Business 212: Business Statistics Ch 12. Analysis of Variance

experiments

• used in business to secure valid, reliable, and actionable data

• helps decision-makers understand the most significant influences that impact their products or services

correlation

• simply means that we observe events which seem to occur in patterns

• when X and Y seem to happen together

causation (or cause)

• means that we know, not only that a relationship exists, but we also know precisely why it exists

• when X is why Y happens

controls

the elements that limit the potential for 'cross-talk' between variables

variables

are all of the things that may exert direct or indirect influence

completely randomized

subjects are simply assigned to a distinct group in random fashion

randomized block designs

• engages two layers of grouping instead of just one

• are complex, but are far more accurate when it comes to determine what exactly is influencing the system

When selecting a business experiment design that includes a high number of variables, proving the validity of the experiment's results will require:

1. A wider hypothesis

2. A longer test and observation phase

3. A smaller control group

4. A non-standard distribution

A longer test and observation phase

Which type of experimental design that divides a sample into several, relatively similar parts which are then compared (as a group) with other groups?

1. Double-Blind

2. Multiple Regression

3. Randomized Block

4. Completely Randomized

Randomized Block

As Danna's Pub & Grill tests the two different kinds of ranch dressing, Danna informs each table that they are receiving the current brand or the new brand. By doing this, Danna's research lacks the typical experimental provision of being:

1. actionable

2. double-blinded

3. normally distributed

4. observable

double-blinded

Experimental designs used in business are similar to those used by researchers in the:

1. humanities

2. sciences and psychology

3. mass media communications

4. liberal arts

sciences and psychology

Danna and her family have owned and operated a bar and grill for the last 30 years. Now, they are considering switching brands of ranch dressing. In an effort to determine the right way to move forward, she designs a simple experiment in which lunch customers use dressing from the current Brand X while dinner customers are given the new dressing (Brand Y). Which statement accurately describes the control group?

1. Both lunch and dinner customers are in the control group

2. Dinner customers are the control group

3. Neither lunch nor dinner customers are part of the control group

4. Lunch customers are the control group

Lunch customers are the control group

ANOVA / Analysis of Variance

a statistical procedure used to test the degree to which two or more groups vary or differ in an experiment

Null Hypothesis

assumption that there will be no differences between groups that are tested and therefore no significant results will be revealed

Alternative Hypothesis

hypothesis stating that there will be a difference between groups as indicated by the ANOVA performed on the data that is collected

What is a null hypothesis?

1. The hypothesis stating that another variable not accounted for is having an effect on the dependent variable

2. The hypothesis proposing that the independent variable will have an effect on the dependent variable

3. The hypothesis stating that the dependent variable will have an effect on the independent variable

4. The hypothesis proposing that the independent variable will have no effect on the dependent variable

The hypothesis proposing that the independent variable will have no effect on the dependent variable

What does ANOVA measure?

1. How an experiment should be designed

2. The degree to which levels or groups of an independent variable differ from each other

3. The response that comes up the most often in a group of participants

4. Whether an experiment should involve data based on numbers or yes/no answers in a survey

The degree to which levels or groups of an independent variable differ from each other

What is the hypothesis stating that there will be a difference between groups as indicated by the ANOVA performed on the data that is collected?

1. Difference hypothesis

2. Obvious hypothesis

3. Alternative hypothesis

4. Null hypothesis

Alternative hypothesis

In which of these disciplines can an ANOVA be used?

1. Social sciences

2. Natural sciences

3. Medical research

4. All of these answers are correct

All of these answers are correct

What does ANOVA stand for?

1. Assessment of vulnerability

2. Analysis of value

3. Assessment of variability

4. Analysis of variance

Analysis of variance

independent variables

the things that can be controlled or changed

dependent variable

what to measure at the end of the study

main effect

the effect of just one of the independent variables on the dependent variable

analysis of variance (ANOVA)

• a statistical test that is used to determine if there are differences between groups when there are more than two treatment groups

• used to find differences between multiple groups of data, not just groups like we had here for the two patients

interaction effect

occurs if there is an interaction between the independent variables that affects the dependent variable

In an experiment in which there are two independent variables, how many effects will an ANOVA test for?

1. Two main effects and one interaction effect

2. One main effect and one interaction effect

3. Two interaction effects

4. Two main effects

Two main effects and one interaction effect

In which situation would you use a two-way ANOVA?

1. When you are testing the effects of two different independent variables on a dependent variable

2. When you are measuring two different dependent variables

3. When you have only main effects and no interaction effects

4. When you have more than two groups within one independent variable

When you are testing the effects of two different independent variables on a dependent variable

Sarah performs an experiment to determine the best amount of sun and water for a certain type of plant. She varies the amount of water the plants get each day and also how much time they are in the sun. At the end of six weeks, she measures how tall each plant is. Which of these is an example of an interaction effect that this experiment might detect?

