t test
compare 2 groups
t = difference in sample means / SD
of difference of sample means
assumption/ prerequisite
random or representative samples
independent observations
population data has Gaussian distribution
populations have equal variance (identical SD
F test
low power
easy to perform
H0: equal variances
F = (SD1/ SD2)^2
what if variances are not equal
ignore? if n >= 30, central limit theorem
transform the data (e.g. log)
use Welch's correction
allows for unequal variances
lower power
if violated
transform data
use non-parametric test (dont assume ur data follow a specific distribution
Shapiro-Wilk-test
high power for 2< n< 50
H0: data follow normal distribution
Komogorov-Smirnov-test
test if 2 sample has the same probability distribution
high n necessary
goodness of fit test
Mann-Whitney U-test
rank all values (independent of group
sum up ranks of both groups
sum of group 2 = N(N+1)/2 - sum group 1
calculate mean ranks
compute P value
H0: distribution of ranks is totally random
testing difference of mean
2 groups #
3 or more groups
multiple t test will lead to add up of alpha
Bonferroni correction
alpha/group number
very conservative
analysis of variation ANOVA
H0: all investigated population have the same means
P value: when H0 is true, the largest probability of observed means
2 components of variance
within group sum of squares
intergroup sum of squares
(µa - µ)2
(µb - µ)2
(µc - µ)2
(µd - µ)2
df = N - n groups
df = number of groups -1
F = within group squares sum/df within / intergroup squares sum/ df inter
check P value
assumptions
the same as t test
post tests
are column arrange in a natural order (age, time, etc
post test for trend
is there a certain control group
Dunnett's test
many-to-one comparison
correct alpha
Bonferroni test
compare all pairs of means
Bonferroni
wide Cl, low power, do not use with5+ group
Tukey
more conservative, misses real difference
Student-Newman-Keuls
more powerful (find false differences
kinds
repeated measures ANOVA
nonparametric ANOVA
Kruskal-Wallis-test
two-way ANOVA
one group, repeated measures
2 factors/ independent variables
how to report results of test
type of test (test variable, df, p-value
asterisk
- p<0.05
** p<0.01
* p<0.001
* is not more significant than
plan an experiment
minimize type I error
predict the nature of your data
distribution of samples, matched group, repeated measures
decide on statistical analysis
minimize type II error
predict effect size
power analysis
decide on sample size