Chapter 11 Flashcards

1
Q

What is ANOVA

A

Analysis of Variance

Def: Allows statistical comparison among samples taken from many populations

The comparison is typically the result of an experiment.

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2
Q

What is the basis for an ANOVA experiment

A

What is a “factor”

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3
Q

Define the levels of a factor

A

The levels of a factor are the groups that comprise the experiment and analysis. They provide the basis for comparison.

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4
Q

What are the three types of experiments that can be conducted with ANOVA?

And which one will we use?

A
  1. Completely randomized design: an experiment with only one factor
  2. Factoral design: An experiment in which more than one factor is considered (Two-way ANOVA)
  3. Randomized block design: An experiment in which the members of each group have been placed in blocks either by being matched or subjected to repeated measurements as was done the two populations of a paired t test

We will only use Completely randomized design

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5
Q

What is the Two Part Process of ANOVA

A
  1. Determine if there is a significant difference among the group means (if you reject H0, continue with #2)
  2. Identify the groups whose means are significantly different from the other group means
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6
Q

What is the purpose of ANOVA

A

To reach conclusions about possible differences month the means of each group

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7
Q

Define the Completely Randomized Design

A

The ANOVA method that analyzes a single factor.

This design is executed using the statistical method one-way ANOVA

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8
Q

Define SST

A

The sum of squares total represents total variation. It is partitioned into 2 groups

  1. Within-group variation (SSW) measures random variation
  2. Among-group variation (SSA) measures differences from group to group
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9
Q

Define n and c

A
  • ‘n’* represents the number of values in all groups
  • ‘c’* represents the number of groups
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10
Q

Review “Partitioning the Total Variation”

A

SST = SSA + SSW

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11
Q

What are the assumptions of ANOVA

A

The c groups represent populations who(se)

  1. Values are randomly and independently selected
  2. Follow a normal distribution
  3. Have equal variances
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12
Q

What is the H0 for ANOVA

A

H0 = μ1 = μ2 = . . . = μc

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13
Q

What is H1 for ANOVA

A

H1: not all μj are equal

where j = 1, 2, . . . , c

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14
Q

Total variation is represented by what

A

The sum of squares total (SST)

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15
Q

What is the grand mean

A

The mean of all the values in all the groups combined

Xdouble-bar

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16
Q

Define SSW

A

“Within-group variation”

Measures random variation

17
Q

Define SSA

A

“Among-group” variation

Measures differences from group to group

18
Q

Review the equation for Total Variation in One-Way ANOVA

19
Q

Review equation for Among-group variation in One-way ANOVA

20
Q

Review Within-group variation in One-way ANOVA

21
Q

Review the equation for the Mean Squares in One-way ANOVA

A

Note: the mean square is just another term for variances that is used in ANOVA

22
Q

Define the F Test for Differences Among More than Two Means

A

Tests to see if there is a significant difference b/t the means.

Note: It does not tell you where the differences are

23
Q

Review the One-way ANOVA FSTAT Test Statistic

24
Q

Review the Area of Rejection and Non-rejection

A

Note: start drawing these for HW and tests

25
Review the ANOVA Summary Table
Summarized the results of a one-way ANOVA
26
What are the One-way ANOVA F Test Assumptions
1. Randomness and independence of the sample selected 2. Normality of the *c* groups from which samples are selected Note: use a Normal Probability Plot to determine normality. (see image) 3. Homogeneity of variance (the variances of the *c* groups are equal) Note: this will require the Levene test
27
What is the Levene Test
A Test for Homogeneity of Variance 1. Compute the absolute value of the difference between each value and the median of the group 2. Perform a one-way ANOVA on these *absolute differences* Note: most statisticians suggest using a level of significance of α = .05 when performing the ANOVA
28
Define the Turkey-Kramer Procedure
Procedure to construct multiple comparisons to test H0 that the differences in the means of all pairs of “items” are equal to 0 Determines with of the *c* means are significantly different
29
What are the four steps of the Turkey-Kramer Procedure
1. Compute the absolute mean differences (|x̄j - x̄j'|; *where j, j' refers to group j & j', and j ≠ j'*) among all pairs of sample means [*c(c - 1)* / 2 pairs] 2. Compute the critical range (Using equation 11.6, attached) 3. Compare each of the *c\**(*c* - 1) / 2 pairs of means against its corresponding critical range. (Declare a specific pair significantly different if the absolute difference in the sample means,|x̄j - x̄j'| , is greater than the critical range) 4. Interpret the results
30
How many degrees of freedom are there in determining * the among-group variation * the within-group variation * the total variation
Among-group variation: *c* - 1 Within-group variation: *n* - *c* Total variation: *n* - 1 Where c = number of groups; n = total number of values in all groups
31
Define the Mean Squares in One-way ANOVA
Mean square among (MSA) = SSA / c-1 Mean square within (MSW) = SSW / n - c Mean square total (MST) = SST / n - 1
32
How do you find the value of FSTAT
MSA / MSW
33
How do you find Fα
Use the **Critical Values of F** Table Numerator = *c* - 1 Denominator = *n* - *c*
34
How do you find Qα
Use the **Critical Values of the Sudentized Range, Q** Table Numerator = *c* Denominator = *n* - *c*