Exam 3 Flashcards
Why use Analysis of Variance? (ANOVA)
Compares more than two groups: Designed for multi-level or multifactor designs
Similar comparison of within group and between group variability
Can be applied to independent groups or repeated measures
F Statistic is the key result; ANOVA yields a number; go to the F table and find the critical value; if the statistic ran is greater than the critical value, there is a positive change; a negative number is a negative change
Describe the characteristics of the One-way ANOVA for independent Measures
For comparison of 3 or more levels of the independent variable; groups do not have a relationship
- Null hypothesis is that all 3 or more means are not different
- Experimental (Alternative) hypothesis is that at least two are different
Comparison of individual scores for each subject in the group compared to the mean of the group
Comparison of individual scores to group mean
Difference of individual scores from group mean squared and summed – sum of squares
Larger the sum of squares the greater the variability within the group
Partitioning of sum of squares -Between-group sum of squares – intervention effect + error -Within-group sum of squares – error Degrees of Freedom -n-1 -Between groups - # groups-1 -Within groups - total # of subjects in all groups -1 Mean Square - Divide sum of squares by degrees of freedom (df) F-value – divide between groups by within group mean square values
Describe the factors (variables) of the ANOVA table for One-way ANOVA for independent Measures
Sigificance level – p-value found from a table of F-value at appropriate df (n -1; number of independent variables minus one) Add Photo
Describe the characteristics of the Two-way ANOVA for independent Measures
Compare multiple factors or interventions
Main effects: -What is the effect of one factor, independent of the other factor
-Interaction effect: What is the effect of interaction between the two factors?
Basically two groups; asks the question, did the intervention help or not?
Describe the factors (variables) of the ANOVA table for Two-way ANOVA for independent Measures
Study -3 types of muscle stretching (df=2) at 2 joint positions (df=1) on joint range of motion (ROM) in 55 subjects
- Sum of squares (SS), Mean square (MS) calculated as before for stretch, position & interaction between stretch & position
- F value for stretch, position & interaction between stretch & position by dividing MS by within group MS (error)
- Significant difference between different stretching techniques (p < 0.001) but not between different positions ( p = 0.694)
- Significant interaction between different stretching techniques and joint positions (p < 0.001) so the effect of stretching depended upon the joint position
- So although position did not have a main effect on it own, position could influence the main effect of stretching
Describe the factors (variables) of the ANOVA for Repeated Measures for Mixed Designs
Study RCT with effect of 6 weeks of stretching on ROM
- Two stretching groups and control (df=2)
- Pre-post repeated measures (df=1)
- Significant difference between groups (p=0.0012) and pre-post (p=0.0001)
- And significant interaction between groups & time (p=0.0111)
- Pre/Post difference depended upon which group subjects were in
What is the purpose for individual pairwise comparisons and what used to make them?
Now that a significant difference has been determined – can do individual pair-wise (same as paired or matched) comparisons
Can use individual T-tests (paired or unpaired where appropriate) to compare individual comparisons to determine where the differences seen in the ANOVA are
What is the Analysis of co-variance (ANCOVA) used for?
- a general linear model which blends ANOVA and regression.
ANCOVA evaluates whether population means of a dependent variable (DV) are equal across levels of a categorical independent variable (IV) often called a treatment, while statistically controlling for the effects of other continuous variables that are not of primary interest, known as covariates (CV) or nuisance variables.
What is the multivariate analysis of variance (MANOVA) used for?
Step above ANOVA
is a statistical test procedure for comparing multivariate (population) means of several groups. As a multivariate procedure, it is used when there are two or more dependent variables, although statistical reports provide individual p-values for each dependent variable in order to test for statistical significance.
It helps to answer:
- Do changes in the independent variable(s) have significant effects on the dependent variables?
- What are the relationships between the dependent variables?
- What are the relationships between the independent variables?
What is the rationale for using parametric and non-parametric statistics?
- When data not normally distributed (there is not a homogeneity of variance within or between groups)
- Small sample sizes where the sample’s distribution may not reflect that of the population
- Use of nominal and ordinal level data which are likely not to be normally distributed
What are the parametric statistics?
Two Independent Groups:
- Unpaired t-test/Mann-Whitney U test
Two Related Scores (Same Individual):
- Paired t-test/Wilcoxon Signed-Ranks test
3+ Independent groups:
- 1-Way ANOVA/Kruskal-Wallis ANOVA by Ranks
3+ Related Scores:
- 1-Way Repeated Measures ANOVA/Friedman 2-Way ANOVA
What is correlation?
- Correlations can determine relationship but not cause and effect
- Often correlations have a restricted range of values – out of that range correlations vary
- Previously looked at tests of group difference – asking the question is group A different from group B?
•Correlation tests ask
–Is there a relationship between two variables?
–What is the degree & direction of this relationship?
–Is the relationship significant or due to chance alone?
What are correlation coefficients and how do you interpret the results?
•Correlation coefficients denoted by “r” give the degree & direction of the relationship
–r = 0 is no relationship –r = 1 is perfect direct relationship –r = -1 is perfect inverse relationship
What tests are used for different forms of data?
•Pearson Product Moment
–Correlation based upon covariance – large values of one group associated with large values of other & visa versa
–Used with metric level data – those that meeting parametric testing standards
•Spearman Rank Correlation
–Used with ordinal level data
•With dichotomous relationships – Phi coefficient & biserial point correlation
Effect Size Calculation
The true magnitude of the effect of an intervention is related: -Not only to the change in means -But also related to the variability of the groups around those means
Statistical significance only looks at the probability that two groups are different, not how much difference exists. (This is the difference between statistical significance and clinical significance)
Effect size was developed to assess the magnitude of differences between groups; Mean difference & SD can be used only if there is a normal distribution
Cohen defined effect size (d) as the difference between the means variability of the groups around the mean, M1 - M2, divided by the standard deviation (SD) of either group
**Effect sizes are generally defined as: -Small (d ≤ 0.2) -Medium (d = 0.2-0.8) -Large (d ≥ 0.8)* **
Effect sizes also represent: -Relative overlap between distributions -Relative percentile of the mean of one group compared to the distribution of the other group