Univariate
1+ IVs
1 DV
Factorial
2+ IVs
1 DV
Bivariate
2 variables, neither identified as IDV or DV (no distinction)
Multivariate
1+ IVs
More than one DVs
Types of Descriptive Statistics
Measures of Central Tendency (mean, median, mode)
Measures of Variability (Range, Variance, SD)
Measure of Relative Position
Measures of Relationship
Standard Deviation Defintion
Square root of the variance
Variance
Average of squared deviation scores
Null Hypothesis
No TRUE difference in the poplution
There is no true difference between groups
Research/Alternate Hypothesis
There is a TRUE difference in the population
There is a true difference between the groups
Where does the decision for Type 1 and Type 2 error comes from?
SPSS output
Type 1 Error
A type 1 error occurs when you reject the null when the null is true because significance was found when there should not be
Type II Error
A type 2 error occurs when you accept the null when the null is false because no significance was found when there should be.
Effect Size
The size of the treatment the researcher wishes to detect with respect a given level of power.
Eta squared
Assumption
A condition that must be met in order to validly carry out an analysis
Four Purposes to Screen Data
Accuracy, Missing data, Outliers, Fit
3 Methods for dealing with Missing Data
Use prior knowledge (research)/well educated guess
Replace missing values with mean score (reduced variance)
Regression Approach
If you use any of these, consider repeating the analysis using only complete cases
Outliers
Cases with unusual or extreme values at both ends of a sample distribution.
Distort statistical tests
How to find:
Small data set:
Inspect visually - frequency distribution or histogram
Graphical Methods: Box plots, stem & leaf
Statistical Methods: Z scor
Robust(ness)
The degree to which a statistical test is appropriate to apply when some if its assumptions are not met
Assumptions of MULTIvariate analyses
Normality
Linearity
Homoscedasticity
Normality
Normal sample distribution
Skewness & Kurtosis - a distribution is normal when both are equal to 0
Histograms, Q-Q Plots
Multivariate Normality: extent to which all observations in the sample for all combinations of variables are distributed normally
Skewness
The degree to which there is symmetry about the mean
Positive skew (Right Skew)
Cluster of cases to the left
Skewness value of greater than 0
Floor Effect: scores pile up at the lower end of the distribution because it is not possible to have a lower score
Negative skew (Left Skew)
Cluster of cases to the right
Skewness value of less than 0
Ceiling effect: scores pile up at the right side of the distribution because it is not possible to have a higher score
Kolmogorov-Smirnov
Test the null hypothesis that the population is normally distributed
Significance indicates the variable is not normally distributed
Homoscedasticity
The assumption that the variability in scores for one continuous variable is roughly the same at all values of another continuous variable
Analogous to the univariate assumption of homogeneity of variance (Levene's test)
If two variables are normal, they
Marginal Means
Used to determine the main effect
Univariate Analyses of Variance (ANOVA)
Hypothesis testing procedure that evaluates the mean differences on the DV between 2 or more conditions/groups/factors
Decisiono based on F test
One-Way ANOVA
1 categorical IV (2or more levels/groups), 1 continuous DV
Difference between T-test and One-way ANOVA
Both have one categorical IV, both have one continuous DV
One-way ANOVA IV has 2 or more levels/groups whereas T-test has 2 groups of the IV
T-test
1 categorical IV with 2 groups and 1 continuous DV
Post hoc
When you need to find where the differences are between groups
Multiple comparisons
Pairwise comparisons
Purpose: controls for type 1 error
ONLY USED WHEN IV HAS 3 OR MORE GROUPS/LEVELS
Run when overal F test is significant on the DV however, you can have
Pairwise Comparison
Compare two conditions/treatments at a time a priori
Researcher decides prior to analysis which analysis/comparison they will make