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statistical hypothesis testing - Coggle Diagram
statistical hypothesis testing
basics of probabilities and statistics
nothing ever repeats (random events are ideal
population = entirety of all possible cases--infinite
sampling = draw a limited number of cases from the population
descriptive
inferential
a single random event may be uni-, bi- or multivariate (dimension)
in data matrix, column
dependent variables in experiment
uni-/bi-/multifactorial： one/ two/ more group factors with 2+ groups /conditions for each factor
in data matrix, row
independent variables in experiment
permutation
has order
P(n, k) = n!/ (n-k)!
combination
without order
C(n, k) = n!/ (n-k)! k!
binomial distribution
hypothesis testing
hypothesis
how you view the statistical values like mean, ration, STD or distribution
hypothesis testing
make assumption for population parameters or distribution, and then test your hypothesis using sample data
type
parametric
non-parametric
step
H0, H1
ensure test statistics value
set significant level alpha
calculate statistics value
make decision
null hypothesis H0
the hypothesis to be tested
alternative hypothesis H1
the opposite hypothesis of H0
test statistics value
basic form
error
Type I or alpha error
H0 is true but reject H0
Type II or beta error
H1 is true but reject H1
conventions: alpha = 0.05, beta = 0.2, 1-beat = statistical power = 0.8
statistical power
the probability to accept H1 when H1 is true = test sensitivity for bias
1-beta >= 16alpha
Neyman-Pearson rationale
alpha is related to 1-beta, so decrease bias in H0 will increase bias in H1, vice versa. the solution is to increase the sample size.which will narrow the probability distribution curve of H0 and H1 and their overlapping part
power+
threshold+
alpha+
sample size+
effect size+
one- or two-tailed test
2-sidead if don't know direction for statistical value
alpha/2
threshold become stricter
power decrease
multiple statistical tests on single hypothesis
each single test with significance alpha/n ( Bonferroni correction
the logic of 2*2 table (bivariate distribution
bayes statistics
fisher's exact test
P(event) =
P(event) =
if P < significance alpha 0.05, reject H0
no restriction for n
Chi square test
steps
calculate expected value
chi square = sum(exp-obs)^2/obs
find chi square in chi square value table, for bivariate table df = 1
find corresponding significance
each single cell must >= 5
N >= 20 is mandatory but not sufficient
can be used to compare any expected frequency distribution, even 2*1 table
additional
for (n * m)table, df degree of freedom = (n-1)(m-1)
