Multivariate multilevel analysis - overview

This page offers structured overviews of one or more selected methods. Add additional methods for comparisons (max. of 3) by clicking on the dropdown button in the right-hand column. To practice with a specific method click the button at the bottom row of the table

Multivariate multilevel analysis
Binomial test for a single proportion
Binomial test for a single proportion$z$ test for a single proportion$z$ test for the difference between two proportionsGoodness of fit testChi-squared test for the relationship between two categorical variablesOne sample $z$ test for the meanOne sample $t$ test for the meanPaired sample $t$ testTwo sample $z$ testTwo sample $t$ test - equal variances not assumedTwo sample $t$ test - equal variances assumedOne way ANOVATwo way ANOVAPearson correlationRegression (OLS)Logistic regressionMann-Whitney-Wilcoxon testKruskal-Wallis testSign testMcNemar's testCochran's Q testMarginal Homogeneity test / Stuart-Maxwell testFriedman testWilcoxon signed-rank testOne sample Wilcoxon signed-rank testSpearman's rho
Independent variablesIndependent variable
One or more quantitative of interval or ratio level and/or one or more categorical with independent groups, transformed into code variables, plus at least one random factorNone
Dependent variablesDependent variable
Two or more quantitative of interval or ratio levelOne categorical with 2 independent groups
THIS TABLE IS YET TO BE COMPLETEDNull hypothesis
-H0: $\pi = \pi_0$

Here $\pi$ is the population proportion of 'successes', and $\pi_0$ is the population proportion of successes according to the null hypothesis.
n.a.Alternative hypothesis
-H1 two sided: $\pi \neq \pi_0$
H1 right sided: $\pi > \pi_0$
H1 left sided: $\pi < \pi_0$
n.a.Assumptions
-
  • Sample is a simple random sample from the population. That is, observations are independent of one another
n.a.Test statistic
-$X$ = number of successes in the sample
n.a.Sampling distribution of $X$ if H0 were true
-Binomial($n$, $P$) distribution.

Here $n = N$ (total sample size), and $P = \pi_0$ (population proportion according to the null hypothesis).
n.a.Significant?
-Two sided:
  • Check if $X$ observed in sample is in the rejection region or
  • Find two sided $p$ value corresponding to observed $X$ and check if it is equal to or smaller than $\alpha$
Right sided:
  • Check if $X$ observed in sample is in the rejection region or
  • Find right sided $p$ value corresponding to observed $X$ and check if it is equal to or smaller than $\alpha$
Left sided:
  • Check if $X$ observed in sample is in the rejection region or
  • Find left sided $p$ value corresponding to observed $X$ and check if it is equal to or smaller than $\alpha$
n.a.Example context
-Is the proportion of smokers amongst office workers different from $\pi_0 = 0.2$?
n.a.SPSS
-Analyze > Nonparametric Tests > Legacy Dialogs > Binomial...
  • Put your dichotomous variable in the box below Test Variable List
  • Fill in the value for $\pi_0$ in the box next to Test Proportion
n.a.Jamovi
-Frequencies > 2 Outcomes - Binomial test
  • Put your dichotomous variable in the white box at the right
  • Fill in the value for $\pi_0$ in the box next to Test value
  • Under Hypothesis, select your alternative hypothesis
Practice questionsPractice questions