Google Interview Hacks

Name an alternative to one-way ANOVA for independent groups (where ANOVA assumptions not met) ?  Name an alternative to Repeated measures ANOVA?  What would be suitable follow-up tests to use instead of T-tests for each respectively? To be used when your data does not meet ANOVA assumptions (e.g. not normally distributed and small sample) Not as powerful as parametric tests Based on 'ranked' data rather than means, so not skewed by extreme scores Kruskal-Wallis: alternative to one-way ANOVA for independent groups Friedman's ANOVA: alterative to RM ANOVA Use pairwise comparisons to follow up if significant (reducing alpha level): Mann-Whitney Tests - independent groups Wilcoxon Test - related groups

How would you find the total number of conditions/levels in a factorial design? E.g. 2x3 It's factorial! (multiplication, multiply it! 2x3=6 conditions/cell means or, draw the table to help visualise it

How to work out what kind of design an ANOVA has!  =Need to work on, working out ANOVA designs. BETWEEN:When different subjects are used for the levels of a factor, the factor is called a between-subjects factor or a between-subjects variable. The term "between subjects" reflects the fact that comparisons are between different groups of subjects. All factors between subjects= a between subjects design WITHIN:When the same subjects are used for the levels of a factor, the factor is called a within-subjects factor or a within-subjects variable. Within-subjects variables are sometimes referred to as repeated-measures variables since there are repeated measurements of the same subjects. Each subject tested within each condition REPEATED MEASURES AND "WITHIN" ARE SYNONYMOUS= SAY "REPEATED MEASURES", OR SAY BOTH! (purely within participants could also potentially be quasi-experimental(?) so say repeated to avoid ambiguity REPEATED MEASURES: same part...

What kind of follow-up tests should you use for within-subjects factorial ANOVA? For follow up testing: WITHIN participants; use RELATED T-tests rather than independent T tests

How does multifactorial ANOVA differ with within-participant factors? Same asssumptions as for between-subjects ANOVA, plus assumption of sphericty (ONLY IF MORE THAN TWO CONDITIONS FOR A WITHIN-SUBJECTS IV) Constant source of error due to having same participants in different conditions is subtracted from the error variance, as a result reducing the error term ("partialling out"; we do this because one assumption of the statistical tests (not earlier covered) is that the data from each condition should be independent of all other conditions. In order to do this, the consistent effects of participants across all conditions (e.g. those who tend to perform well will do so over all conditions) are removed statistically, so that the conditions will effectively be independent of each other and analysis can continue Extra table: "Within Subjects Effects": because same participants in each condition, we are able to calculate the degree of error associated with e...

If you find a significant interaction in ANOVA, what should you do? Explore that interaction further! How should you do that? Simple effect tests: corrected T-tests!

What are the assumptions of multifactorial ANOVA?  normal distribution homogeneity of variance (one way of telling = similar SD values, e.g. 3.97, 3.73, 3.09, 4.22) If more than two conditions in any of the within-factors IVs, have to check whether the assumption of sphericity has been violated: Mauchley's test of sphericity Sphericity= an assumption of within participant's ANOVA If Mauchley's test of sphericity 's sig is 0.5 or lower, then this means the assumption of sphericity is violated, use Greenhouse Geisser

Give all the sources of variance for: two way between ANOVA, factors A and B and three way between ANOVA, factors A,B,C Main effect A Main Effect B Interaction A and B Error Main effect A Main effect B Main effect C Interaction A and B Interaction A and C Interaction B and C Interaction ABC Error (IDs. experimental errror) 

What are the sources of variance in MULTIfactorial ANOVA? -Some variance attributable to the IV's (their main effects) -Some variance attributable to their interaction effects (e.g. Beatles produced music together they never could have produced alone, whole is greater/different than the sum of its parts) -Error variance (experimental error, individual differences (except IDs are also partitioned in repeated/within ANOVA)

When is partial eta squared useful, and when is d useful? Partial eta squared= global measure of magnitude of effect D= magnitude of difference between two conditions

What are the sources of variance in two way ANOVA? (main effects and interactions) Variance due to Factor 1 Variance due to Factor 2 Variance due to the interaction between these factors Error variance ('within-groups' variance) Need to report the F value (with associated d of f and p value) for both of the "main effects" and the "interaction"

Define simple effect (sometimes called simple main effects). How would you calculate them? THE SIMPLE PICTURE OF JUST MAIN EFFECTS If you do get a significant interaction, you can find out what is happening in each of your conditions by analysing the simple effects. Where you find a difference between simple effects, you have spotted an interaction! *Simple effects show the difference between any 2 conditions of 1 IV in one of the conditions of the other IV ** Simple effect analyses are equivalent to t-tests, but involve the calculation of F values, and you can get SPSS to calculate them for you, but this is v complex, so instead, use t-tests!! Simple effects= a comparison of two cell means of 1 IV, within one condition of another IV (see diag!) The more simple effects you calculate, the higher your family wise errors will be. You should therefore be selective in your simple effects calculations: Your hypothesis(prediction about how cell means will differ (based on pr...

What are the three main types of multifactorial ANOVA? Independent/BETWEEN Groups ANOVA= the analysis of unrelated designs, a design where all factors contain independent samples, Repeated Measures/WITHIN Groups ANOVA= Only related factors are involved (repeated measures or matched pairs) Mixed Design ANOVA= ANOVA analysis where both unrelated and related factors are involved

How to abbreviate factorial ANOVA designs(and how to refer to them: x factors = x Way Anova) FxF 3x3= two factors, three levels of each factor 2x3x2 ANOVA 3 factors, two levels, three levels Two way ANOVA= compares effects of two factors on 1 DV - No matter how many levels there are in each factor, we will (at most) just find a main effect for each factor, and the interaction between them Three way ANOVA= compares effects of three factors on 1 DV 

What are the benefits of using factorial ANOVA designs?  Factorial designs can test the effect of 2 or more FACTORS on 1 DV at the same time. Enables us to find out if there is an INTERACTION between the two factors! 1)Two factor design moves one step closer to reality- testing the effects of two IVs on a DV simultaneously. [Manipulation of a single IV with all other variables held constant is criticised for its extreme separation from reality- in life we are affected by several influences together at any one time]. 2) By manipulating more than one factor in an experiment, we get to see the ways in which one factor INTERACTS with another E.g. comparing effects of caffeine on driving performance, against placebo, after five hours' sleep and after none. (2X2 DESIGN) 3) Use of two factors is often demanded by the research question, but often simply convenient- two experiments in one, plus the interaction effects. E.g. Coffee on driving, sleep on driving, and interaction...