Extras Flashcards
What is the square of the standard deviation?
The variance
Levenes test for equality of variances is an assumption for what?
Independent samples T -test
One- way ANOVA
Should not be sig. Report the second line if it is sig.
How do you get a one tailed probability from your p value?
Divide by 2
What is the normal error term used for the standard deviation of the sampling distribution of mean difference used in a t-test called
The standard error of mean difference (SEDMest)
Square root of
Variance 1 / n1 + variance 2 /n2
Variance of the sample is used which makes this error term an estimate (population variances are rarely known)
This is used to check how likely our mean difference is under our null hypothesis
What is the pooled error term?
This is used when the sample sizes are unequal in an independent t-test.
This is because each sample is contributing differently to the estimates of the variance in the sampling distribution. So one sample may give you more information than another.
The pooled term weights the variances by the degrees of freedom
How to calculate the DF for the error term for a simple t-test
Two parameters have been estimated (variance1 and variance2)
So you subtract 2 from the total sample size
N1+N2 -2
What are the assumptions of independent samples t-test?
Population
- normally distributed
- have the same variance
Sample
- independent, no two measures are drawn from the same participant
- independent random sampling (no choosing of respondents in any kind of systematic basis)
Data (DV scores)
- at least 2 observations per sample (factor level)
Measured using a continuous scale (interval or ration)
Homogeneity of variance Levees tests (with equal sample sizes heterogeneity of variance and mild non-normality is no problem, e.g dice example)
If the groups are skewed in opposite direction can force a…
Non parametric alternative
Mann-Whitney u test : wilcoxon rank-sum test
Parametric tests are…
Calculated using an estimate of the population parameters from the samples
More restrictive, because a range of assumptions must be met? However they are generally robust to violations
In addition they are more powerful, thus we generally use a parametric test unless the assumptions are not met
What is the F ratio?
F = MS effect / MS error
MS = mean square
F ratio is a a ration of the systematic variance (i.e. Your experimental manipulation) to the unsystematic variance
If you square a t statistic what do you get?
F (1, DF)
Conventionally ANOVA is never 1-tailed so choose a t-test if you want this
When you run a one way ANOVA and you get the output table the mean square box relating to the between groups = what?
MS effect
Mean square
When you run a one way ANOVA and you get the output table the mean square box relating to the within groups = what?
MS error
Mean square
How to calculate the DF for the MS effect?
Number of groups - 1
What is the MSerror term?
It is a pooled variance term, it’s a weighted average of the k sample variances
Aka MS within as it estimates variance within groups
An estimate of the error variance within the population whether or not the null is true or false
What is MS effect?
Variance of the k sample means multiplied by N
Estimated variance among, or between means
An estimate of the population variance when the null is true
So if null is true exp. MS effect = exp. MS error and F = 1
If null is false exp. MS effect > exp. MS error and F > 1
How do you calculate the DF total for the whole ANOVA?
N - 1
N = total number of participants
How do you calculate DF effect?
K - 1
K = number of groups
How do you calculate DF error?
K (n-1)
K = number of groups N = participants in one group when group = equal
What are the extra assumptions for ANOVA?
Homogeneity of population variances (variance in each of the k populations samples is the same) - levenes test (equality of error variance, we want this to be not sig. Correcting we can you boxs test… But it’s conservative so you could also transform/trim raw data).
Robustness of above
If largest variance 30)
Independence of observations (each observation is independent of every other, we randomly sample/assign, error terms are independent)
What is an omnibus test?
Any test resulting from the preliminary partitioning of variance in ANOVA, but doesn’t tell us where the effect lies.
Why is the probability of making a type 1 error is generally higher for post hoc comparisons than a priori?
As you are usually making more comparisons
What is a type 1 error?
False positive… Find an effect that isn’t real
There are two types of type 1 error rate what are they?
Per comparison rate (alpha pc or alpha)= probability of type 1 error on and single comparisons (e.g. .05)
Familywise error rate (alpha fw) = probability of making at least 1 type 1 error in a family (or set) of comparisons.
