PHORM Inferential Statistics

Comparing Groups

Parametric

Normal!!

P value > 0.05

Normality tests

•Kolmogorov-Smirnov (more sensitive to outliers)

•Shapiro-Wilk (higher power than K-S)

small sample sizes are less likely to have small P value while large sample sizes may generate significant P values even for small deviations from normality. Judgement call!

Non parametric

Not normal

<0.05

Skew -0.50 to +0.50

normal

Skew <-1.00 or >+1.00

not normal

Kurtosis near 3

normal

Kurtosis less than 0

not normal

Independent t Test

- sample size 30-100

- Test for normality (must be normal)

- equal or unequal variance

- calculate t and corresponding P

- P (probability they are from the same population)

- accept or reject the null

If we are testing two different groups (ex with dyslexia and without dyslexia)

independent t test

ANOVA

if we are testing BEFORE and AFTER (before treatment compared to after treatment on same person)

Matched pair t test

Repeated measures ANOVA

independent vs paired t test

independent - different groups

paired - same person is control and experimental

T tests are only appropriate for _______ data sets

continuous

normally distributed

MUTIPLE COMPARISONS

If you do a t test for one variabel lets say(25 times)

there is a chance of finding one comparison statistically significant at the p<0.05 level, purely by chance

•Need a correction factor

Bonferroni correction

•a / n comparisons

•0.05/25 = 0.002 new a criteria

•Other corrections are available

ANOVA

makes multiple comparisons simultaneously

takes into account different sample sizes

measures interaction

one way anova p< 0.05

at least one of the groups is statistically different from the others

reject the null

then do post Hoc analysis

one way anova p > 0.05

accept the null

not different

ANOVA is for ______ data

parametric

Two way ANOVA

2 treatments

2 groups

•Two-way ANOVA reports an F statistic for between atropine groups and between low and high myopia groups and for the interaction between refractive groups

Independent t test if not normal use

Mann-Whitney U

Matched Pair t test if not normal use

Wilcoxon signed rank test

ANOVA for non parametric

Kruskal-Wallis