MKT 367 - Statistical Testing - Student Notes

8/13/2019 MKT 367 - Statistical Testing - Student Notes

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Statistical Testing

MKT 367Marketing Research

April 16, 2013


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Quick Recap

Data Processing:1. Coding

2. Data Entry

3. Validation and Editing

4. Cleaning the Data

5. Statistical Analysis


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Agenda

Hypothesis Testing

Common Statistical Tests

One Mean Z and t tests

Two Mean Z and t tests

Paired observations t test


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Agenda

Hypothesis Testing


One Mean Z and t tests

Two Mean Z and t tests

Paired observations t test


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The average familiarity with the University ofWisconsin-La Crosse for community members

is 4.95/5.00

The average familiarity with the University of

Wisconsin-La Crosse for La Crosse visitors is2.95/5.00


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Average for Ad 1 = 4.95/5.00

Average for Ad 2 = 4.94/5.00


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PracticalDifference

StatisticalDifference

MathematicalDifference


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Hypothesis TestingHypothesis

A research idea that can serve as a premise or a supposition to organizecertain facts and thereby guide observations

A possible answer to a research question

Not yet proven true

Stated in population parameters, not sample statistics (i.e. Greek letters notEnglish)

Commonly used/tested:Means:

Proportions: pVariances:

HYPOTHESIS TESTING

The process of determining whether or not a given hypothesis is true


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Hypothesis Testing (cont)

The average word of mouth for the 2012 SummerSession was 4.00 out of 5.00 for all students

The average satisfaction with the waiting list wasgreater than 4.00 for all students Juniors are less satisfied with the 2012 SummerSession than Sophomores


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Hypothesis Testing Procedure1. Specify the null and alternative hypotheses

2. Choose the appropriate statistical test3. Specify the desired level of significance

4. Compute the value of the test statistic

5. Compare the test statistic to the critical value

6. State the conclusion and discuss the practicalsignificance


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1. Specify the Hypotheses

Null Hypothesis

Denoted by H 0

Is an assertion (belief) about a population parameter

This is the assertion that we hold to be true until thereis sufficient statistical evidence to conclude otherwise

Typically a statement of no effect, no relationship, or nodifference among the variables (independence)


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1. Specify the Hypotheses (cont)

Alternative Hypothesis

Denoted by H 1

Negates the assertion stated in the null hypothesis

Covers all situations not covered by the nullhypothesis

Typically a statement in which some effect,relationship, or difference is expected(dependence)


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Null (H 0) and Alternative (H 1) Hypotheses are:

Mutually exclusive

Only one can be true at any single time

Collectively exhaustiveTogether they cover all possibilities , so one or theother must be true

FALSIFIABLE


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1. Identify the specific claim to be tested and put itinto symbolic form

2. Identify all the other possibilities not covered by the

claim in part 1Rule of Thumb

The statement that contains some form ofequality (=, , ) is the null hypothesis (H 0)The statement that contains some form ofinequality (,>,


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Example 1

Bo Ryan claims

that his basketball teamscores 86 points perGame on average.How would you set upthe null and alternativehypothesis to test his claim?


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Example 2

Government agencies are devoted toensuring that food producers package theirproducts such that the volume listed on labelsis correct. For example, bottles of beer labeled12 oz. must contain at least 12 oz. It isimpossible to check all bottles, so samplingis used in order to check whether there isenough evidence to infer that the mean volume

of all bottles is under 12 oz.


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The average word of mouth for the 2012 SummerSession was 4.00 out of 5.00 for all students

The average satisfaction with the waiting list wasgreater than 4.00 for all students Juniors are less satisfied with the 2012 SummerSession than Sophomores


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2. Choosing the Appropriate Statistical Test

Retrospectively, the choice is made given thehypothesis and situational characteristics(sampling procedure, sample size, level ofmeasurement, etc.)

Proactivelythe marketing research process isdesigned after the hypothesis


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Flashback: The Marketing Research Process

1Identify the Problem

and State theResearch Objectives

2

Create the ResearchDesign

3

Choose the ResearchMethod

4

Select the SamplingProcedure

5

Collect the Data

6

Analyze the Data

7

Write and Presentthe Report

8

Follow-up


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3. Specify the Desired Level of Significance

Choose the probability that is too low to fail toreject the hypothesis ( level)

Rule of Thumb: = 0.05

AND

Get the Critical ValueFind the correct value from the table.


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4. Compute the Value of the Test Statistic

Use the appropriate formula to calculate thevalue of the test statistic


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5. Compare the Test Statistic to the Critical Value

Shortcut:

p-value < Reject H 0

p-value > Fail to Reject H 0

p-value is the probability that you would getthe test result given that the null hypotheses is

true


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6. State the Conclusion and Discuss the Practical Significance

What does Fail to Reject H 0 or Reject H 0 mean?


