ANOVA - Analysis of Variance Flashcards
Very flexible and general technique, and the principles can be applied to a wide range of statistical tests.
- Has a wide range of applications.
- Many of applications make some tricky assumptions about the data.
ANOVA
In ANOVA we measure an _____ (also called a dependent variable).
outcome variable
This outcome must be measured on a ______
continuous scale.
- It is called _____because it depends on one or more predictor variables.
dependent
_______ can be Manipulated (Treatment) or variables we simply measure (Sex).
Predictor variable
In ANOVA, predictor variables are mostly _____, although continuous variables can also be used in the same framework.
categorical
When predictor variables are categorical, they are also called_____ or _____
FACTORS or INDEPENDENT VARIABLES
measurement of differences.
ANOVA
Differences happen for two reasons: (a) because of the effect of ______ (b) because of ____
a. predictor variables
b. other reasons
In ANOVA, we want to know two things:
- How much of the variance (difference) between the two groups is due to the predictor variable
- Whether this proportion of variance is statistically significant, that is, it is larger than we would expect by chance if the null hypothesis were true?
We can divide (statisticians sometimes say partition) variance into three different types:
The Total Variance
Variance due to treatment, (Differences between Group)
Variance due to Error (Differences within Group)
In ANOVA, the ______ is conceptualized as sums of squared deviations from the ____
- variance
- mean
It is usually shortened to sum of squares and denoted by _____
SS or Sum of Squares
The 3 Sum of Squares
- Between-groups Sum of Squares
- Error Sum of Squares
- Total Sum of Squares
Total Sum of Squares, called
SStotal
We are asking whether the _____ (or the effect of the predictor) is big enough that we could say it is not due to chance.
difference between the groups
________
this is the variance that represents the difference between the groups, and this is called ____
. Sometimes it refers to the
between-groups sum of squares for one predictor, in which case it is called SS predictor. Sometimes it is called
- Between-groups Sum of Squares
- SSbetween
- SStreatment
The between-groups variance is the_____ that we are actually interested in
variance
also called within-groups sum of squares.
Error sum of squares
It’s within the groups, because different people, who have had the same treatment, have ____
different scores.
They have different scores because of error. So this is called either ___ or ___
SSwithin or SSerror
We need to calculate the three kinds of Sum of Squares,____ and _____
- TOTAL
- WITHIN GROUPS
- BETWEEN GROUPS.
sum of squared differences between the mean and each score
SStotal
- Step 1: Find the Mean of the scores.
- Step 2: Calculate the difference between each score and the mean score.
- Step 3: Calculate the Squared deviations
- Step 4: Find the Sum of the Squared Deviations
Calculating the SS total
- Procedure is very similar.
- This time we are looking for the sum of squares within each group.
- Rather than using the total mean, we use the mean for each group.
Calculating the SSwithin
Easy way and hard way.
- SStotal = SSwithin + SSbetween
- Thus: SS Between = SS Total – SS Within
Calculating SSbetween
To know how large the effect of the treatment has been.
Effect size
The same as asking what proportion of the Total Variance (or Total Sum of Squares) the treatment effect has been responsible for
effect size
calculating the effect size
This is just: SS Between / SS Total.
Effect Size goes under two different names: these are
R -Squared or eta-Squared.
1st: Calculate the Mean Squares. Often written as MS. * These are MSbetween, MSwithin, MStotal
Calculating Statistical Significance
this gives us the statistic for ANOVA, which is called___, or sometimes the ____
F or F-ratio.
____ and___ are exactly the same test
ANOVA and t-test
To find the probability value associated with F we need to have two sets of ____, the between and within.
degrees of freedom
In fact, if we take the value of t and square it. We get the value of ____
F
This is a general rule when there are 2 groups
F = t-squared
restricted to comparing 2 groups.
t-test
extends in a number of useful directions.
ANOVA
Can be used to compare 3 groups or more, to calculate the p-value associated with the Regression Line, and in a wide range of other situations.
ANOVA and T-test
When there are 2 groups, ANOVA____ is equivalent to a t-test, and it therefore makes the same assumptions as the t-test.
and it makes these assumptions regardless of the number of groups that are being compared
When there are 2 groups, ANOVA is equivalent to a t-test, and it therefore makes the same assumptions as the t-test.
ASSUMPTIONS IN ANOVA
We do not assume that the outcome variable is normally distributed.
What we do assume is that data within each group are normally distributed.
Normal distribution within each group
ASSUMPTIONS IN ANOVA
- As with the t-test, we assume that the standard deviation within each group is approximately equal.
- the variance being the square of the SD.
- However, as with the t-test, we don’t need to worry about this assumption, if we have approximately equal numbers of people in each group.
- Formulae are all the same.
Homogeneity of Variance
most elementary analysis of variance
one way ANOVA
one way ANOVA also called as
1.
2.
3.
4.
simple-randomized groups design, independent groups design, or the single factor experiment, independent groups design.
not limited to single factor experiments.
ANOVA
The effect of many different factors may be investigated at the same time in____
one experiment
one in which the effects of two or more factors or IVs are assessed in one experiment.
Factorial experiment
used are combinations of the levels of factors.
Conditions or treatments
more complicated. However, we get a lot more information
- It allows in one experiment to evaluate the effect of two IVs and the interaction between them.
TWO WAY ANOVA
Since this is an independent groups design, subjects would be_____to each of the cells so that a different group of subjects occupies each cell.
randomly assigned
Two-Way ANOVA
We want to determine whether factor A has a significant effect, disregarding the effect of factor B. This is called the ____
main effect of factor A.
the levels of each factor were systematically chosen by the experimenter rather than being randomly chosen.
Fixed effects design
Two-Way ANOVA
We want to determine whether factor B has a significant effect, without considering the effect of factor A. This is called the ___
main effect of factor B.
Two-Way ANOVA
we want to determine whether there is an interaction between factors A and B.
interaction effect of factors A and B.
In analyzing data from a two-way ANOVA, we determine four variance estimates:
- MS within cells
- MS rows
- MS columns
- MS interaction
The estimate MS within cells is the within cells variance estimate and corresponds to the within groups variance estimate used in the ____
one-way ANOVA.
The other estimates are sensitive to the effects of the____
IVs. or independent variables
The estimate MS rows is called the ____.
It is based on the variability of the row means and, hence, is sensitive to the effects of variable A.
row variance estimate
The estimate MS columns is called the ____
It is based on the variability of the column means and, hence, is sensitive to the effects of variable
column variance estimate.
If variable A has no effect, MS rows is an independent estimate of the____
σ-squared.
Finally, if there is no interaction between variables A and B, MS interaction is also an independent estimate of ____
σ – squared.
Thus, the estimates MS rows, MS columns, and MS interaction are analogous to the between-groups variance estimate of the _____
one-way ANOVA design.
Each F (or F obtained) value is evaluated against F crit (critical value) as in the____
one way analysis.
In a_____, we can essentially two one-way experiments, plus we are able to evaluate the interaction between the two independent variables.
two-way ANOVA
In a ____, we partition the total sum of squares (SS total), into four components:
2-way ANOVA
the within-cells sum of squares,
the row sum of squares,
the column sum of squares, and
the interaction sum of squares.
When these Sum of Squares (SS) are divided by the appropriate degrees of freedom, they form four variance estimates.
(MS within-cells, MS rows, MS columns and MS interaction)
