Week 5 MANOVA From Laerd Website Flashcards
From Laerd website
In what way is MANOVA an extension of ANOVA?
MANOVA is an extension of the one-way ANOVA that incorporates two or more dependent variables rather than just the one dependent variable
How is MANOVA different to ANOVA?
ANOVA tests for differences in mean values between groups whereas MANOVA tests for the ‘linear composite’ or vector of the means between groups
What is MANOVA, in essence?
Essentially, MANOVA combines the dependent variables to form a ‘new’ dependent variable in such a way as to maximize the differences between the groups of the independent variable. It is between this new, composite variable that you test for statistically significant differences between the groups.
What is required to run a MANOVA?
One independent Variable that is categorical (2 or more groups - e.g. Transport type: bus, train, tram, pedestrian, car)
2 or more dependent variables that are continuous (e.g. satisfaction score, motivation score)
What are the seven assumptions of MANOVA?
- independence of observation
- adequate sample size
- no univariate or multivariate outliers
- multivariate normality
- Linear relationship
- Homogeneity of the variance-covariance matrix
- no Multicolinearity
MANOVA assumption 1 is independence of observations. What does this mean?
Independence of observations means there is no relationship between the observations in each group or between the groups themselves.
e.g. there must be different participants in each group with no participant being in more than one group. This is more of a study design issue than something you can test for, but it is an important assumption of the one-way MANOVA.
MANOVA assumption 2 is adequate sample size. What does this mean?
Although the larger your sample size, the better; for MANOVA, you need to have more cases in each group than the number of dependent variables you are analysing.
MANOVA assumption 3 is no univariate or multivariate outliers. What does this mean?
There can be no (univariate) outliers in each group of the independent variable for any of the dependent variables. This is a similar assumption to the one-way ANOVA, but for each dependent variable that you have in your MANOVA analysis. Multivariate outliers are cases which have an unusual combination of scores on the dependent variables.
MANOVA assumption 4 is multivariate normality. What does this mean & how can we test it?
This is an assumption that cannot be directly tested in SPSS. Instead, the normality in each group of the independent variable for each dependent variable is assessed.
MANOVA assumption 4 cannot be tested directly in SPSS, so how do we test this assumption?
normality of each of the dependent variables for each of the groups of the independent variable is often used in its place as a best ‘guess’ as to whether there is multivariate normality.
i. e. If there is multivariate normality, there will be normally distributed data (residuals) for each of the groups of the independent variable for all the dependent variables. However, the opposite is not true; normally distributed group residuals do not guarantee multivariate normality.
So, how do we test for Normality?
- Q-Q Plots if large sample size
- Shapiro-Wilk if smaller sample size & not confident interpreting Q-Q Plots
- Greater is good - sig of greater than .05 means normality assumption is met
What do I do if my normality assumption is violated?
You can transform the DV(s) so that, hopefully, your transformed DV(s) is normally distributed.
If a DV is not normally distributed for any particular category of the IV(s), the DV needs to be transformed for all groups. You cannot just transform the data for one particular group without transforming the data of all the other groups (i.e., you have to transform every value of the DV).
How do I transform my data if it is Positively skewed?
- Moderately positively skewed data = Square root transformation
- Strongly positively skewed = logarithmic transformation
- Extreme Positively Skewed = Inverse or reciprocal transformation
How do I transform my data if it is Negatively skewed?
- Moderately negatively skewed data = reflect & square root transformation
- Strongly negatively skewed = reflect & logarithmic transformation
- Extreme Negatively skewed = Reflect and Inverse Transformation
MANOVA assumption 5 is Linear relationship. What does this mean & how can we test it?
There is a linear relationship between the dv(s) for each group of the iv. If the relationship is not linear, it can lead to a loss of power to detect differences. This assumption can be tested with scatterplot matrices.
MANOVA assumption 6 is Homogeneity of the variance-covariance matrix. How do we test this assumption?
Homogeneity of variance-covariance matrices can be tested using Box’s M test of equality of covariance
MANOVA assumption 7 is no Multicollinearity. How do we test this assumption?
One of the most straightforward is to run correlations between the dependent variables to see if there are any relationships that are too strongly correlated.
Okay, so my data has multicollinearity, what do I do?
- Remove one of the DVs that is highly correlated
* This is the normal thing to do - Combine the scores to achieve a new DV that is a combination of the 2 (often requires using PCA & is tricky)
What do I do if I find my data violates the assumption of linearity?
- Transform one or more DV
- Remove the offending DV
- Run the analysis anyway and expect a loss of power
What do I do if I find I have outliers?
- check whether I have made any data entry errors (i.e., simply keyed in any wrong values into SPSS). If any of your outliers are due to data entry errors, replace them with the correct values & re-run the tests of assumptions.
* Any new values entered could still result in the outlier remaining an outlier, or could lead to other data points now being classified as outliers!
Okay, I have checked for Data Errors and still have outliers, now what?
- consider whether they are measurement errors (e.g., equipment malfunction or out-of-range values).
- Treatment of Measurement errors: an out-of-range value can be replaced with the largest valid value (i.e. if scale goes to 100, then a value of 100) it is better than loosing the data
Okay, I have established no data errors and no measurement errors, I still have outliers, now what?
These are genuine data points: options:
- keep the outlier
- remove the outlier
How do I decide whether to keep or remove the outliers?
Removing the outlier requires providing information about that data point so that a reader can make an informed opinion about why you removed it and how it might have affected your results. It can also help dispel any accusations that you might have removed a data point just to make your results look better.
Okay, so I want to keep the outliers, what do I do?
Keeping 3 choices:
1. modify the outlier by replacing the outlier’s value with one that is less extreme (e.g., it is common to use the next most extreme value that is not an outlier or a value slightly larger, in order to maintain the order of values);
2. transform the affected DV(s)
3. include the outlier in the analysis anyway, as you do not believe the outlier(s) will materially affect the result.
With respect to point two (2), transformation can be an option as it can lead to outliers being disproportionately affected (“reduced in size”) so that they are no longer classified as outliers. However, transformations are usually not warranted unless your data is not normally distributed.