1. Plants that receive the most sunlight require the same amount of water as plants that receive the least sunlight

2. Some plants grow best with no water

3. Plants that receive more sunlight also require more water

4. Plants that receive the most water require the same amount of sunlight as plants that receive the least water

Plants that receive more sunlight also require more water

A two-way ANOVA is performed and the F-ratio for the interaction effect is calculated to be 4.32. In an F-ratio table, you find that the critical F-ratio is 3.21. Can you say that the interaction effect is statistically significant or not?

1. Yes, because the two F-ratios are not equal

2. No, because the two F ratios are not equal

3. No, because the calculated F-ratio is bigger than the critical F-ratio

4. Yes, because the calculated F-ratio is bigger than the critical F-ratio

Yes, because the calculated F-ratio is bigger than the critical F-ratio

Sarah performs an experiment to determine the best amount of sun and water for a certain type of plant. She varies the amount of water the plants get each day and also how much time they are in the sun. At the end of six weeks, she measures how tall each plant is. What is the independent variable in this experiment?

1. The height of the plants

2. The amount of water

3. Both the amount of sun and the amount of water are independent variables

4. The amount of sun

Both the amount of sun and the amount of water are independent variables

sum of squares

measures how far individual measurements are from the mean

variation

measures the amount of variability in the data

ANOVA

can also be used if there are multiple factors that might affect a measurement

An experiment is performed and the sum of squares is calculated. Which of the following sum of squares values would indicate the largest amount of variability in the data?

1. 50

2. 10

3. 100

4. 500

500

Calculate the sum of squares for the following data set:

20

23

28

32

30

24

20

23

1. 25

2. 142

3. 156

4. 0

142

Calculate the sum of squares for the following data set:

100

150

120

130

140

120

110

130

1. 100

2. 125

3. 1800

4. 180

1800

An experiment is performed and the sum of squares is calculated. Which of the following sum of squares values would indicate the smallest amount of variability in the data?

1. 1000

2. 10

3. 100

4. 50

10

Which of these is sum of squares used to calculate?

1. Sum of squares is required to calculate all of these

2. standard deviation

3. standard error

4. variance

Sum of squares is required to calculate all of these

Analysis of Variance (ANOVA)

statistical test that you can use to determine if there are differences between three or more groups

factors

conditions that can affect the measured variable

two-way ANOVA

determine if either of two factors caused differences in the measured variable and if there were any interaction effects between the two factors 

treatment group

contain a different combination of the two factors

A two-way ANOVA is performed and the f-ratio for factor A is calculated to be 4.8. The critical f-ratio at a significance level of alpha = 0.05 is 4.3. From this information, what can you conclude about how factor A is influencing the measured variable?

1. You need to know how many factors there are total before you can conclude anything about the effect of factor A.

2. There are not any differences in the measured variable due to factor A.

3. There are differences in the measured variable due to factor A.

4. You need to know how many measurements were made before you can conclude anything about the effect of factor A.

There are differences in the measured variable due to factor A.

In which of these situations would you use a two-way ANOVA?

1. All of these could be analyzed with a two-way ANOVA

2. An advertising agency shows three new ads for a product to a focus group and asks the group to rate how likely they are to buy the product after viewing each ad. The company wants to know if one ad is more effective than the others.

3. A pet food company uses four different manufacturing plants to make a certain kind of dog food. They want to make sure that each plant produces food with the same concentration of a certain nutrient. Data is collected on the concentration of the nutrient in food made by each plant, and the data is analyzed to determine if there are any differences between the four different plants.

4. A pharmaceutical company has developed three new blood pressure medications. The company gives the drug to patients in three different age ranges. The company wants to know if there are differences in blood pressure due to the medication, the age of the patients, or if there is any interaction between the type of medication and the patient age.

A pharmaceutical company has developed three new blood pressure medications. The company gives the drug to patients in three different age ranges. The company wants to know if there are differences in blood pressure due to the medication, the age of the patients, or if there is any interaction between the type of medication and the patient age.

An advertising agency has created five new ads for a product. They show the ads to 4 different focus groups that each contain consumers of different age ranges. Each consumer then records how likely they are to purchase the produce after viewing each ad. The company performs a two-way ANOVA to determine if there any different effects on purchasing decisions between the ads or between consumer age. If consumer age is factor B, how many degrees of freedom are in this factor?

1. 3

2. 5

3. 4

4. 20

3

A two-way ANOVA is performed and for the interaction effect, the mean square for the interaction (MS-I) is found to be 270. The within-group variation (MS-W) is 45. A table of critical f-ratios tells you that the critical f-ratio for this experiment is 6.21 at the alpha = 0.01 significance level.

