Comparing multiple means Flashcards
What can multiple comparisons of means do to the p- value?
- if we run many comparisons these possibilities combine together and inflate the possibility that we observe a false positive (test that come out as significant when its not)
What is anova?
- Tests for any possible difference between multiple groups, not a specific one
- If anova detects an overall difference then we can use multiple t-tests to find where that difference is
What is the experimental hypothesis for anova?
States there will be a difference between groups (directions can be added)
E.g. Taking a large, medium or small dose of caffeine will have different effects on short term memory
What are factors and levels in anova variability of difference
Factor = A categorical (nominal) variable
Levels = different groups within a factor
E.g if we are comparing a Large, medium or small dose we would have one factor (size) with three levels (Large medium small)
What does avona null hypothesis graph look like?
- The null hypothesis states all groups are well modelled with the same mean
- So if we draw one line through the mean of all these groups then it fits everyone
- We take a data point and compute the distance in between the overall mean and the data point (we repeat that for every single point)
We then multiply each value by itself (squaring it)
We then add this up and get = An SS total
What does avona alternative hypothesis graph look like?
- The alternative hypothesis states that we are better off modelling each group by their own means
- We can get the sum squared differences within each group and then add all these up
And this gives us = A SS within
What does an avona graph do?
splits the variability of all the separate data sets
What is SS between?
the middle of the Null and alternative avona graphs
How do you go from the split variability to a hypothesis test?
We have to take our sum squared errors (SS within & between) and turn them into Mean square errors
What is the calculation for MSE within?
(SS within) divided by (the number of participants) minus (the number of groups)
What is the calculation for MSE between?
(SS between) divided by (number of groups) minus (one)
What is an anova stat called and what is the calculation?
F = (MSE between) divided by (MSE within)
What does a large F statistic mean?
- occurs when the MSE between groups is large compared to the variability within groups
- suggests there is a substantial benefit from modelling the data with the individual group means (rejecting the null that states all the groups are well modelled with the same mean)
What are the 5 assumptions of anova?
- Independance = data observations must be unrelated
- Normal distributions
- Equality of variance
- Categorical factors = Predicting factors must be divided into separate groups
- Data type of interval or ratio
What is the non parametric alternative to anova?
Kruskall wallace test
