Anova_1_ingles_ejercicio, Diapositivas de Estadística

¡Descarga Anova_1_ingles_ejercicio y más Diapositivas en PDF de Estadística solo en Docsity!

Analysis of Variance

Chapter 12

Learning Objectives

LO1 List the characteristics of the F distribution and locate values in an F table. LO2 Perform a test of hypothesis to determine whether the variances of two populations are equal. LO3 Describe the ANOVA approach for testing difference in sample means. LO4 Organize data into ANOVA tables for analysis. LO5 Conduct a test of hypothesis among three or more treatment means and describe the results. LO6 Develop confidence intervals for the difference in treatment means and interpret the results. LO7 Carry out a test of hypothesis among treatment means using a blocking variable and understand the results. LO8 Perform a two-way ANOVA with interaction and describe the results.

Characteristics of F -

Distribution

1. There is a “family” of F Distributions. A particular member of the family is determined by two parameters: the degrees of freedom in the numerator and the degrees of freedom in the denominator.
2. The F distribution is continuous 3. F value cannot be negative. 4 The F distribution is positively skewed.
3. It is asymptotic. As F   the curve approaches the X -axis but never touches it.

LO

Comparing Two Population Variances

The F distribution is used to test the hypothesis that the variance of

one normal population equals the variance of another normal

population.

Examples:

 Two Barth shearing machines are set to produce steel bars of the same length.

The bars, therefore, should have the same mean length. We want to ensure

that in addition to having the same mean length they also have similar variation.

 The mean rate of return on two types of common stock may be the same, but

there may be more variation in the rate of return in one than the other. A

sample of 10 technology and 10 utility stocks shows the same mean rate of

return, but there is likely more variation in the Internet stocks.

 A study by the marketing department for a large newspaper found that men and

women spent about the same amount of time per day reading the paper.

However, the same report indicated there was nearly twice as much variation in

time spent per day among the men than the women.

LO2 Perform a test of hypothesis to determine

whether the variances of two populations are

equal.

Test for Equal Variances - Example

Lammers Limos offers limousine service

from the city hall in Toledo, Ohio, to

Metro Airport in Detroit. The president of

the company, is considering two routes.

One is via U.S. 25 and the other via I-75.

He wants to study the time it takes to

drive to the airport using each route and

then compare the results. He collected

the following sample data, which is

reported in minutes.

Using the .10 significance level, is there a

difference in the variation in the driving

times for the two routes?

LO

Test for Equal Variances - Example Step 1: The hypotheses are: H 0 : σ 12 = σ 22 H 1 : σ 12 ≠ σ 22 Step 2: The significance level is .10. Step 3: The test statistic is the F distribution.

LO

Test for Equal Variances - Example

The decision is to reject the null hypothesis , because the computed F

value (4.23) is larger than the critical value (3.87).

We conclude that there is a difference in the variation of the travel times

along the two routes.

Step 5: Compute the value of F and make a decision

LO

Test for Equal Variances – Excel Example

LO

 The Null Hypothesis is that the population means are all the

same. The Alternative Hypothesis is that at least one of the

means is different.

 The Test Statistic is the F distribution.

 The Decision rule is to reject the null hypothesis if F (computed) is

greater than F (table) with numerator and denominator degrees of

freedom.

 Hypothesis Setup and Decision Rule:

Comparing Means of Two or More Populations H

: μ

= μ

=…= μ

k

H

: The means are not all equal Reject H

if F > F

,k-1,n-k

LO5 Conduct a test of hypothesis among three or

more treatment means and describe the results.

Analysis of Variance – F statistic  (^) If there are k populations being sampled, the numerator degrees of freedom is k – 1.  (^) If there are a total of n observations the denominator degrees of freedom is n – k.  (^) The test statistic is computed by:   SSE  n k  SST k F    1

LO

Comparing Means of Two or More Populations – Example

Recently a group of four major

carriers joined in hiring Brunner

Marketing Research, Inc., to

survey recent passengers

regarding their level of satisfaction

with a recent flight. The survey

included questions on ticketing,

boarding, in-flight service,

baggage handling, pilot

communication, and so forth.

Twenty-five questions offered a

range of possible answers:

excellent, good, fair, or poor. A

response of excellent was given a

score of 4, good a 3, fair a 2, and

poor a 1. These responses were

then totaled, so the total score

was an indication of the

satisfaction with the flight. Brunner

Marketing Research, Inc.,

randomly selected and surveyed

passengers from the four airlines.

Is there a difference in the mean

satisfaction level among the four airlines?

Use the .01 significance level.

American Delta United US Airways

LO

Comparing Means of Two or More Populations – Example Step 1: State the null and alternate hypotheses. H 0 : μA = μD = μU = μUS H 1 : The means are not all equal Reject H 0 if F > F ,k-1,n-k Step 2: State the level of significance. The .01 significance level is stated in the problem. Step 3: Find the appropriate test statistic. Because we are comparing means of more than two groups, use the F statistic

LO

Comparing Means of Two or More Populations – Example Step 5: Compute the value of F and make a decision

LO4 Organize the data into tables for analysis

Comparing Means of Two or More Populations – Example American Delta United US Airways

LO