Alpha fw = 1 - (1 - alpha pc) c (this should be the power of c)
Where c is the number comparisons made and where comparisons are assumed to be independent
Explain the familywise error rate through the example of a dice
Think of each comparison as being like rolling a fair die and imagine a type 1 error is a 6
Each comparison is one roll
What are be odds of getting a 6 on the first roll
(1/6 and 5/6 of not)
Make another roll (nb each roll is the die is independent of any other)
What are the odds now (1/6 and 5/6 the same)
So what are the odds of not getting a 6 at all over the 2 rolls
(5/6) * (5/6) = .68 or 68%
So the chance of getting at least one 6 = 32%
(Over 20 throws there is a very high chance of getting a 6 - 98% or something so this demonstrates type 1 error)
Most methods use a correction which maintains alpha familywise at p
Bonferroni correction basically evaluates t at a
More conservative level
Alpha pc = alpha/comparisons
Aka sidak or Dunn-sidak (esp. For t test)
Alpha PC = 1 - (1 - alpha) to 1/c
There are two ways to report a result that has used a bonferroni correction
Keep alpha = 0.05 as sig, level and adjust alpha PC (p sig. Level) by multiply by c
Or adjust the alpha critical 0.05 / c
This is more common but spss does the top one
Pairwise comparisons are t-test
discuss these
Just do t-test afresh on the pairs of cells of the data you want to compare
But it’s better to use to overall error term from the omnibus ANOVA as this increases power
Useful if you want to make a few specific pairwise comparisons
Assuming homogeneity of variance, use MS error from the overall ANOVA as the pooled error term and the DF error (from the whole ANOVA which will be larger) to evaluate t)
Assuming heterogeneity of variance, but equal sample sizes, use pooled error term
Or if unequal sample size use welch-satterthwaite correction (spss gives this automatically)
What are linear contrasts?
Useful if you want to know if one group or set of Groups is different from another group or set of groups
Set up weights or coefficients to set up a comparison of your groups
Coefficients have to add up to 0 in linear contrasts (0 means you are not interested in a particular group)
The linear contrast
L = sum across all the cells of the coeffient weights * the means
So you basically multiple the mean for each groups by the weight you give them
This is the tested using another formula that includes the MS error
This gives you a t statistic which then is as usual checked against the critical
What are orthogonal contrasts?
This is simply a set of linear contrasts that are each independent of one another
Nothing about the nature of a contrast should be influenced by any other contrast
So we want correlations between out contrast to be 0, so you have to look at the cross-products of each coefficients you want them to be 0
Imagine a set of 3 contrasts defined by coefficients a, b and c
Sum ab = 0 sum of a c = 0, sum b*c = 0
Add those all together = 0
Number of comparisons in set = DF effect (DF = groups -1 )
How do you check if a contrast is orthogonal
Contrast coefficients = 0
Cross products = 0
Number of contrasts = DF effect (group -1)
What is a problem with a within-subjects (repeated measures) design compared to a between subjects ANOVA?
Each participant now participates in each condition
Which violates the assumption of independence
HOWEVER
we can calculate and remove (partition) any variance due to dependence
Which reduces our error term and increases power
Why is the MS error in a between subjects design over estimated? (In a way)
Because the error term contains the individual differences variance and the error term
Is the error term in a between subjects design over estimated?
Within?
No because we can take out the between subjects effect
This makes the MS error smaller so the f ratio is bigger
What is an advantage of between subjects design?
Increase power due to a reduced error term
And less participants required as they take part in all conditions - potentially cheaper
What is the means squares?
It’s the sum of squares / degrees of freedom
How do you calculate the DF for total sums of squares for a between subjects ANOVA?
N-1
N = the total number of cells
E.g 4 participants in 3 conditions = 12 cells
How do you calculate the DF subjects for a between subjects ANOVA?
n-1
n = sample size
How do you calculate the DF for within subjects for a between subjects ANOVA?
n(K-1)
n = sample size
And K = number of group levels
How do you calculate the DFeffect for a between subjects ANOVA?
K-1
K = number of treatment levels
How do you calculate the DFerror for a between subjects ANOVA?
(n-1) (k-1)
K = number of levels n = of participants
What are the assumptions of one-way within-subjects ANOVA?
Normality
-observations are normally distributed
The error terms are normally distributed around 0
Compound symmetry:
Homogeneity of variances in levels of repeated measures factors
Homogeneity of covariances (equal correlations/covariances between pairs of levels of the factor)
Compound symmetry is a very restrictive assumption - sphericity is a related but less restrictive assumption. What test in spss tests sphericity?
Mauchlys test of sphericity
Determines whether values in the main diagonal (variances) are roughly equal, and if values in the off diagonal are roughly equal (covariances)
Evaluated as chi square with DF = k-1. If sig.
Assumption is violated.
K= number of levels of repeated factors
How can you correct for violations of sphericity?
Boxs adjustment
Gives us a more stringent critical value but it’s usually too conservative
Epsilon adjustment this is for the lower bound
Epsilon is simply a value by which the degrees of freedom for the test of F-ration is multiplied. You basically multiply you DF with
1/(K-1)
K = the number of repeated measures factor
Equal to 1 when sphericity assumption is met (hence no adjustment, and
How important is the violation of sphericity?
