analysis of variance Flashcards
simplest linear model and most commonly used
analysis of variance, ANOVA
it is an extension of the two-sample t-test to a comparison of the means for three or more groups
The analysis of variance (ANOVA)
paired vs unpaired variable
■ Paired:
Pre test and post test
■ Unpaired:
The 2 data are independent from each other. Meaning it is not
interconnected between both data.
one-way ANOVA vs two-way ANOVA
One -way ANOVA
1 independent variable with at least 2 treatments/ levels.
■ Example: check for differences in
parasitology quiz scores between three schools.
Two-way ANOVA
2 independent variables.
■ Interact with each other and somehow may cause an effect to the dependent variable.
independent variable vs dependent variable
Independent variable:
not affected by any types of variable present in your experiment or data.
Dependent variable:
depends on the changes in independent variables.
For example, Experimental research
what are the ANOVA assumptions
○ Samples from each group are independent.
■ Usually achieved through random sampling.
■ Must not exhibit any form of multicollinearity.
■ Strict!
○ Dependent variable is normally distributed from each population.
○ The variances of the dependent are the same across
populations.
■ Should be homogenous
variances.
what happens if one of the ANOVA assumptions are violated/ not achieved
we move on to the non parametric equivalent - Kruskal-Wallis Test
how do we use hypotheses testing use one way anova
○ H0: u1 = u2 = … uk
■ All sample means are equal. No significant difference between the means of the data.
○ H1: ui ≠ uj for i ≠ j
■ At least 1 sample mean is significantly different from the other means.
■ Mean 1 = mean 2 ≠ mean 3
anova analyzes the variances of the data to determine whether there is a difference between group means.
sum of squares
it is the overall variability which is partitioned into two parts
Total Variation (SST) - total sum of squares
○ Between group variation (SSB)
is the variability explained by the independent variable.
sum of squares btwn grps
○ Within group variation (SSW)
is the variability not explained by the independent variable.
It is called the error sum of squares.
sum of squares within grps
it measure the variability of the variations means
mean squares
○ Mean square between group (MSB)
measures variability between group means.
○ Mean square within group (MSW)
measures variability within group means.
*basically it utilize the data from SST and SSW to get the mean squares
formula of
SSB
SSW
MSB
MSW
index card
how many degrees of freedom of anova and what are they
2 degrees of freedom denoted by x and y
df= (x,y)
x: k-1
y: N-k
Can answer for the presence of an interaction effect.
Two-Way ANOVA
○ Interaction effect usually represents the combined effects of the two independent variables to the dependent variable.
○ Two-way ANOVA answers the question “does the interaction between the two independent variables statistically affect the value of the dependent variable?”
briefly explain the set of hypotheses for two-way anova
there are total of 3 sets
