Class Notes 9 Sept 2004
overview stuff, review of ANOVA (1
way)
EPSY 6301 9 Sept
2004
No meeting next week, we will take this week off rather than a week in Oct so Dr O can go collect data
Tabaachnick is a good reference book, but I wouldn't call it a statistics book
That is why we are also using chapters
we will skip trend and contrast analysis
Our project is chapter 5, problem 5
- make believe data set
- we can work together and compare
- do parts a through i
- the write up is where we show we understand the problem, the mathematics will probably be figured out by everyone
- the depth of understanding is shown in the dscussion section (2 pages)
-- what statistical significance tells us, the power, the omega square, include what the dv and iv are, etc
Fisher-Hayter test is same as Tukey test we did in 5381
Chapter 5 does a good job of building a hierarchy
Kirk uses alpha with a subscript for the treatment effect (he is the only one who seems to do this, others use T for treatment variable)
If you see alpha without a subscript, that indicates level of significance
subscript i always = subjects
lower case n = total sample size
p = limit of how many treatment levels
DV = mew + treatment effect + error
x (sub i j) = mew + alpha (sub j) + error (sub i j)
We don't look at the variance itself, but instead look at the sums of squared between (the alpha) and the sums of squares within (the error)
with good design, we can reduce the error in this formula (so we have a larger sums of squares betweeen, and a smaller sums of squares within)
this is an additive model, can't be multiplicative
Chap 7 model will be randomized block design
remember for subscripting reference, it is always rows first then columns
- Kirk likes dot notation
- X.1 = mean for first column / treatment
- X.. is grand mean
Kirk uses y instead of x as the treatment variable
- Hinkle uses y
if we have a given variable x (sub i j) the question is how do we deconstruct / decompose that single score (determine how much of the value is the treatment effect as well as the error)
x (sub i j) = grand mean (Xbar..) + (Xbar j - Xbar..) + (X sub i j - Xbar .j )
we are just partitioning our variable into its component parts
this is the key to ANOVA:
- we are really comparing the deviation of the averages between treatment groups
- alpha (treatment effect) is generated by a
from sums of squares we will create variances
sums of squares is just one step ahead of variance
Variance (S squared) = sums of squares divided by (n-1)
Ultimate goal is to get to the F test
- we create an ANOVA table to tabulate all this
- find the sum of squares of the treatment, between groups, and within (the error)
in SPSS you must be able to identify which sums of squares you are dealing with
ANOVA is basically a special case of regression (but regression usually uses the t distribution)
- we use the F distribution because we are using small numbers of treatment groups
-- if we are using many more treatment groups, then our distribution will more accurately reflect the normal distribution, and for that reason we could/should use the t distribution
degrees of freedom are a very powerful friend, because of the mean of squares calculations in the ANOVA table
can't do multiple / sequential t-tests because the error gets so inflated
- that is why we can do the simultaneous ANOVA
Scheffe uses F distribution
- all others use studentized Q or t distribution
Tukey is a t-test but it is an adjusted t-test
Fixed Effect models in contrast to random effects models are not as discussed in earlier courses
- fixed effect models: we select values for the treatment variable that are exhausted (we are studying all the possible intervention types for that variable)
regression is easier to do that ANOVA and also more powerful
pairwise comparisons is called "going fishing"
No meeting next week, we will take this week off rather than a week in Oct so Dr O can go collect data
Tabaachnick is a good reference book, but I wouldn't call it a statistics book
That is why we are also using chapters
we will skip trend and contrast analysis
Our project is chapter 5, problem 5
- make believe data set
- we can work together and compare
- do parts a through i
- the write up is where we show we understand the problem, the mathematics will probably be figured out by everyone
- the depth of understanding is shown in the dscussion section (2 pages)
-- what statistical significance tells us, the power, the omega square, include what the dv and iv are, etc
Fisher-Hayter test is same as Tukey test we did in 5381
Chapter 5 does a good job of building a hierarchy
Kirk uses alpha with a subscript for the treatment effect (he is the only one who seems to do this, others use T for treatment variable)
If you see alpha without a subscript, that indicates level of significance
subscript i always = subjects
lower case n = total sample size
p = limit of how many treatment levels
DV = mew + treatment effect + error
x (sub i j) = mew + alpha (sub j) + error (sub i j)
We don't look at the variance itself, but instead look at the sums of squared between (the alpha) and the sums of squares within (the error)
with good design, we can reduce the error in this formula (so we have a larger sums of squares betweeen, and a smaller sums of squares within)
this is an additive model, can't be multiplicative
Chap 7 model will be randomized block design
remember for subscripting reference, it is always rows first then columns
- Kirk likes dot notation
- X.1 = mean for first column / treatment
- X.. is grand mean
Kirk uses y instead of x as the treatment variable
- Hinkle uses y
if we have a given variable x (sub i j) the question is how do we deconstruct / decompose that single score (determine how much of the value is the treatment effect as well as the error)
x (sub i j) = grand mean (Xbar..) + (Xbar j - Xbar..) + (X sub i j - Xbar .j )
we are just partitioning our variable into its component parts
this is the key to ANOVA:
- we are really comparing the deviation of the averages between treatment groups
- alpha (treatment effect) is generated by a
from sums of squares we will create variances
sums of squares is just one step ahead of variance
Variance (S squared) = sums of squares divided by (n-1)
Ultimate goal is to get to the F test
- we create an ANOVA table to tabulate all this
- find the sum of squares of the treatment, between groups, and within (the error)
in SPSS you must be able to identify which sums of squares you are dealing with
ANOVA is basically a special case of regression (but regression usually uses the t distribution)
- we use the F distribution because we are using small numbers of treatment groups
-- if we are using many more treatment groups, then our distribution will more accurately reflect the normal distribution, and for that reason we could/should use the t distribution
degrees of freedom are a very powerful friend, because of the mean of squares calculations in the ANOVA table
can't do multiple / sequential t-tests because the error gets so inflated
- that is why we can do the simultaneous ANOVA
Scheffe uses F distribution
- all others use studentized Q or t distribution
Tukey is a t-test but it is an adjusted t-test
Fixed Effect models in contrast to random effects models are not as discussed in earlier courses
- fixed effect models: we select values for the treatment variable that are exhausted (we are studying all the possible intervention types for that variable)
regression is easier to do that ANOVA and also more powerful
pairwise comparisons is called "going fishing"
Posted: Thu - September 9, 2004 at 08:57 PM
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Published On: Sep 09, 2004 08:57 PM
Total entries in this category: 2
Published On: Sep 09, 2004 08:57 PM
