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
Relative risk (RR) is the risk of an event (or of developing a disease) relative to exposure
Relative risk is a ratio of the probability of the event occurring in the exposed group versus a non-exposed group
- If relative risk =1, the risk of event under study is equal to the comparison event
- If relative risk >1, the risk of the event is more likely
- An odds ratio < 1 indicates that the condition or event is less likely to occur in the first group
Definition - Ratio of the odds of an event occurring in one group to the odds of it occurring in another group
The odds of an event occurring is the ratio of the probability of its occurrence (p) divided by the probability of non-occurrence (1-p)
- If an odds ratio =1, the condition or event under study is equally likely to occur in both groups
- If an odds ratio >1, the condition or event is more likely to occur in the first group
- An odds ratio < 1 indicates that the condition or event is less likely to occur in the first group
To have significantly higher or lower odds of something occurring, the 95% confidence interval cannot overlap 1
What are the 5 traditions of qualitative inquiry?
What are the purpose(s) of biography?
–Study of an individual and his/her experiences
–“Studied use and collection of the life documents that describe turning-point moments in an individual’s life”
–Interpretative biography – done from a particular perspective
What are the different forms of biography?
–Biographical study – life story written by someone else
–Autobiography – life story written by themselves
–Life History –individual’s life & how it reflect cultural themes of society, personal themes, institutional themes told by the individual but supported by other evidence
–Oral History – telling events through personal recollections supported by documents
What are the procedural steps in biography?
–Begin – objective facts of life – noting chronologic, course of life path
–Next – gathering stories which expand upon the basic facts
–Organizing around themes or pivotal events
–Exploration of further meaning form stories in context of the organizational principle
–Explain historical context, social events, ideologies, cultural issues and placing life stories into these contexts
–Example - James Madison by Richard Brookhiser begins in 1814 during the War 1812 with the attack on Washington. DC by British to illustrate characteristics of Madison that he then ties back through other phases of Madison’s life
What are the challenges of doing a biographical study?
–Need to collect extensive information about subject
–Must have clear understanding of the context to position subject correctly in larger milieu
–Get the right slant to develop a multilayered life
–Bring personal perspective into the story but clearly define & acknowledge those personal viewpoints
What are the approaches to a biography?
–Objective – little interpretation
–Scholarly – interpretative within larger context of history
–Artistic – tell good story & may include fictionalized accounts of scenes to illustrate life & may be a fictionalized biography – based upon the life of Michelangelo (“Agony & the Ecstacy” by Irwin Stone)
–Classical VS interpretative
•Classical review materials, develop hypotheses from the perspective of the author
•Interpretive – using materials creatively including transforming writings into thoughts/conversations expanding upon the personal insights of the author – great deal of latitude
What are the purpose(s) of a phenomenological study?
–Describe the meaning of the “lived experience” from several individuals standpoint about the concept of phenomenon being described
–Search for the essential, invariant structure or essence or central underlying meaning
–Taking basic statements and reducing them to themes
What are the 4 principles that link subject and object in phenomenological studies?
Intentionality of Consciousness
- Reality of the object is related to one’s consciousness of it
- No separation of subject and object but
- Exploring the nature of the object from the perspective of the viewer
- Reality of the object stems solely from the experience of that object by the individuals’ perceptions – REALITY IS WHAT IS EXPERIENCED
-Suspension of all preconceived notions about what is real
-Expression of findings as conceptual not empirical (perception not evidence)
What are the procedural steps in a phenomenological study?
Research must understand the philosophical perspectives behind the approach – particularly how people experience the object removing all preconceptions
Investigator writes the research question to frame the way she/he will explore the meaning of the phenomenon through the lived experiences of the participants
–Data collected through prolonged interview and self reflection with a small number of informants (5-25)
–Data is divided into related statements
–Clusters of meaning are then derived from these statements to derive what was experienced (textural description) and how it was experienced (structural description)
–Write up this analysis so the reader can understand the essential, invariant structure or meaning of the experience
What are the challenges of doing a phenomenological study?
–Researcher must be solidly grounded in principles of phenomenological research
–Finding participants who have experienced the phenomenon
–Bracketing out personal experiences about the phenomenon under study
–Research must decide how her/his experiences may have entered in the analysis and explain that interference
What are the purpose(s) of a grounded theory study?
–Phenomenonology explores meaning of experience to participants
–Grounded theory attempts to generate an abstract analytical schema about how individual will react , interact or take action based upon the phenomenon being studied
–Statement of plausible relationship among concepts or between concepts in the form of a narrative statement, visual picture or series of hypotheses/propositions
What is the basic methodological approach to grounded theory studies?
–20-30 interviews based upon several visits to the field and saturate (collect data until no more can be found) the categories (events, occurrences)
–Begin analysis as data is being collected in “zig-zag” pattern between collecting and analyzing data in a constant comparative manner
–Participants are selected to optimize the data collection process
What are the procedural steps of data analysis in grounded theory studies including the different types of coding?
- Forms initial categories as data is being collected and segmenting information
- Within each category – properties or subcategories are ID & used to dimensionalize or show a continuum of properties
- New ways of assembly of information after open coding
- Uses coding or logic diagram to identify the entire phenomenon
- Explores causal conditions – categories of conditions that influence the phenomenon under investigation
- Explores strategies or actions/interactions that result from the central phenomenon
- Intervening conditions - the narrow and broad conditions that influence the strategies
- Delineates consequences – outcomes of the strategies
- Integrates the categories along a “story line” developed from the data analysis
- At this point conditional hypotheses – propositions – are presented
- Elucidates, visually portrays other factors that may be influencing the central phenomenon
- This may not be part of traditional grounded theory
Result is the substantive-level theory which the researchers which can be later empirically tested (This will be verbatim on exam!)