chpt 13 review Flashcards
What are the different types of situations do we use just ANOVA
- single factor ANOVA (completely randomzied design)
- Randomized block design
- Factorial experiment
Why do we use single factor (completely randomized design) for?
Do all 3 populations come from the same pop
what is the null hypothesis for a single factor ANOVA
Ho: M1=M2=M3
Ha: Not all pop means are equal
What is a key word for ANOVA
Avg or Mean = Randomized block design
What test do we use for significance for ANOVA
F test
What is the formula for the F test
MSTR/MSE
If we reject Ho for a single factor ANOVA, what can we conclude
that the means of 3 pops are NOT equal
there is a significant difference b/w at least one mean
If not all means are equal in a single factor ANOVA, what can we do
- use fisher’s LSD (a multiple comparsson procedure)
What is the HO for Fisher’s LSD
Ho: Mi = Mj
What is the test for LSD
xbar1 -xbar 2 compare to lsd = ta/2 x square root of MSE (I/n + 1/n)
remember ta/2 is dividing the a by 2
- use df = total - k
What is the degrees of freedom for LSD
total - k
WHat is the randomized block design used for
to remove variation form the MSE term
what is the null hypothesis for the randomized block design
M1=M2=M3 (same as single factor ANOVA)
If we reject Ho for randomized block design, what can we say
conclude that the mean for the 3 differ
How do you calculate overall mean
do it and check sheet
how do you calculate Randomized block design for all levels
refer to sheet
What is the confidence interval for ANOVA
Xbar 1 - x bar 2 +/- LSD
How do you reject LSD
when xbari - x barj is greater than or equal to LSD
If we reject Ho for LSD (xbar1 - xbar 2 is greater than lsd) what can we say
significant and therefore there is a significant differences
if we do not reject Ho: not significant, does not appear to be any significant difference b/w the mean1 and mean 2
what is the formula for bonferoni
a EW/C
c- test pairwise comparisons
ex. a = 0.05
and there are 3 pops
then a = 0.05/3 = 0.017
what is the formula for bonferoni
a EW/C
c- test pairwise comparisons
ex. a = 0.05
and there are 3 pops
then a = 0.05/3 = 0.017
Comparing x bari-x bar j and lsd when do you reject ho and what is the conclusion
Reject ho if
x bari-x bar j is > LSD
This one is different
In block design, how do you know what is the treatment
the treatment is what we are interested in
Degrees of freedom for Factorials
SSA: a-1 (# of levels of factor A -1)
SSB: b-1 (# of levels of factor B-1)
SSAB: (a-1)(b-1)
SSE: ab(r-1) R= # of replications
t - test is to test for signficance of what in simple linear regression
slope
What is the confidence interval for in ANOVA??
the mean value of y for a given value of x
What is the prediction interval for
predict the value of the dep variable y for a NEW observation
What is the formula for a confidence interval
see notes
What is the formula for a prediction interval
see notes
When are the confidence interval and prediction interval more precise
when the value of the independent value of x* is closer to x bar
x* - given value of x
y* - predicted value of y when x given
What does x * mean
given value of x
what does y* mean
predicted value of y when x is given
which interval is wider
prediction interval will be wider than the confidence interval (confidence interval is closer to the mean)
