inferential statistics

inferential statistics

aka analytical statistics

used to determine if relationships or differences exist btwn variables/groups

superior to descriptive statistics

types of inferential statistics

parametric

non-parametric

parametric

use statistics such as mean, standard dev, CIs, p value

t-tests, ANOVAs, certain types of correlation, regression

key assumptions: normally distributed populations, traditionally use continuous data

non-parametric

use rank or freq info

Mann-Whitney, Wilcoxon rank sum, Chi-square, Kruskal-Wallis, Friedsman test, etc.

key assumptions: nominal or ordinal level data, not a normal distribution

independent samples

unpaired, presents measures from 2+ groups of unrelated subjects

values from 1 group not related to values from other group

dependent samples

paired, presents repeated measures on same or very similar subjects

values collected at 1 point in time are related to values collected at another

options for inferential statistical tests

depends on:

• type of relationship or difference analyzed

• nature of data (nominal, ordinal, etc.)

• whether parametric assumptions are met

• whether samples are independent or dependent

• # of groups being compared

linear regression

dependent/outcome variable is continuous

may be simple or multiple (1 or 2+ predictors/factors)

relationship btwn factors and DV is demonstrated by regression equation

estimates often presented as means or proportion w/ CIs

y=a+b1×1+b2×2+b3×3…

logistic regression

dependent/outcome variable is categorical: binary (most common), multinominal, ordinal

may be simple or multiple

presented as odds ratio w CIs

cox proportional regression

used in deriving incidence estimations (burden: ex. hazard rate of per 1000 person-years) and relationships/rate estimates (predictors: hazard ratio) for categorical outcomes w considerations for time to event, esp in longitudinal cohort studies

poison regression

used in deriving incidence estimates (burden: ex. incidence rate per 1000 hrs) and relationships/rate estimates (predictors: incidence rate ratio) for count outcomes w/ considerations for exposure (i.e. participation) time

chi square test

non-parametric test of association btwn categorical variables

uses a contingency (2×2 table): row=level of IV, column=outcome of interest

assesses relative proportions of subjects w a particular characteristic in each group

compares observed vs expected frequencies if H0 were true

\chi^2 and obtained p-value

alpha levels

probability that a difference occurred due to chance

predetermined by researcher, 5%/0.05 and 99%/0.01 most common to establish statistical significance

inflated when there is repeated statistical testing=type I error; bonferroni adjustment to correct bias

lower=better

p value 0.05

5% of event likely occurred by chance

p value 0.01

1% of event likely occurred by chance

type I error

conclude that a relationship or a difference exists when there is none (false positive)

\alpha =probability of making this error

often associated with/ bias of multiple statistical tests or over sampling

type II error

conclude that no difference exists when there is one (false negative)

\beta =probability of making this error

inversely related to \alpha

often associated w bias of under sampling

type III error

conclude that no difference exists when there is one (false negative)

often associated with bias of non-adherence or lack of intervention fidelity

confidence intervals

can also determine statistical significance

95% implies that alpha is 0.05, 99% implies 0.01 and results should be interpreted as such

for LogR and HCR: values crossing 1 suggest no significance (ex. 1.5-3.2 is significant, 0.5-3.2 is not)

for LinR: “coefficients” (mean difference) 0 would be benchmark (ex. 0.5-3.2 suggests significant finding, -1.5-3.2 is not)

power

likelihood that one will detect a relationship when one exists

rule of thumb: \ge80\% (higher=better)

too much→type I error

too little→type II error

what determines sample size?

desired level of statistical power (\beta ); often \ge80\% /0.08

\alpha level to be used in research; often 5%/0.05

estimate of effect size (from past studies or guess of clinically meaningful relationship btwn groups)