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One Meanz testt test

Two Meansz-testt-test

Paired Observationst test

ProportionsOne sample: z-testTwo samples: z-test

More Than TwoMeans

ANOVA

Goodness of FitChi-Square


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One Mean Statistical Tests

Z testn 30 H0: =, , or # H1: , >, or < #

t testn < 30note: df = n-1H0: =, , or #

H1: , >, or < #

n

X Z

nS

X t


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One Mean Z Test Example

Ford substituted a different engine in cars thatwere known to have an average mpg rating of31.5 on the highway. Ford wants to test whetherthe engine changes the mpg rating of the carmodel. A random sample of 100 trial runs gives

= 29.8 mpg and s = 6.6 mpg.

Is the average mpg rating on the highway forcars using the new engine different from thempg rating for cars using the old engine?

n

X Z


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One Mean t Test Example

RE/MAX conducted a survey to determinecustomer satisfaction with recent changes tocompany policies. Suppose that the averagecustomer satisfaction before the changes was 77 (scaleof 0 100). A random sample of 25 people whopurchased a home after the changes found averagecustomer satisfaction to be 84 and the samplestandard deviation was found to be 28.

Did customer satisfaction improve?


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Paired Observations

Observes the same group of person or things

Before and After

At different times or under different circumstances

Why pair samples?

Removes extraneous variation


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Paired Observations (cont)

Two Tailed TestH0: D = 0H1: D 0

Right Tailed TestH0: D 0H1: D > 0

Left Tailed TestH0: D 0 H1: D < 0

D = 1 2


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Paired Observations (cont)

Always a t-test with degrees of freedom of n-1

n

s Dt

D

D n

Di

D

n

i 1

1

22

n Dn D

s i D

Di = Xi1 Xi2


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Paired Observations Example 1

The performance ratings of two sports cars, theChevrolet Camaro and the Dodge Challenger,are to be compared. A random sample of 40drivers is selected to drive the two cars. Eachdriver drives each car once and the time of eachtest drive is recorded. The average difference intime (Chevrolet Dodge or ) is 5.0 seconds and

SD = 2.3.

Which model has higher performance?


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Paired Observations Example 2

A study is undertaken to determine howconsumers reach to energy conservation efforts.A random group of 60 families is chosen. Theirconsumption of electricity is monitored in a

period before and after the families are offeredcertain discounts to reduce their energyconsumption. The average difference in energyconsumption (Before After or ) is 0.2kilowatts and S D = 1.0 kilowatts.

Did conservation efforts reduce consumption?


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Two Means Statistical Tests

Problem: We want to compare the averagevalues of two independentpopulations on a variable

Do men charge more on their VISA credit cardsthan women?

Does one product outsell another?

Does one ad generate more sales than another?


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Two Means Statistical Tests (cont)

Independent Populations

Observes different groups of persons or things

At same time or under the same circumstances

The values of one population do not influencethe values of the other population


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Possible Hypotheses:

Two Tailed TestH0: 1 - 2 = D0H1: 1 - 2 D0

Right Tailed TestH0: 1 - 2 D0H1: 1 - 2 > D0

Left Tailed TestH0: 1 - 2 D0H1: 1 - 2 < D0

Notes:

1. D0 = HypothesizedDifference or ( 1 - 2)0

2. D0 does not have to equal 0,although it often does

3. Must specify whichpopulation is 1 and 2


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When to Use a Z- or a t-Test

If population 2 is known use a Z-test

If population 2 is not known:

Use a Z- Test if n 30 for both samples

Use a t-Test if n < 30 for either sample


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t Test Formula

n < 30

note: df = n1 + n2 2

Where:

21

2

021

11 t

nn s

D x x

P

2

11 21

2

22

2

112

nn

sn sn s P


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Two Mean Statistical Tests Example 1Until a few years ago, the credit card industry was considered to

segmented with higher income consumers using American Expressand lower income consumers using Visa. Over the last few years,however, Visa intensified efforts to break into the higher incomemarket segment by using magazine and television advertising. Visahired a consulting firm to determine if average monthly charges on theAmerican Express Gold Card are equal to the average monthly charges

on the Preferred Visa Card.A random sample of 1,200 Preferred Visa cardholders revealed anaverage monthly charge (x 1) of $452 and an independent randomsample of 800 Gold cardholders revealed an average monthly charge(x2) of $523. Assume s 1 = $212 and s 2 = $185.

Is there evidence to conclude that the average monthly charge ofAmerican Express cardholders is different than the average monthlycharge of Visa cardholders?


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Two Means Statistical Tests Example 2

Suppose that Duracell wants to demonstrate thattheir size AA batteries last on average 45 minuteslonger than Energizers size AA batteries. Twoindependent random samples of 100 batteries ofeach kind are selected and the batteries are run

continuously until they are no longer operational.The sample average life for Duracell is 1 = 308minutes and 2 = 254 minutes. Assume s 1 = 84minutes and s 2 = 67 minutes.

Is there evidence to support Duracells claim that its batteries last on average 45 minutes longer thanEnergizers batteries?


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Today In Review

A hypothesis is a possible answer to a researchquestion

The best status a theory can hope to achieve is not yetdisproven

Hypotheses are tested using a 6 step procedure

One means Z or t test to test

Paired observations t-test

Two means Z or t test

MKT 367 - Statistical Testing - Student Notes

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