a CI over
What is the population correlation coefficeint. Can we calculate it
p (Rho).
It can only be estimated
What do associations of categorical variables aim to do
Measure strength and direction of 2 variables
- Note: It is just like a continous one. There’s both strength and direction!
OLS Estimator - Which is bias/unbias
Unbias
- Unbiased in maximising SSreg if assumptions hold (like residuals)
- Unbiased in estimating sample regression coefficients
Bias
- Bias, but Consistent, in R2
- Adjusted R2 is only LESS bias (not no bias)
What is the model equation for simple linear regression?
Y_hat = a + bxi
Note: b does not have a hat
In regression diagnostics, what do we look for in
(a) Linearity
(b) Hetereoscadescity
(c) Outliers / Influential Cases (From normality)
Linearity
- See misfit between the 2 lines (probability different colours)
Heteroscadescity
- See fanning out of residual
- nCV and Residual plots MAY NOT be consistent
Outliers & Influential Cases
- Influential
- Change regresion coefficients and R2
- Cook’s D >1 is definitely a problem
- Outliers
- Look for +- 3
- Though for smaller samples, might be 3.5 to 4
- Large studentized residuals is maybe a problem
In t-tests, what if the design is unbalanced and violated homogenity?
We must use adjustment separate variance estimates
If Levene and Flinger comes out p < .05 and p > .05
What should we do?
Assume hetereogeneity. Be conservative.
When are standardized mean differences useful
Hedges g and Bonnet’s d
- Useful if it has an arbitary scaling and can’t be meaningfully intepreted
- stop mixing up arbitrary. arbitrary = sucky!!!!
In observed mean differences, will the mean differene estimates be the same?
Yup.
There is only one mean difference. However, all the other statistics will be different! (e.g. SE, t , etc)
Does homogeneity of variance matter at all in dependent group t-test
Yes
- While it is not an assumption
- g and d will differ and they still consider homogenity of group variances
How many standard errors are there in a dependent group?
One.
Standard Error of the Mean Difference
How are dummy and ANOVA similar?
Almost everything
- F-Statistic for R2
- T-Statistic for Coefficients
- Proportion of DV explained
- df
- P-values
How many contrasts do we need to establish orthogonality? What is the maximum number of linear contrasts
Two.
Don’t mix this up with number of linear contrasts.
- The maximum number of linear contrasts to account for differences among means is k - 1
In a one-way within-subject design, does the interval spacing have to be the same?
The interval spacing must be the same for all participants, but the distance between each interval can vary, as long as all same
What does g and delta estimate based on (uni/multi). When is uni/ multi used
- Hedges’ g and Bonett’s delta estimate the effect size and associated confidence interval using a univariate method.
- The multivariate method is only used in the omnibus test of the null hypothesis.
Does hedges g and bonnet’s d require spherecity?
Only g requires sphericity
HOWEVER
Both Hedges’ g and Bonett’s delta may be biased due to violation of the sphericity assumption
Wtf does Pillai examine
Multivariate
- Test omnibus hypothesis of no difference between all levels of the factor
- Test polynomial orthogonal linear contrasts
- Only tell significance
- No effect size
What is the defitnition of sphericity. Hence?
Sphericity
Homogenity of variances of all possible difference scores between pairs of three or more within-subject conditions (or levels) at a population level
Hence
Epislon
- Estimated from sample covariance matrix
- Calculated from population covariance matrix
What does the epislon estimators do?
Estimate epislon in sample data
- Greenhouse-Geisser estimator - E_hat
- Huynh-Feldt estimator E-wave
- Adjustments to null hypothesis tests under the univariate approach.
Define main effect contrast. And what is the scaling
Main effect contrasts
- Compare cell means of the two-way table to investigate contrasts of each factor in the two design.
Order-0 Scaling
- Scaling for a difference in means
- Absolute sum to 0
Define interaction contrast. And what is the scaling
Interaction Contrast
- Compare the cell means of the two-way table using
the cross-product of contrast weights from the linear comparisons for the main effect linear contrasts
Order-1 Scaling
- Scaling for the difference two sets of differences between
means
What happens to CI in multiple NHSTs
The CI coverage for capturing the true population parameter may be lower than nominal rate requested.
How many NHSTs is the mark where probability of type 1 error is high
By 25 NHSTs,
High probability of at least one type 1/false rejection error due to chance alone
What is the SEm. Why do we need it? And what is the Formula?
Average Error Score.
rxx does not tell us what is typical
𝑆𝐸𝑚= 𝑠𝑥 √1−rxx
- Sx
- Standard Deviation of Observed Scores
What is the first classical theory equation
Xi = T + Ei
Ei is unsystematic error variance
What is the third classical theory equation. Can we calculate it?
p2xt = True Score Variance / Observed Score Variance
Note
p2xt
- Theoratical reliability coefficient
- It can only be estimated using the sample reliability coefficient rxx
What are the equations for reliability using variances
(a)
- True Score Variance / Observed Score Variance
(b)
- 1 - (Error Score Variance/Observed Score Variance)
Note
- Observed is always the denomintor.
What is criterion validity in theory. What are the types?
Extent to which test scores predict scores on an relevant criterion variables.
- Concurrent
- Evaluated against a criterion measured at the
same time
- Evaluated against a criterion measured at the
- Predictive:
- Evaluated against a criterion measured later
What is criterion validity in practice
In practice:
- Validity Coefficient
- Exclusive to criterion validity
- Will be attenuated due to measurement error
- Pearson Correlation
If estimator A is more efficient than estimator B, what is the observed test statistic
Observed test statistic derived from A will be larger than the one from B
Efficient = Smaller S.E. = Larger Test Statistic Value
What do we need to calculate an observed test statistic?
- Known sample statistic value
- aka. “Assumed population parameter value”
- Can use a known population parameter value if we wish
- Standard Error
What do we need to calculate a critical test statistic?
- Alpha
- Relevant probability distribution stuff
- t-distirubtion: one-dfs
- F: two-dfs
