Midterm 2 Flashcards
How is an observed value defined?
True value + Residual error
what does the mean stand for in the algebraic notation for an observed value?
mean = true value, benchmark.
Is the mean part of the true value of an observation?
Yes
What do the integers Si, Oj, Bk stand for, in regards to the value of the observation?
They are all true values based on the number of factors present in the model.
Can the subscripts of the algebraic notation for a true value be replaced by actual numbers?
Yes, the new subscript numbers relate the observed value to the factor levels of the factor they came from.
What is the Standard Deviation of the residual error?
Sqrt(MSE)
What is the Benchmark value in a decomposition?
Benchmark is the grand average of all the observed values
What is another name for Benchmark?
Grand mean
What is the estimated effect for a factor?
Factor average - grand average (benchmark)
True/False
The estimated effect for an individual in the experiment is the individuals average observations - grand mean.
False
The estimated effect for an individual in the experiment is the individuals average - the group average for that individual.
What is the formula for the residual error?
Observation - (grand mean + efffect 1 + effect 2)
What two types of variability make up an observation?
planned and unplanned
What does the F statistic tell us?
How much bigger the average variability of the factor is than the average variability from the MSerror
How do you find the SS?
Square all the numbers in the table, and ad them up. the total is a measure of hte overall variability in the table.
What do the degrees of freedom represent?
This number counts the number of units of information about residual erro rcontained in the table
How do you find the means squared value?
Divide the Sum of Squares by the degrees of freedom
How do you find the sum of squares?
Square each number in the box and then add them all up! It literally means exactly what it says.
If the residuals are grouped relatively close together, will the sum of squares be large or small?
The sum of squares will be small
If the residuals are spread out will the sum of squares be large or small?
The sum of squares will be large
What does the sums of squares measure?
The overall variability of a set of numbers, provided those numbers add to zero.
What does SS measure average variability?
No, it measures overall variability?
How do you know when to transform data?
When SDmax/SDmin is greater than 3
What is the computation to find an F ratio?
MSfactor/MSerror
What does an F ratio mean if it is close to 1
There are no real differences due to planned variability. The differences are probalby due to chance error
What do we infer if the F ratio is further away from 1?
We have enough evidence to assume that the differences are too big to be due to just chance error.
True/False
An F ratio tells you how big the true differences are, and whether they are big enough to be scientifically interesting.
False
An F ratio tells you whether the true diffrences are big enough to be detected by your experiment, but not what size the differences are - not whether they are big enough to be scientifically interesting.
What does the standard error tell us
The typical size of a chance part of an observation
Can we say that a 95% confidence interval will contain 95% of the distance of a given value?
No, all we can say is that the interval was created by a method that works 95% of the time. Or, in 95% of the cases where we use this method to construct an interval, it will contain the true values.
What three values go into a standard error?
- Sqrt(MeanSquarederror)
- a leverage factor based on the number of observations
- a t-value from a table (or computer)
What will be the result of the confidence interval if the standard deviation is large?
The SE will be large as well, and the confidence interval will be wide
What does it mean if you get a large MSerror?
Each observed value tends to include large chancer error: the data are “noisy,” and the estimate will not be very precise.
What are two things you can do to make MS smaller?
Better design and better lab techniques
What is the leverage factor for an estimate?
The square root of the averages used in an experiment/ the number of observations used to find that average.
Or in other words, if I used two different averages in my experiment, and they each had four observations, my leverage factor would be SQRT(1/4+1/4)
Does random assignment only apply for assigning treatments?
No, it applies to all parts of the experimental process.
Why is randomization important?
- It allows us to use the probability distribution
- It protects against bias
What does it mean to have “balanced data”?
Having equal sized treatment groups
True/False
Unbalanced often refers to the factor structure of an experiment
True
What is another name for an experimental BF experiment?
Completely Randomized Design
How do you gather data for a BF observational study?
Take a simple random sample of each of the population of interest.
What is the definition of a simple random sample?
A randomly chosen subset of the population such that all subsets of size N are equally likely
What does a simple random sample imply?
That each member of the population is eqully likely to be picked.
What is the bias of using the BF structure and ANOVA to analyze observational data?
Bias may taint results
What are the steps of Exploratory Data Analysis?
- Find group means and SD’s
- Plot data by group
What should we look for when plotting data by groups in EDA?
- Group diffences
- outliers
- equal variances
- normality
What are two universal factors that occcur in all designs?
- Grand Mean
- Residual Error
What is a structural factor that is unique to the study?
Treatment factor
What is the benefit of a multiway ANOVA?
- Study the factors in one experiment instead of multipleexperiments
- Study how conditions interact
When are two factors crossed?
If all possible combinations of the factor’s levels occur in the design
When do we say a design has a factorial structure, and is a factorial design?
When all possible combinations of the factor’s levels occur within the design.
When do we say that two factors interact with one another?
When the effect of Factor A on the response changes for different values of factor B.
Why is replication so important?
Replication gives more precision to our estimates of model parameters
True/False
Replication does not give us information about our errors
False
Replication gives us information about our errors, which then allos us to make inferences on model parameters
What two things are taken into consideration when finding the T value in a confidence interval?
The level of confidence (i.e, 95%, 90%) and the degrees of freedom for the mean squared error.
