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Statistical Analysis > Comparing Means: Analysis of Variance > Flashcards

Comparing Means: Analysis of Variance Flashcards

1
Q

It compares more than two populations’ means by analyzing the sample variance.

A

ANOVA / Analysis of Variance

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2
Q

Where can ANOVA be applied?

A

Psychological Research
Consumer Behavior
Marketing Management

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3
Q

What are we considering in ANOVA as it relates to one or more categorical independent variables?

A

Quantitative Dependent Variable

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4
Q

Example of ANOVA being used in practical problems

A

A marketing manger want to know which kind of promotional campaign leads to the greatest income (Independent: Kinds of promotional campaign; Dependent: Income)

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5
Q

These are independent variables that can assume a limited number of possible values.

A

Factors

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6
Q

Factors are also known as what?

A

Factor Levels

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7
Q

It is the generalization of the t-test for independent samples to situations with more than two groups.

A

One-way ANOVA

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8
Q

One-way ANOVA is also known as what?

A
  1. Single classification ANOVA
  2. One-factor ANOVA
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9
Q

It is used to test the difference in a single dependent variable among two or more groups form by a single independent variable.

A

One-way ANOVA

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10
Q

What are the hypotheses that are tested to determine if different levels of the factors affect measured observations differently.

A

H0 : There is no significant difference among means.
HA : At least one of the population means is different from the others.

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11
Q

What are the assumptions that must be satisfied when applying one-way ANOVA?

A
  1. Observations are obtained independently and randomly from the populations defined by the factor levels.
  2. Dependent variable should be normally distributed for each category of the independent variable.
  3. These should be a homogeneity of variance.
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12
Q

SCCMC

Hypothesis Testing Using One-way ANOVA

A
  1. State the null and alternative hypothesis, then set the alpha level.
  2. Calculate the degrees of freedom and the F-critical value.
  3. Calculate the F-value.
  4. Make a statistical decision.
  5. Conclude.
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13
Q

It is the ratio of the mean square between samples to the mean square within samples.

A

F-Value or F-statistic

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14
Q

Decision rule using the F-critical value.

A

F-value ≤ F-critical value : Fail to reject the null hypothesis

F-value > F-critical value : Reject the null hypothesis

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15
Q

Decision rule using the p-value.

A

p-value ≤ significance level : reject null hypothesis

p-value > significance level : fail to reject null hypothesis

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16
Q

It requires two independent variables or factors and is used to know the effect of these factors on the same dependent variable.

A

Two-way ANOVA

17
Q

It allows us to compare the means when the data are classified according to two factors.

A

Two-way ANOVA

18
Q

Since two-way ANOVA requires two independent variables, each factor’s levels are what?

A

Are arranged in rows and columns

19
Q

Can two-way ANOVA have two or more three sets of hypotheses?

A

YES.

20
Q

Cite the null hypotheses for each set in a two-way ANOVA.

A
  1. The means of the first factor are equal.
  2. The means of the second factor are equal.
  3. There is no interaction between the two factors.
21
Q

This is like a one-way ANOVA for the row factor.

A

The means of the first factor are equal.

22
Q

This is like a one-way ANOVA for the column factor.

A

The means of the second factor are equal.

23
Q

There is no interaction between the two factors. It only exists if the data set consists of more than one observation at each combination of levels.

A

There is no interaction between the two factors.

24
Q

What are the assumptions when applying two-way ANOVA?

A
  1. Should have independence in observations which means that there is no relationship between the observations in each group or between the groups themselves.
  2. Dependent variable at each factor level combination should be normally distributed.
  3. Should be a homogeneity of variances.
25
Q

SCCMC

Hypothesis Testing Using Two-way ANOVA

A
  1. State the null and alternative hypothesis, then set the alpha level.
  2. Calculate the degrees of freedom and the F-critical value.
  3. Calculate the F-value.
  4. Make a statistical decision.
  5. Conclude.
26
Q

It is calculated by the respective mean squares divided by the mean square of the residual quantity.

A

F-Value or F-statistic

27
Q

Formula for df of a one-way ANOVA

A

dfB = k-1
dfW = N - k
dftotal = dfbetween + dfwithin

df = N-1

28
Q

Formula for df of a two-way ANOVA

A

dfR = r-1
dfC = c-1
dfE= (r-1)(c-1)

dfr = rc-1

Statistical Analysis (10 decks)

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