301 Flashcards
How do we explain where variability comes from and measure it?
1) Calculate the total variability in the entire data set
2) Decompose the total variability into separate components
Total Variability=Variability within groups and variability between groups
In an ANOVA variance is know as…
Mean squared or MS
Define grand mean
Is the mean summed over all subjects over all groups
Define SST
-The total sum of squared deviation scores.
How do you find SST
-All the subjects and all groups, subtract each score from the grand mean. Then square them and sum them
What does SSB do?
Looks at the deviation of the treatment mean from the grand mean
What does SSW do?
The deviation of the raw scores from their respective group means
Is SS the numerator or denominator of variance
numerator
What is the equation for dfT
N-1
What is the equation for dfB
N-K
What is the equation for dfW
K-1
What is H1
The alternative hypothesis
What shape is the F stat
Positively skewed
What does the total area under the F curve equal?
1
Define F critical
The critical value that separates the rejection region from the rest of the curve
Define F obtained
The obtained value from the data
Before calculating power what do you need to find?
Effect size
What symbol represents effect size for ANOVAs
f with a little hat on it
What are two types of power tests
1) A post hoc determination of power
2) a priori power test
If you find inadequate power in a post hoc test what should you do? (less than medium)
Replicate with more participants
How do we determine effect size when doing an a priori power test?
Refer to similar past research
How can you improve power
ATMNI
A - Use a more lenient alpha level
T - Use a one tailed test: when the literature supports a directional hypothesis
M - Lower in group variability: by repeated measures or through sample selection ( like buying ridiculously expensive mice!!!)
N - Have equal n throughout groups
I - Increase n
When do we use the Harmonic mean?
When we have unequal n from group to group
What is the equation for the Harmonic mean?
nh=number of treatment groups/E(1/Sample size)
Define outliers
A data point that is very different from the rest of the data
What do you do with outliers and why?
they need to be detected and removed otherwise they will have dramatic effects on the results
Why do outliers exist?
1) Human error
2) Instrumentation
3) Subject scores ( they may actually be from another population)
How do we determine the largest possible z score of a data set?
(n-1)/√ N
For a small sample we would scrutinize any data point greater than 2.5
For a large sample 99% of the scores are withing 3 SD of the mean so any score over 3
Should you run subjects after the analysis? Why?
No.
Because it tends to increase variability, which reduces the probability of finding significant
What happens when N is really large
-We tend to get statistical significance even if there is not practical significance. This is why statistical significance is not worth much
When N increases…
standard error of the mean decreases
What is the difference between a planned comparison and an ANOVA
- They are the same thing (look at the equations)
- The only difference is that a planned comparison uses specific comparisons among pairs of the treatment means
Can you have a significant planned comparison with a non-significant omnibus F?
Yes!
Can you choose to do a planned comparison whenever you want?
No, it has to be stated in your hypothesis
What questions should you ask before doing a planned comparison?
1) Is something better than nothing?
2) Do the two treatments differ in effectiveness?
3) Is there combination of treatment better than either alone
- By using these as a guide we now know what planned comparisons to test
How many df does each planned comparison have?
1
When comparing groups how many treatment means do you use in a planned comparison
All of them, even when comparing only two groups
What happens to alpha when we have many planned comparisons?
It increases
When can you do a post hoc comparison?
Only after you start, and you don’t need omnibus F to be significant
How many types of post hoc tests are there?
There are many and we don’t need to know them all!
What do post hoc tests do?
They determine which treatment means are significantly different from each other
What are the two purposes of a post hoc test?
1) To indicate where the mean differences lie
2) Maintain family wise alpha at the same pre determined level
What post hoc test do we have to know how to use?
Tukey
Tukey is often called…
- HSD test ie Honestly significant difference test
When do we use Tukey?
When making all possible pairwise comparisons
What effect does Tukey have on alpha?
If controls alpha when you have homogeneity of variance
Critical differences is equal to
Honestly significant difference
Step one (Tukey)
Find the Omnibus F
Step two (Tukey)
Construct a table where you can rank the means from high to low
Step three (Tukey)
Subtract the means and ignore the signs
Step four (Tukey)
Calculate HSD.
Any numbers on the table greater than the calculated HSD are significantly different
What if we have unequal n for our groups
Use the harmonic mean for each pair of groups?
Tukey-Krammer proe
What is the difference between planned comparisons and post hocs?
Planned comparisons have more power. But you can use both
What do we do if variance is heterogeneous? (Tukey)
We use Welch’s t statistic (this controls family wise alpha when variance is heterogeneous or when we have unequal n)
What is the assumption of Normality?
