statistical analysis of differences

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non parametric tests

1. a test that does not require the population's distribution to be characterized by certain parameters 2. requires rankings and/or frequencies

what is ANOVA?

1. analysis of variance 2. total variance = between group + within group variance 3. it is a test (F-test) that only tells you at least TWO groups differ, but not which ones differ

parametric tests

1. assumptions are made about the distribution of the population values 2. use mean, SD, etc 3. assume samples are from a normally-distributed population ex. t-test, ANOVA

one-way ANOVA with repeated measures

1. assumptions based on the difference score 2. if significant, run paired t test as post hoc (with bonferroni adjustment)

critical values of t-score

1. critical t score value - harder to reach significance 2. SD value - easier to get a big t score pros overpower the cons when using a paired t test (dependent)

interpretation of statistical results in factorial design?

1. is there a significant interaction? 2. if no interaction, check if the main effect of any IV is significant -if yes, perform proper post hoc pairwise comparison for the significant IV by combining data of all levels of the other IV 3. if there is a significant interaction? main effect of any IV is useless -perform proper post hoc analyses to examine the "simple main effects" (to examine the effect of IV1 for each level of IV2 separately)

why are parametric tests preferred if possible?

1. more powerful if normality assumption holds 2. can refer to the collected data when interpreting the results

nonparametric tests

1. no assumptions about the distribution of the population 2. use rank/frequency ex. Mann-Whitney, Kruskal-Wallis, etc

2 -way clinic-by-intervention

1. no interaction 2. IV1 main effect 3. IV2 main effect

requiring rankings and frequencies

1. nominal and ordinal 2. interval and ratio can be converted (via ranking)

two types of statistical tests

1. parametric 2. nonparametric

differences between two independent groups

1. parametric - independent t test 2. non parametric - mann-whitney and chi-square

differences among 3 or more dependent groups

1. parametric - one-way ANOVA with repeated measures 2. non parametric - friedman's ANOVA or mcnemar test

differences between two dependent groups

1. parametric - paired t test 2. non parametric - wilcoxon signed rank test and mcnemar test

differences between 3 or more independent groups

1. parametric tests - one way ANOVA 2. non parametric tests - kruskal-wallis test (if significant, run Mann-whitney with bonferroni adjustment) and chi-square

level of measurement

1. parametric tests require data for which means and SD can be calculated 2. interval and ratio data (maybe ordinal but not recommended) - no nominal data

parametric test assumptions

1. sample data are normally-distributed 2. homogeneity of variance 3. level of measurement

friedman's ANOVA

1. the statistic is run on the ranks of the difference scores 2. if significant, run wilcoxon post hoc (with bonferroni adjustment)

if more than 1 IV....

2-way, 3-way ANOVA etc

mann-whitney test

for 2 independent samples

wilcoxon

for 2 paired samples

chi-square test of association

for nominal data: to compare the difference in # of subjects achieving a goal

types of dependent data

identical twins, left vs right limb of same person, intervention 1 vs intervention 2 by the same person

a significant ANOVA?

indicates there are differences among the groups

shape in non parametric

is skewed, unequal variances, etc

disadvantage of dependent

loss of DF (degree of freedom) to a higher statistical threshold score

slides 32-34

main effect and interaction

commonly used non parametric tests

mann-whitney test, kruskal-wallis, wilcoxon

kruskal-wallis

more than two groups

if normality does not hold or for ordinal data...

non parametric tests are more appropriate

one way ANOVA

one way means only 1 independent variable (IV); can be many levels though

paired t test

or dependent t test 1. CHECK the difference score (one score minus the other) not the raw score alternative hypothesis

example of dependent samples

outcome of the same patients at 3 weeks, 6 weeks, and 6 months after surgery

example of independent samples

patient outcome in clinic 1 vs clinic 3

advantage of dependent

reduce data variability (SD of the difference instead of all raw data)

what to do when the data are not normal?

run a nonparametric test (transform the data to make them more normally distributed) - try square root, square, etc

what to do if homogeneity of variance is violated?

run nonparametric tests

factorial design

N-way ANOVA (repeated measure or not)

independent t test

alternative hypothesis

what if ANOVA is significant?

determine which groups differ by running the t test for all post hoc pairwise if no specify comparisons of interest----Tukey's (most common)

wilcoxon signed rank test

the statistic is run on the ranks of the different scores

parametric vs nonparametric tests

there is not a large loss of power in using nonparametric tests compared to parametric tests even when the normality assumption holds

homogeneity of variance

this means that the population variances of the groups being tested is equal

mcnemar test

to compare the difference in # of subjects achieving a goal

chi-square test

to compare the difference in # of subjects achieving a goal (nominal)

mcnemar test

to compare the difference in # of subjects achieving a goal among multiple repeated testing conditions (nominal)

sample size for non parametric

too small for asymptotic distributions (cannot use central limit theorem)

mann-whitney test

when assumptions of parametric tests are violated

kruskal-wallis test

when assumptions of parametric tests are violated; if significant, run mann-whitney as post hoc test to determine which groups are different (need to apply bonferroni adjustment)

dependent samples

when values in one set are related (dependent) to their corresponding values in another set

independent samples

when values in one set have no relation (independent) to values in the other set


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