Week 5 (Correlation, Nonparametric tests, Nonparametric Analysis for Relationships/Associations) Flashcards
Factors are seen as what in exploratory and observational research?
Exposures
Conditions are seen as what in exploratory and observational research?
Outcome
Longitudinal studies are studies that are…
overtime
What are the 2 types of longitudinal studies?
Prospective and retrospective
prospective longitudinal studies
into the future
Retrospective longitudinal studies
into the past
Cross-sectional studies are studies that are…
a “snapshot”
Correlation can be shown using…
scatter plots, pairs of scores
How do you know the strength of the correlation?
values between -1.0 and 1
- “0” is no relationship
- 1.0 = perfect positive relationship
- -1.0 = perfect negative relationship
what does the ‘sign’ imply on the correlation?
sign implies direction of the relationship
Assumptions of correlation
- scores represent the underlying population
- scores are normally distributed
- each subject has a score for both X and Y
- X and Y are independent measures
- X and Y are observed, not controlled
- relationship between X and Y is linear
Correlation coefficient: <= .25
little or no relationship
Correlation coefficient: .25 to .50
low to fair
Correlation coefficient: .50 to .75
moderate to good
Correlation coefficient: >= .75
strong relationship
limitations of correlations
- relationship between 2 variables only
- only quantifies linear relationships
- does not tell us “cause and effect”
- does not account for agreement
- range of observations
Coefficient of Determination (r^2)
- coefficient of determination
-“the percent of variance in y that is explained by x”
the coefficient is very sensitive to…
sample size
Small effect size for r
r = .10
medium effect size for r
r = .30
large effect size for r
r = .50
non-parametric statistics are based on:
- comparisons of ranks of scores
- comparisons of counts (yes/no) or “signs” of scores
data can be “collapsed” from Ratio to…
ordinal/nominal
advantages of nonparametric methods
- appropriate for a wide range of situations
- can use with categorical data
- simple computations
- outliers have LESS effect
Disadvantages of Nonparametric Methods
- they waste information
- less power (65-95%; increase sample size)
- if outliers are not errors, effects may be underestimated
nonparametric test for: 2 independent groups
- Mann-Whitney U (BEST)
- wilcoxon rank sum test
nonparametric test for: >= 3 independent groups
Kruskal-Wallis ANOVA by ranks
nonparametric test for: two related samples
- Sign test
- Wilcoxon Signed-ranks test**
nonparametric test for: >=3 related samples
Friedman two-way ANOVA
Non-parametric analog of Pearson r
- 1 continuous, 1 ordinal variable
- 2 ordinal variables
- non-normal distribution of ratio/interval data
Chi-square (x^2)
- measures association between 2 categorical variables
- tests the difference between observed frequencies (O) and frequencies expected by chance (E)
what are the 2 types of Chi-square (x^2)
goodness of fit
tests of independence (association)
what is goodness of fit?
- coin flip
- compare observed frequencies of 1 variable to uniform frequencies of another
- with enough tests will end up being 50/50
what is tests of independence (association)?
- much more common
- compare observed frequencies from 1 variable to observed frequencies of another variable
- ex: male or female?
assumptions of chi-square
- frequencies represent individual counts
- categories are exhaustive and mutually exclusive
- no subject is represented twice
Most common application of chi-square is…
test of independence
