Ch.10&13
What is ANOVA?
(Analysis of Variance)- statistical study used to analyze the data obtained from experimental or observational studies
Mean Square Error (mean square within groups)
(MSE) the estimate of sigma squared based on the variation of the sample observations within each sample individually
Sum of squares due to error
(SSE) is in the top numerator of calculating MSE
ANOVA can be used to test the equality among how many means?
3 or more
For four means in a one-way analysis of variance, how many differences among means result?
6
Some patients receive a placebo and others receive the actual drug. All other factors are controlled besides this difference. What type of study is this?
Experimental
What is used to get the p-value in an ANOVA test?
F-statistic
in matched samples, what curve do we use and what part of the curve?
For matched samples we use the t-curve and find the p-value that is two-tailed
How is MSE calculated?
MSE = SSE/dfError (which is Nt-K)
Test statistic F formula
MSTR/MSE
the variance of the dependent variable is denoted ________. Is it the same or different for all populations
Sigma squared- it is the same for all populations
within-treatments variance
The differences that exist inside each treatment condition.
two independent random samples are independent because...
They are independent because the variables of one sample don't depend on the variables of the other sample
between-treatments variance
Values used to measure and describe the differences between treatments (mean differences).
If we reject H0 in the ANOVA test, what do we conclude?
We can not conclude that ALL population means are different. We can only conclude that at least 2 population means are different
matched samples
an observational technique that involves matching the average of the participants in the experimental and control groups in order to eliminate the possibility that a third variable (and not the independent variable) caused changes in the dependent variable
Nt-K
degrees of freedom associated with SSE
For each population in an ANOVA test, the _________ variable is normally distributed.
dependent
two populations with sigma unknown are _________.
dependent
What do matched samples tell us?
each pair of data values is related somehow
What kind of study is it when one or more factors are controlled so that the data can be obtained about how the factors influence the variables of interest?
experimental
cause and effect relationships are easier to establish in what type of study?
experimental
Two ways to classify statistical studies
experimental or observational
What is the variable called that an experimenter selects for investigation?
factor
what is k?
how many different treatments you have
The observations in an ANOVA test must be __________.
independent
two populations with sigma known are ________________.
independent
degrees of freedom associated with SSTR
is the denominator used to solve for SSTR
Sum of squares due to treatment (SSTR)
is the top numerator used to solve for MSTR.
treatment
levels of the factor or how many methods they are using -ex. Method A,B, and C
observational study
no attempt is made to control the factors. You just are observing the data that's there
In comparison of three means, there are three differences (1vs2, 1 vs 3, and 2vs 3.) If F is significant, does this mean that all three differences are significant?
no because this just means only one of the differences is significant, not necessarily all of them
experimental units
objects of interest in the experiment -ex. patients in a treatment
SST/NT-1
overall sample that would be obtained if we treated the entire set of observations as one data set
As a result of an ANOVA, this conclusion was drawn: the difference between the means was significant at the .05 level. What decision has been made about the null hypothesis?
reject the null
Large F-statistic means it's farther _______________ (right or left) on the curve
right
the P-value is the area to the ______________ (right or left) of the calculated F-statistic
right
What does it mean when we DO NOT reject H0
the ANOVA assumptions are valid, meaning the sampling distribution of MSTR/MSE is an F distribution with MSTR degrees of freedom equal to K-q and MSE degrees of freedom is equal to Nt-k
what determines the skewness of the f-curve?
the degrees of reedom
Mean Square due to treatments (MSTR)
the estimate of sigma squared based on the variation of the sample means
For the typical consumer of research, what statistic is an ANOVA table is of greatest interest?
the p-value
completely randomized design
the treatments are assigned to all the experimental units completely by chance -ex. a design is random if the patients in the experiment have no pre-concieved idea about what treatment they are going to
If the means of the K populations are not equal, what happens to the value of MSTR/MSE?
the value will be inflated because MSTR overestimates sigma squared
SST
total sum of squares= SSTR+SSE
within-treatments variance tells us the error of _____________ within each group.
variability
experimental factor
variable that the experiment has selected for investigation
Why do matched samples often lead to a smaller sampling error?
variation between sampled items is eliminated as a source of sampling error
If the resulting value of MSTR/MSE appears to large to have been selected at random from the appropriate f distribution, what do we do?
we will reject H0
