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Statistics > Chapter 11 > Flashcards

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

A
19
Q

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

A
20
Q

Review Within-group variation in One-way ANOVA

A
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

A
24
Q

Review the Area of Rejection and Non-rejection

A

Note: start drawing these for HW and tests

25
Q

Review the ANOVA Summary Table

A

Summarized the results of a one-way ANOVA

26
Q

What are the One-way ANOVA F Test Assumptions

A
  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
Q

What is the Levene Test

A

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
Q

Define the Turkey-Kramer Procedure

A

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
Q

What are the four steps of the Turkey-Kramer Procedure

A
  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
Q

How many degrees of freedom are there in determining

  • the among-group variation
  • the within-group variation
  • the total variation
A

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
Q

Define the Mean Squares in One-way ANOVA

A

Mean square among (MSA) = SSA / c-1

Mean square within (MSW) = SSW / n - c

Mean square total (MST) = SST / n - 1

32
Q

How do you find the value of FSTAT

A

MSA / MSW

33
Q

How do you find Fα

A

Use the Critical Values of F Table

Numerator = c - 1

Denominator = n - c

34
Q

How do you find Qα

A

Use the Critical Values of the Sudentized Range, Q Table

Numerator = c

Denominator = n - c

Statistics (11 decks)

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