Session 3a Flashcards
Independent Variable terminology
X or IV
Independent Variable (X or IV) Also called what
a factor or a treatment variable
Independent Variable (X or IV) have multiple what
levels
what are levels in IV
Levels (treatments) = different values or categories of the independent variable/factor
Single-factor (one-way) designs
Involve what
a single IV with two or more levels
Single-factor (one-way) designs have what 2 subcategories
One-way independent-groups design (one way ANOVA) which is the point of this lecture
One-way design with repeated measures
what are Factorial designs
Involve more than one independent variable with two or more levels
Example: two-way independent-groups designs
what is this an example of
factorial design
When an experimental design has two factors with two levels each, it is called what
a 2 × 2 factorial design
If two factors, one factor has 2 levels and the other factor has how many levels
3 levels, 2×3
Purpose of one way ANOVA
To test whether the means of k (≥ 2) populations significantly differ
k is the number of groups
Prior requirements/assumptions of one way ANOVA
The population distribution of the DV is normal within each group The variance of the population distributions are equal for each group (homogeneity of variance assumption)
Independence of observations
If H0 is true what is the distribution like
normal, all groups are the exact same
If H0 is NOT true, there are several possibilities: what could the distribution be like
2 of the distributions are the same and one is not, all of the distribution s are different, etc
Why not just test all possibile differences with t-tests? instead of doing one way ANOVA
This would lead to an inflated experiment-wise Type I error rate
The chances of at least one significant difference are > α
ANOVA therefore usually consists of how many tests
two types of tests
ANOVA therefore usually consists of two types of tests what are are they
Overall F-test
Post-hoc tests
what does Overall F-test show
is H0 false?
what do Post-hoc tests show
Post-hoc tests to look at pairs of groups
Better Type I error control
Only interpretted if the overall F -test is significant
ANOVA stands for what
ANalysis Of VAriance
what are the 3 steps of ANOVA
1 Divides the variance observed in data into different parts resulting from different sources
2 Assesses the relative magnitude of the different parts of variance
3 Examines whether a particular part of the variance is greater than
expectation under the null hypothesis
how many types of variance ar din one way ANOVA
There are TWO sources of variance
what are the TWO sources of variance
The variance explained by the model (MSM)
The variance within groups, or the residual variance (MSR)
what is The variance explained by the model (MSM)
MS = mean squares (“mean” of sum of squared deviations)
The subscript “M” stands for “model”
This is variance between groups that is due to the IV, or different treatments/levels of a factor
what is The variance within groups, or the residual variance (MSR)
Within each group, there is some random variation in the scores for the
subjects
We can assess the relative magnitude of the two different parts of variance which what
the F -statistic (or F ratio)
If group means differ from each other, MSM tends to bewhat compared to MSR
large
If group means differ from each other, MSM tends to be large compared to MSR, and in turn F tends to be what
large
If F is found to be significantly large, this may be evidence for what
rejection of the null hypothesis
The F-statistic follows a what distribution
F distribution
The F-statistic follows an F distribution which varies in shape according to what
dfM and dfR
what is dfM
between group or model degrees of freedom
what is dfR -
within group or residual degrees of freedom
The F distribution is skewed hw
right-skewed distribution used most commonly in ANOVA
When referencing the F distribution, dfM or dfR is given first
dfM = df for numerator (sometimes: df1) dfR = df for denominator (sometimes: df2
With only two groups what can be used for testing for a significant difference between means
either a t test or an F test
With only two groups, either a t test or an F test can be used for testing for a significant difference between means
Both procedures lead to what conclusion
the same one
When the number of groups is 2, then F = what
= t^2
