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Analysis of Variance > Midterm 2 > Flashcards

Midterm 2 Flashcards

1
Q

How is an observed value defined?

A

True value + Residual error

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2
Q

what does the mean stand for in the algebraic notation for an observed value?

A

mean = true value, benchmark.

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3
Q

Is the mean part of the true value of an observation?

A

Yes

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4
Q

What do the integers Si, Oj, Bk stand for, in regards to the value of the observation?

A

They are all true values based on the number of factors present in the model.

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5
Q

Can the subscripts of the algebraic notation for a true value be replaced by actual numbers?

A

Yes, the new subscript numbers relate the observed value to the factor levels of the factor they came from.

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6
Q

What is the Standard Deviation of the residual error?

A

Sqrt(MSE)

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7
Q

What is the Benchmark value in a decomposition?

A

Benchmark is the grand average of all the observed values

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8
Q

What is another name for Benchmark?

A

Grand mean

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9
Q

What is the estimated effect for a factor?

A

Factor average - grand average (benchmark)

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10
Q

True/False

The estimated effect for an individual in the experiment is the individuals average observations - grand mean.

A

False

The estimated effect for an individual in the experiment is the individuals average - the group average for that individual.

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11
Q

What is the formula for the residual error?

A

Observation - (grand mean + efffect 1 + effect 2)

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12
Q

What two types of variability make up an observation?

A

planned and unplanned

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13
Q

What does the F statistic tell us?

A

How much bigger the average variability of the factor is than the average variability from the MSerror

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14
Q

How do you find the SS?

A

Square all the numbers in the table, and ad them up. the total is a measure of hte overall variability in the table.

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15
Q

What do the degrees of freedom represent?

A

This number counts the number of units of information about residual erro rcontained in the table

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16
Q

How do you find the means squared value?

A

Divide the Sum of Squares by the degrees of freedom

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17
Q

How do you find the sum of squares?

A

Square each number in the box and then add them all up! It literally means exactly what it says.

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18
Q

If the residuals are grouped relatively close together, will the sum of squares be large or small?

A

The sum of squares will be small

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19
Q

If the residuals are spread out will the sum of squares be large or small?

A

The sum of squares will be large

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20
Q

What does the sums of squares measure?

A

The overall variability of a set of numbers, provided those numbers add to zero.

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21
Q

What does SS measure average variability?

A

No, it measures overall variability?

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22
Q

How do you know when to transform data?

A

When SDmax/SDmin is greater than 3

23
Q

What is the computation to find an F ratio?

A

MSfactor/MSerror

24
Q

What does an F ratio mean if it is close to 1

A

There are no real differences due to planned variability. The differences are probalby due to chance error

25
Q

What do we infer if the F ratio is further away from 1?

A

We have enough evidence to assume that the differences are too big to be due to just chance error.

26
Q

True/False

An F ratio tells you how big the true differences are, and whether they are big enough to be scientifically interesting.

A

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.

27
Q

What does the standard error tell us

A

The typical size of a chance part of an observation

28
Q

Can we say that a 95% confidence interval will contain 95% of the distance of a given value?

A

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.

29
Q

What three values go into a standard error?

A
  1. Sqrt(MeanSquarederror)
  2. a leverage factor based on the number of observations
  3. a t-value from a table (or computer)
30
Q

What will be the result of the confidence interval if the standard deviation is large?

A

The SE will be large as well, and the confidence interval will be wide

31
Q

What does it mean if you get a large MSerror?

A

Each observed value tends to include large chancer error: the data are “noisy,” and the estimate will not be very precise.

32
Q

What are two things you can do to make MS smaller?

A

Better design and better lab techniques

33
Q

What is the leverage factor for an estimate?

A

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)

34
Q

Does random assignment only apply for assigning treatments?

A

No, it applies to all parts of the experimental process.

35
Q

Why is randomization important?

A
  1. It allows us to use the probability distribution
  2. It protects against bias
36
Q

What does it mean to have “balanced data”?

A

Having equal sized treatment groups

37
Q

True/False

Unbalanced often refers to the factor structure of an experiment

A

True

38
Q

What is another name for an experimental BF experiment?

A

Completely Randomized Design

39
Q

How do you gather data for a BF observational study?

A

Take a simple random sample of each of the population of interest.

40
Q

What is the definition of a simple random sample?

A

A randomly chosen subset of the population such that all subsets of size N are equally likely

41
Q

What does a simple random sample imply?

A

That each member of the population is eqully likely to be picked.

42
Q

What is the bias of using the BF structure and ANOVA to analyze observational data?

A

Bias may taint results

43
Q

What are the steps of Exploratory Data Analysis?

A
  1. Find group means and SD’s
    1. Plot data by group
44
Q

What should we look for when plotting data by groups in EDA?

A
  • Group diffences
  • outliers
  • equal variances
  • normality
45
Q

What are two universal factors that occcur in all designs?

A
  1. Grand Mean
  2. Residual Error
46
Q

What is a structural factor that is unique to the study?

A

Treatment factor

47
Q

What is the benefit of a multiway ANOVA?

A
  1. Study the factors in one experiment instead of multipleexperiments
  2. Study how conditions interact
48
Q

When are two factors crossed?

A

If all possible combinations of the factor’s levels occur in the design

49
Q

When do we say a design has a factorial structure, and is a factorial design?

A

When all possible combinations of the factor’s levels occur within the design.

50
Q

When do we say that two factors interact with one another?

A

When the effect of Factor A on the response changes for different values of factor B.

51
Q

Why is replication so important?

A

Replication gives more precision to our estimates of model parameters

52
Q

True/False

Replication does not give us information about our errors

A

False

Replication gives us information about our errors, which then allos us to make inferences on model parameters

53
Q

What two things are taken into consideration when finding the T value in a confidence interval?

A

The level of confidence (i.e, 95%, 90%) and the degrees of freedom for the mean squared error.

54
Q
A

Analysis of Variance (3 decks)

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