- For every X value Y are approximately normally distributed
- We can check this by doing a frequency distribution
What happens when normality is violated?
- Increased risk for types 1/2 errors
- This only has a slight effect on type 1 error ( even when very skewed/kurtotic)
What is the difference between nominal and actual alpha
- Nominal is what we set alpha at and what we want it to be
- Actual alpha may be different, it is the alpha level we end up with
- These can be difference when working with a non-normal population
What do we say if nominal alpha is near actual alpha?
F is robust to violations of normality
Because of the central limit theorem
If the distribution is very skewed resulting in a lack of normality, how does it effect power
It only has a slight effect on power
Does a lack of normality due to platykirtosis effect power
Yes, especially if n is small
What do we do it there are big violations of normality with a small n?
Conduct a non-parametric test
What is another word for Homogeneity of Variance
Homoscedasticity
Is variance is effected by the treatment (IV) what do we have
Error variance
Define Heteroscedasticity
When scores are largely varied
F is robust for unequal variances when
when n are nearly equal or equal
When is unequal n an issue of homogeneity of variance
When n’s are sharply unequal and variances are sharply unequal ( need to determine through a test)
An approximately equal n is
less than 1.5, other wise sharply unequal
How do we know we have sharply unequal variance
we do a test and if it is greater than 3 we determine variance is sharply unequal
if the largest variance is associated with the group with the smallest n
- F is liberal
- Actual alpha is less than nominal alpha
-So we reject Ho too often
Solution: adjust nominal alpha downwards
If the largest variance is associated with the group with the largest n
- F is conservative
- Actual alpha is less than nominal alpha
- We don’t usually make an adjustment
Independence of observations is…
when observations within a group are independent from one another
How do we satisfy the independence of observations assumption
it is satisfied if you have unrelated subjects ran individually and alone
What happens we have small violations of (IO)
Small violations have substantial effects on alpha and power
What is the solution to small violations of (IO)
set a more stringent nominal alpha level
What is the forth assumption of an Anova
That the dependent variable is measured on an interval or ratio scale
Define ratio scale
An interval scale with an absolute zero
Define interval scale
Consisted of ordered categories and equal intervals no true zero
What is the 5th assumption of an Anova?
That the IV and DV are linearly related
The independent variable is represented by
X
The dependent variable is represented by
Y
A subject score is comprised of three parts
1) General effect (grand mean)
2) an effect that is unique and constant within a given treatment ( treatment effect)
3) an effect t hat is unpredictable (random error)
Steps of a hypothesis
1) State the research hypothesis
2) State the null hypothesis
3) Collect data
4) Test Ho
5) Make a decision
6) Make a conclusion
Define the central limit theorem
The standard deviation of the mean will be normally distributed if:
A) The raw scores are normally distributed in the population
B) Will approach a normal distribution a n increases as n approaches 30
How do you accept a Hypotheis
You fail to reject Ho, X likely affects Y
What is the Bonferoni Inequality?
It calculateds the alpha level per comparison ie alpha prime
How to you assess F
Either compare to F crit or determine the probability of your F score and test against alpha
What does power depend on
Alpha, n, and effect size
Define power
The probability of rejecting Ho when Ho is false
What test controls for experimental alpha?
HSD or Tukey
Define F from overall ANOVA
Gives us an average effect for all possible pairwise comparisons
Define Actual alpha
The alpha if one ore more assumptions are violated
Define Family wise alpha
The alpha you end up with after all analyses and calculations
Define effect size
It is the degree of non overlap of frequency distributions
Define Nominal alpha
The alpha if all assumptions are met
What is persons r
Another measure of effect size . It is the proportion of variance in Y attributed to X
What is the second violation of homogeneity of variance?
If the largest variance is associated with the group with the largest n
What violation is it when the largest variance is associated with the group with the smallest n
It is a violation of the homogeneity of variance
What is psi with a hat?
The difference between means for a given comparison
What is Ci
The weighted coefficient assigned to each treatment mean
What are the rules to a coefficient
- It must equal 0 for each comparison
- It must accurately reflect which means are being compared
What is alpha prime
It is the alpha level per comparison
What is Tukey based on
A statistic called the studentized range statistic
What do we say if we get a number greater that the HSD while doing Tukey
That a1 is significantly different from a2
Turkey Kramer Proe
It is when you used the harmonic mean with to determine HSD
Define MS
It is the mean of the squared deviation scores (ie variance)
What is a small, median and large effect size (f)
.1, .25, .4(and up)
Fmax=
The test for sharply unequal variance
In the assumption of independence of observations how do we measure dependence
With the interclass correlation
Define Standard error
It is the standard deviation of a sampling distribution the mean
