ANCOVA - 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

ANCOVA
One way MANOVA
Binomial test for a single proportion
You cannot compare more than 3 methods
Independent variablesIndependent/grouping variableIndependent variable
One or more categorical with independent groups, and one or more quantitative control variables of interval or ratio level (covariates)One categorical with $I$ independent groups ($I \geqslant 2$)None
Dependent variableDependent variablesDependent variable
One quantitative of interval or ratio levelTwo or more quantitative of interval or ratio levelOne categorical with 2 independent groups
THIS TABLE IS YET TO BE COMPLETEDTHIS 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.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.n.a.Assumptions
--
  • Sample is a simple random sample from the population. That is, observations are independent of one another
n.a.n.a.Test statistic
--$X$ = number of successes in the sample
n.a.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.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.n.a.Example context
--Is the proportion of smokers amongst office workers different from $\pi_0 = 0.2$?
n.a.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.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 questionsPractice questions