Assumptions and MAGIC Flashcards
What are the key assumptions underlying ANOVA and t-test?
Normality
Homogeneity of variance
Independence of observations
________ are often responsible for violations of normality and homogeneity of variance
Outliers
How do we evaluate normality?
Statistical tests
- Kolmogorov-Smirnov test and Shapiro-Wilk test
Descriptive statistics
- Skew
- Kurtosis
Graphical displays
- q-q plot
What is the role of sample size when testing assumption of normality?
When sample size is very small, power is low, which means that if we have violations of normality, the statistical test will fail to detect!
If data are normal, describe what a q-q plot would look like?
The scatterplot dots would be clustered together in a straight line
Skew that is equal to or greater than absolute value of 2 means what?
non-normality
Kurtosis equal to or greater than absolute value of 7 means what?
non-normality
Assumption of normality
Scores on the DV within each group are assumed to be sampled from a normal distribution
Null hypothesis: no difference from distribution of your data and normal distribution of data
Assumption of homogeneity of variance
The variance in scores on the DV within each group are the same across groups
Null hypothesis: variances are identical between groups
Assumption of independence of observations
Each observation (or set of scores) is contributed by someone totally independent of another
3 examples of common outliers
- Data entry/coding errors
- Response latency data
- Open-ended estimate data
What is the logic of standardized residuals? What distribution do they follow?
These residuals are scores that represent the magnitude of deviation from the mean of your sample
These scores follow a normal z distribution
What is the logic of studentized deleted residuals? What distribution do they follow?
Logic is the same as standardized residuals.
These scores follow a t distribution with a df of n-2
What are the 4 levels of measurement that a DV can have?
Nominal, ordinal, interval, or ratio
Nominal level of measurement
Assignment of numbers reflects categorical distinctions (i.e., nationality, gender, etc.)
Ordinal level of measurement
Assignment of numbers reflects rank ordering but magnitude between values is not interpretable (i.e., What are your top 5 dessert foods)
Interval level of measurement
Assignment of numbers reflects rank ordering and magnitude between values is interpretable (i.e., celsius scale, mark grading)
Ratio level of measurement
Assignment of numbers reflects rank ordering, magnitude between values, and ratio of difference. Meaningful zero point and no negative numbers (i.e., Kelvin temperature scale)
It has been argued that t-tests and ANOVA are only meaningful when DV has at least ________ properties
interval
