Lecture 5 - Statistical Power Flashcards
What are three examples of post-hoc tests?
Tukey hsd
T test
Scheffé
What does hsd stand for? As in tukey hsd test
Honestly significant difference
What does the tukey hsd test do
It establishes the smallest possible difference between two means
It uses a critical difference value. This comes from a fancy equation.
Any mean difference greater than the critical difference is significant.
How can a t test be used as a post hoc test?
It is modified - t is given by 0.05/c where c is the number of comparisons being made.
This is called a bonferroni correction
What do post hoc tests mean for error rates?
They’re conservative, which means they reduce the chance of type one errors but greatly increase the chance of a type two error
This means we can be very confident when we do find an effect
But it does mean null results are hard to interpret. There may still be an effect but we just can’t find it. (Low power??)
What are the four assumptions of the f ratio
Independence of numerator and denominator
Random sampling
Homogeneity of variance
Normality (normally distributed populations)
How can we test the assumptions of an ANOVA?
Independence and random sampling are down to the experimenter so we assume they’ve been met
But we can test homogeneity of variance and normality
How can we test for homogeneity of variance?
In a between groups design:
Hartley’s F-Max
Bartlett
Cochran’s C
Within or mixed designs:
Box’s M
How would you do Box’s M by hand?
You’d do (largest variance/smaller variance)
What are the three most common tests of normality and how do they work?
Skew
Lilliefors
Shapiro-Wilks
(The bottom two are very hard to do by hand but SPSS has them)
They compare the actual distribution of data to a model of normal distribution
They are all pretty sensitive, and more so with large samples
How do we test skew?
We can test if the skew is significantly different from 0. If everything was perfectly normally distributed skew would be 0.
We use a z-score distribution to do this
If the z score is greater than + or - 1.96 then the sample is significantly different than a normal distribution
What is a transformation and why would we use one?
Mathematical operations that we can apply to the data before we conduct an ANOVA
we use them if we don’t meet the assumptions of an ANOVA but we really want to perform one
What are the three circumstances where no transformations will make the data fit the ANOVA assumptions
Heterogenous (different) variances
Heterogenous distributions
Both of the above
What is defined as moderate, substantial and severe skew?
Moderate - 1.96-2.33
Substantial - 2.34-2.56
Severe - 2.56 and above
What transformation would you use for moderate positive skew
Square root
What transformation would you use for moderate negative skew
Square root (K-X)
In a transformation what is K?
The largest number in the data plus one
What transformation would you use for substantial positive skew
Logarithm
What transformation would you use for substantial negative skew
Logarithm (K-X)
What transformation would you use for severe positive skew
Reciprocal
What transformation would you use for severe negative skew?
Reciprocal (K-X)
How does transforming the data affect error chances?
Increases type one error rate but decreases type two error rate
What do we do if we can’t transform the data? (Eg those three situations)
We proceed with analysis but we take care to caution the reader when we are interpreting the results.
What should you say instead of saying you can accept H0?
You must say you ‘fail to reject the null hypothesis’ it sounds much better and is more accurate!