Is there enough evidence here to show that there is an interaction effect?

1. Yes, the f-ratio for this experiment is 6 and f-critical is 6.21. Because f < f-critical, you can reject the null hypothesis. There is enough evidence to show that there is an interaction effect.

2. Yes, the f-ratio for this experiment is 45 and f-critical is 6.21. Because f > f-critical, you can reject the null hypothesis. There is enough evidence to show that there is an interaction effect.

3. No, the f-ratio for this experiment is 45 and f-critical is 6.21. Because f > f-critical, you cannot reject the null hypothesis. There is not enough evidence to show that there is an interaction effect.

4. No, the f-ratio for this experiment is 6 and f-critical is 6.21. Because f < f-critical, you cannot reject the null hypothesis. There is not enough evidence to show that there is an interaction effect.

No, the f-ratio for this experiment is 6 and f-critical is 6.21. Because f < f-critical, you cannot reject the null hypothesis. There is not enough evidence to show that there is an interaction effect.

A two-way ANOVA is performed and the sum of squares for factor B (SS-B) is found to be 312. If there are 5 groups in factor B, what is the value for the mean square (MS-B)?

1. 1560

2. 52

3. 62.4

4. 78

78

within-group variance

the variance between the groups and within the groups

When should you use an ANOVA to determine if there are differences between groups?

1. When you have less than 100 measurements

2. When you have more than two different groups to compare

3. When you have at least 20 measurements

4. When you only have two groups to compare

When you have more than two different groups to compare

In an experiment, there are 8 different groups with 4 measurements per group. To calculate the within group variance, what would you use for N and g?

1. N = 32 and g = 8

2. N = 8 and g = 4

3. N = 32 and g = 4

4. N = 4 and g = 8

N = 32 and g = 8

What is the sum of squared deviations for the following set of data?

43

59

48

52

54

56

1. 120

2. 26

3. 52

4. 166

166

You perform an ANOVA and determine that the within-group variance is 89.9, while the between-group variance is 57.2. What can you conclude about this data?

1. There are no differences between the groups because the between group variance is less than 100

2. There are likely to be differences between the groups because there is more variance within the groups than between the groups

3. There are no differences between the groups because there is more variance within the groups than between the groups

4. There are likely to be differences between the groups because the between-group variance is more than 50

There are no differences between the groups because there is more variance within the groups than between the groups

A data set in which all the values are very close to the mean value would have a small _____.

1. Between group deviation

2. Error rate

3. Variance

4. ANOVA

Variance

analysis of variance (ANOVA)

a statistical procedure for locating a difference between multiple levels of a single independent group mean

One-way

one independent variable independent variable has multiple levels

Between Subjects

a study in which the subjects are placed in mutually exclusive groups and will be compared to each other

F-Ratio

a score to determine the level of difference between the means

Repeated Measure

study uses the same group of participants for each level of the variable

Carryover Effect

previous levels or conditions that may cause subsequent assessments to be altered

Two-Way ANOVA

two independent variables each independent variable has levels one dependent variable

Factorial ANOVA

tow independent variables each independent variable has levels one dependent variable

Mixed Design

a study that uses both between subject and repeated measures

The purpose of running an ANOVA is to find the _____ .

1. characterizations shared between means

2. differences between means

3. most effective score

4. similarities between means

differences between means

Brian is conducting a study to determine whether meditation affects body weight. Brian plans to have three different groups, where each group will be assigned a different length of meditation time. When Brian gathers his data, he will compare the body weights of the participants between groups. Which type of ANOVA is Brian using?

1. Repeated measure

2. Between subject

3. Mixed method

4. Multivariate

Between subject

Brian plans to have one group participate in different lengths of meditation time for his study to determine whether meditation affects body weight. After each length of meditation time, he will measure the body weight of each individual in the group. Brian's assistant, Barney, is worried that they will not see a big difference in the body weight of the participants from the first post-meditation weigh-in to the subsequent weigh-ins. What phenomenon is Barney worried about?

1. Correlation effect

2. F-ratio effect

3. Carryover effect

4. ANOVA effect

Carryover effect

In order to conduct a study to determine whether meditation affects body weight, Brian plans to have one group participate in different lengths of meditation time. After each length of meditation time, Brian will measure the body weight of each individual in the group, which is _____ form of ANOVA.

1. repeated measure

2. mixed method

3. multivariate

4. between subject

repeated measure

Brian wants to know if there is a significant difference between the means in the study he is conducting. What value does Brian need to examine?

1. ANOVA score

2. p-score

3. F-Ratio

4. Carryover value

F-Ratio