In between subjects design it don’t matter because treatments are unrelated (note the assumptions of homogeneity of variance still holds)
When within-subjects factors have two levels it ain’t a problem as only one covariance is being estimated it can’t be heterogenous as there isn’t anything to compare to)
When it does matter
In all other within-subjects design
When the sphericity assumption is violated, F rations are positively biased
(Liberal F test & so Probability of type 1 error increases)
Pooling error term is recommended for between subjects designs where possible, is this recommended for between subjects ANOVA?
(Pooled across all of the levels because this gives us a higher DF, better estimation and more power - unless heterogeneity of variance as the errors wouldn’t be similar enough)
No you use the error term associated with just what you are looking at
What are some disadvantages of within subjects designs
Restrictive statistical assumptions (sphericity)
Sequencing effects: learning, practice, fatigue, habituation
Counterbalance to reduce sequencing effect
What is a two-way design?
Two factors (discreet iv)
Each factor has 2 or more levels (male, female)
One way design vs two designs what are the research questions?
One-way design: are the means of the population (of DV scores) corresponding to the factor difference?
Two-way design
Is there a main effect of factor 1?
Is there a main effect of factor 2?
Is there a factor 1 X factor 2 interaction
List the three types of two-way designs?
Two-way between subjects design
2 between subjects factors
Two-way within-subjects design
1 between
Mixed design (or split-plot designs) 1 within and 1 between
Why bother with two-way designs?
Fewer participants required
Allows us to examine INTERACTIONS
Does the effect of one factor depends on levels of the other factor
The generalisability of results can be assessed - is the difference described by a main effect the same over levels of another factors?
What are the marginal means?
It’s the cell means for one factor ignoring the other.
E.g. Means for males and females ignoring profession
Or profession ignoring the effect of gender
In a two-way ANOVA what is different for the MS effect?
There are MSeffect for each effect
MSa - first main effect
MSb - second main effect
MSab -interaction
nB
F = MS effect / MS error
If you get a significant interaction in a two-way ANOVA how can you understand it?
Sig. Interactions should be supplemented by graphs and analysing ‘simple main effects’
- simple main effects describe differences among cell means within a row or column, or the effects of one factor at each level of the other factor
- just like a series of one-way ANOVA conducted at each level of a factor, except the pooled error term is used (MS error)
If you don’t look at the normal 3 main effects of a two-way ANOVA and instead run simple main effects of contrasts on no more than 3 different comparisons so you need to protect your analysis from type 1 error rate inflation?
No
More than 3 comparisons and you would need to, but remember to keep to as few as possible
What is your acronym for remembering the steps in data cleaning?
Mysterious Octopi Near Leicester Have Measles
Missing data Outliers Normality Linearity Homoscedasticity Multicollinearity
There are three types of missing data what are they and how problematic are they?
Missing completely at random (MCAR)
- best possible solution, should not be a problem if relatively small loss (
How do you deal with univariate outliers?
Standardise variables and look at absolute values above z> 3.29
- use histograms and box plots
How do you test for multivariate outliers
Mahalanobis distance (the distance of a case from the centroid - centroid is the intersection of the variable means).
MD is tested using the chi square distribution and usually conservative alpha p
What is the assumption of normality?
Is the assumption that each variable, and all linear combinations of the variable and normally distributed.
Skewness 7
Skewness is the degree of symmetry in the distribution
Kurtosis is the peaked was or flatness
Of the distribution
Check the normal probability plot or histograms
Transform
Windsorised/trim
What is the assumption of linearity?
That variables have linear (straight line) relationships with each other
Can assess using bivariate scatter plots
What is the assumption of homoscedasticity?
Is the assumption that variance in scores for one continuous variable is roughly the same at all levels of another continuous variable
For grouped data, the homogeneity of variance assumption: variability in DV expected to be similar across all levels of the discreet iv
For grouped data use the levenes test
For ungrouped data can inspect the bivariate scatter plots, heteroscadasticity us caused by nonnormality in one or both of the variables
Test usually robust to some heteroscadasticity
What is multicollinearity?
Is a problem that occurs in a correlation matrix when variables are too highly related to each other (e.g. > .90).
What are the problems with multicollinearity?
Conceptually, it indicates redundancy in the variables. Either remove or combine relevant variables
Statistically it can result in unstable matrix inversion, which can cause large standard errors or problems in solution convergence
